The nematode worm C. elegans chooses between bacterial foods as if maximizing economic utility

  1. Abraham Katzen
  2. Hui-Kuan Chung
  3. William T Harbaugh
  4. Christina Della Iacono
  5. Nicholas Jackson
  6. Elizabeth E Glater
  7. Charles J Taylor
  8. Stephanie K Yu
  9. Steven W Flavell
  10. Paul W Glimcher
  11. James Andreoni
  12. Shawn R Lockery  Is a corresponding author
  1. Institute of Neuroscience, University of Oregon, United States
  2. Center for Neural Science, New York University, United States
  3. Neuroscience Institute, New York University School of Medicine, United States
  4. Department of Economics, University of Oregon, United States
  5. Department of Neuroscience, Pomona College, United States
  6. Department of Chemistry, Pomona College, United States
  7. Picower Institute for Learning and Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, United States
  8. Department of Economics, University of California, San Diego, United States

Abstract

In value-based decision making, options are selected according to subjective values assigned by the individual to available goods and actions. Despite the importance of this faculty of the mind, the neural mechanisms of value assignments, and how choices are directed by them, remain obscure. To investigate this problem, we used a classic measure of utility maximization, the Generalized Axiom of Revealed Preference, to quantify internal consistency of food preferences in Caenorhabditis elegans, a nematode worm with a nervous system of only 302 neurons. Using a novel combination of microfluidics and electrophysiology, we found that C. elegans food choices fulfill the necessary and sufficient conditions for utility maximization, indicating that nematodes behave as if they maintain, and attempt to maximize, an underlying representation of subjective value. Food choices are well-fit by a utility function widely used to model human consumers. Moreover, as in many other animals, subjective values in C. elegans are learned, a process we find requires intact dopamine signaling. Differential responses of identified chemosensory neurons to foods with distinct growth potentials are amplified by prior consumption of these foods, suggesting that these neurons may be part of a value-assignment system. The demonstration of utility maximization in an organism with a very small nervous system sets a new lower bound on the computational requirements for utility maximization and offers the prospect of an essentially complete explanation of value-based decision making at single neuron resolution in this organism.

Editor's evaluation

In this thought-provoking study, the authors adopt a framework from economic decision-making theory to food choice behaviours in the nematode C. elegans. Based on their findings, they propose that worms behave consistently with the Generalized Axiom of Revealed Preference, a classic measure of utility maximization.

https://doi.org/10.7554/eLife.69779.sa0

Introduction

One of the primary functions of the brain is to make decisions that maximize a person’s welfare. Welfare, meaning satisfaction of needs and desires, is subjective, based on values the individual assigns idiosyncratically to goods and outcomes. Can welfare maximization nevertheless be investigated in objective terms? One solution to this problem is revealed preference theory (Samuelson, 1938) which identifies the patterns of behavior, observable as such, that are necessary and sufficient evidence that subjects are choosing in ways consistent with welfare maximization or, in economic terminology, utility maximization. These patterns have been defined mathematically by the Generalized Axiom of Revealed Preference (GARP; Houthakker, 1950; Afriat, 1967; Varian, 1982). Previous studies have utilized GARP to quantify utility maximization in children and adults under a variety of economic and physiological conditions (Harbaugh et al., 2001; Andreoni and Miller, 2002; Burghart et al., 2013; Lazzaro et al., 2016).

GARP is significant for decision neuroscience because it provides a definitive behavioral test for utility maximization, or its absence. This test can be applied to almost any organism that makes choices between desirable goods that incur costs. The basic concept underlying this axiom is that a maximizing agent’s choices must be internally consistent. If a person is observed to prefer X over Y when both are available then, other things being equal, this person should not also prefer Y over X, a pattern that is obviously inconsistent. Furthermore, internal consistency must extend to preferences revealed indirectly, through transitivity. For example, a persons observed to choose X over Y and Y over Z, have indirectly revealed that they would choose X over Z. If instead Z is chosen over X, then their decision making cannot be an instance of goal-directed maximization in any significant sense of the term. The number and severity of GARP violations (assuming the chooser is motivated to maintain or improve his or her welfare), has been taken as a measure of cognitive function (Camille et al., 2011). In humans and non-human primates, it can also be correlated with physical variables such as neuroanatomy and neuronal activity (Chung et al., 2017; Pastor-Bernier et al., 2019). These studies reveal the range of insights that can be gained by combining revealed preference theory and neuroscience.

To our knowledge, however, tests for utility maximization using GARP have yet to be applied to organisms more amenable to mechanistic studies such as mice, zebrafish, fruit flies, and nematodes. A major goal of this study was to determine whether food choices of the nematode C. elegans, a microscopic round worm with a nervous system of only 302 neurons, are consistent with GARP and thus exhibit a form of utility maximization. A positive result would establish a simple experimental system in which neuronal activity correlated with utility could be manipulated both physiologically and genetically to establish behavioral causality. Such a finding would also be interesting from a comparative perspective, extending the domain of utility-based decision making far beyond the boundaries of organisms that are generally considered to have cognition.

A worm might seem a surprising choice for investigating utility maximization. However, C. elegans possesses a sophisticated behavioral repertoire that can be organized into three broad functional categories (Faumont et al., 2012; Yapici et al., 2014): (1) maintenance behaviors, such as feeding, defecation, mating, and egg laying; (2) escape reflexes, for avoiding life threatening conditions such as noxious heat, ultraviolet light, high oxygen or CO2, toxins, desiccation, and predation by fungi, mites, and other nematodes; and (3) habitat and resource-localization behaviors, including a variety of spatial orientation strategies that enable C. elegans to obtain goods such as hospitable living conditions and resources (e.g. food and mating partners), and to avoid inhospitable conditions and the lack of resources.

C. elegans exhibits a considerable range of decision making behaviors (Faumont et al., 2012; Yapici et al., 2014): (1) action versus inaction, such as probabilistic withdrawal responses Culotti and Russell, 1978; Chalfie et al., 1985; Shinkai et al., 2011; (2) approach versus avoidance, such as when an initially attractive odor or taste is made aversive by pairing it with the absence of food Colbert and Bargmann, 1995; Saeki et al., 2001; Torayama et al., 2007; (3) appetitive responses, such as when worms are presented with a choice between benign or pathogenic food Zhang et al., 2005; and (4) choice under risk, such as when worms must decide whether to risk crossing a potentially lethal chemical barrier to obtain food (Shinkai et al., 2011; Ghosh et al., 2016). Other examples include the choice to remain in a food patch rather than to leave to find a mate (Barrios et al., 2008) or the choice to remain in a dwindling patch of food rather than leave for a possibly better patch Bendesky et al., 2011; Milward et al., 2011; the latter has strong parallels with optimal foraging theory (Busch and Olofsson, 2012). C. elegans has also been shown to exhibit bounded rationality (Simon, 1957), a property it shares with humans and most other animals. Its pairwise preferences for attractive odors generally obey transitivity but with a considerable number of exceptions (Iwanir et al., 2019). Similarly, its pairwise preferences are not generally influenced by introduction of a third option in the choice set, another classical mark of rationality, but again with a considerable number of exceptions (Cohen et al., 2019). However, none of these preference tests provide necessary and sufficient evidence for utility maximization.

We selected food choice for our investigation of utility maximization. C. elegans is an omnivorous bacterivore that mainly inhabits rotting plant material such as decaying fruits and fleshy stems (Frézal and Félix, 2015). Its natural habitat contains thousands of different species of bacteria (Samuel et al., 2016), including both beneficial and pathogenic varieties. Each beneficial species has a characteristic nutritional quality defined in terms of the growth rate of individual worms cultured on that species (Avery and Shtonda, 2003; Samuel et al., 2016). In contrast, pathogenic species can be lethal (Tan et al., 1999). Therefore, food choice has immediate fitness consequences for the worm, and it is reasonable to expect that C. elegans food-choice mechanisms have been shaped by evolution to be efficient and therefore internally consistent.

There is considerable evidence that, with the exception of some species of pathogenic bacteria (Zhang et al., 2005), food preference in C. elegans is not innate. Over the time course of a standard chemotaxis assay (1 hr), previously unfed L1 larvae accumulate equally in high (H) and medium (M) quality food patches located on the same test plate. Similar results were obtained for eight of nine other pairs of beneficial bacteria that differed in quality (Shtonda and Avery, 2006). This observation suggests that innate preferences based on chemotaxis to odors are mostly absent. Differential accumulation in larvae develops gradually, reaching a maximum at 24 hr. During this period which worms leave and re-enter the patches many times, providing the basis for a comparative mechanism. Mutants with compromised feeding ability (eat-2, eat-5), accumulate more strongly than wild type worms in the better of two strains of E. coli that differ in quality but are unlikely to differ in smell. The most plausible explanation for this observation is that food consumption provides feedback that drives food choice. Preferences acquired in one food environment (a bacteria laden agar plate) are retained when worms are transferred to a second environment containing different foods. For example, worms pre-exposed to high-quality food on the first plate become fussy eaters, exhibiting a bias against medium-quality food when transferred to a second plate containing novel high- and medium-quality foods (Shtonda and Avery, 2006). Worms also exhibit a preference for previously encountered food relative to novel food. Food preferences can be reversed by pairing the less preferred food with methamphetamine or cocaine, drugs of abuse that are associated with reward in humans (Musselman et al., 2012). Together, these observations show that worms behave as if they form memories of previously encountered food in a process can be described as food quality learning.

In this study, we utilized GARP to test for utility maximization and investigated its behavioral and neuronal mechanisms. This was accomplished by means of a microfluidic device that enabled us to offer single, semi-restrained worms high- and medium-quality bacteria at a range of different relative abundances while monitoring consumption electrophysiologically. We found food choices of naïve and trained animals are consistent with utility maximization. Worms behave as if they employ an underlying representation of utility that they were acting to maximize. Preference data were well fit by a utility function widely used to model the behavior of human consumers. At the behavioral level, utility maximization relies on a chemotaxis strategy known as klinotaxis. In this strategy, head bends during sinusoidal locomotion are biased by chemosensory input such that bends are deeper on the side where attractant concentration is increasing. At the neuronal level, we found that chemosensory neurons known to modulate head position are able to discriminate between high- and medium-quality food, and that food quality training increases this ability. These findings establish a new model system in which to investigate the neuronal and genetic basis of subjective value and its behavioral expression.

Results

Revealed preference theory

In a typical experiment testing utility maximization with human participants (e.g. Harbaugh et al., 2001), each person is given a series of choice sets. A choice set comprises a list of consumption options, called bundles, from which participants are asked to pick the bundle they most prefer. Choice sets are constructed so that the available bundles are made from varying quantities of goods (e.g. apples and oranges; Figure 1A). Some experiments use more than two goods, but for exposition will we focus the simple case of two goods. Each choice set is defined by a unique combination of a budget and prices, and the cost of each bundle equals the budget. Budget and prices can be in units of money or of time. As a result of the budget constraint, a bundle with more of one good necessarily has less of the other, yielding an inherent trade-off between goods.

Design of a GARP experiment and tests for utility maximization.

(A) Direct violation of utility maximization. Diagonal lines indicate choice sets (n=11). Choice sets are distinguished by having different values of the overall budget and/or different prices for at least one of the goods. Within a choice set, the expenditure implied by each bundle of goods is constant and equals the budget. In A (blue), the budget is $8, oranges are $2 per unit, apples are $1 per unit. In B (red): the budget is $8, oranges are $1 per unit, apples are $2 per unit. Filled circles, chosen amounts; plus signs, available amounts not chosen. Given the choices shown and the more is better rule, adbab and bcaba. Therefore, choices a and b directly violate utility maximization. (B). Indirect violation of utility maximization. Symbols as in A. The choices a and c constitute an indirect violation of utility maximization as described in the text.

Figure 1A shows an ensemble of such choice sets, each of which can be conceptualized as offering two goods at different prices and under different budgets. The lines in the figure, called budget lines, depict the pricing constraints and trade-offs particular to each choice set. In A, for example, oranges are twice the price of apples so the chooser must forgo two units of apples for each additional unit of oranges. Choosing is construed as selecting the most preferred option from those available in the choice set. While in theory a person might choose a bundle inside the budget line and leave money on the table, in practice we assume more is preferred to less, and so these choices are typically not offered.

The constellation of choices a person makes across the many different choice sets in the ensemble is analyzed for the presence of combinations that violate the Generalized Axiom of Reveled Preference (GARP) which has been shown to be a necessary and sufficient condition for observed choices to be consistent with utility maximization. Here, we provide a non-technical explanation of the underlying theory; technical treatments are available elsewhere (Varian, 1982; Harbaugh et al., 2001; Burghart et al., 2013).

Revealed preference violations can be direct or indirect. Both types of violations depend on the assumption that more of a good is better than less of it (strong monotonicity of utility). The filled circles in Figure 1A are one possible pair of choices, a and b, selected to exemplify a direct violation. In choice set A, a was selected over d, which was also in the choice set but was not chosen. We infer from this choice that a is at least as good as d, which we write as ad. (We cannot conclude that a is better than d because the person could have been indifferent between them, with a being chosen randomly.) Noting that d has the same number of oranges but more apples than b, we infer (by strong monotonicity) that d is strictly preferred to b, written as db. Combining the inferences ad and db, we conclude that a should be strictly preferred to b, that is, it should also be true that ab. This preference is said to be revealed directly, because when people choose a, they do so over another option on the same budget line, d, that has more of at least one of the goods than b. Similar logic applies to choice set B such that b is directly revealed preferred to a, that is, ba. These two preferences constitute a violation because they are inconsistent; there is no underlying maximization process of any kind that could allow for this combination of choices.

A person indirectly reveals a preference for one bundle over another when there is a sequence of directly revealed preferences that link the two by transitivity. Figure 1B illustrates an indirect violation. In addition to the original choices a and b, the person picked c in choice set C. We observe that c is preferred to b because it has more of at least one good than the latter, so cb. And, as before, ba, from which we conclude by transitivity that c is preferred to a. We write this as c*a, where the asterisk indicates indirectness. However, at the same time the person reveals ad while dc, from which we conclude a*c. These two preferences constitute a violation because they are inconsistent; again, no maximization process could allow for this combination of preferences. Further, it can be shown that when only two goods are available, the presence of direct violations is a necessary condition for indirect violations (Rose, 1958; Heufer, 2009). This fact is the foundation for the neuronal mechanism of utility maximization proposed in the Discussion.

Adherence to GARP demonstrates rationality in the technical economic sense (henceforth technical rationality). As discussed above, this form of rationality is based on choice consistency. Technical rationality stands in contrast to other forms of rationality (Kacelnik, 2006). These include psychological rationality which emphasizes the process by which decisions are made, namely logically consistent reasoning, rather than decision outcomes. There is also biological rationality which refers to decisions that are consistent with inclusive fitness. None of these forms of rationality are necessary prerequisites for any other. Of particular importance to our study is that demonstration of technical rationality neither presupposes nor establishes psychological rationality. A technically rational agent may or may not use reasoning to make choices.

Finally, tests of adherence to GARP have been utilized to quantify technical rationality. Although strict adherence to GARP is binary, Afriat, 1972 proposed a measure, called Afriat’s efficiency index (AEI), to quantify the severity of GARP violations. This measure has been utilized to quantify the extent of deficits in technical rationality in patients with damage to their ventromedial frontal lobe (Camille et al., 2011). It was also utilized to correlate mathematical ability with the degree of technical rationality in children (Harbaugh et al., 2001).

GARP for worms

The foregoing examples illustrate that testing adherence to GARP entails the following prerequisites:

  1. Two different goods to choose between, with more preferred to less for each good.

  2. Measurement of the consumption choices.

  3. Consumption trade-offs, such that consuming more of one good always means consuming less of the other.

  4. Observation of decision outcomes on budget lines that intersect.

The first step in this study was to develop and validate the means to fulfill these prerequisites in ecologically realistic ways for C. elegans.

Prerequisite (i): Two different goods

As goods, we used bacteria species having high (H, Comamonas) and medium (M, Bacillus simplex) quality as a food source, defined in terms of the growth rate of individual worms (Avery and Shtonda, 2003; Shtonda, 2004; Shtonda and Avery, 2006). Chemical analysis of volatile organic compounds released by these bacteria revealed that each species emits a different blend of compounds (Table 1). These include three compounds that are unique to M food (a, c, d). One (a) is a chemoattractant Hsueh et al., 2017; two are uncharacterized in C. elegans chemotaxis assays (c, d). The two remaining compounds (b, e) are common to both species. Compound b was shown to be attractive in two out of three studies, otherwise neutral (Hsueh et al., 2017; Worthy et al., 2018b; Choi et al., 2022) and e is an attractant except at high concentrations (Choi et al., 2022). Compound c is nematicidal (Xu et al., 2015). Our chemical analysis establishes the olfactory substrate for qualitative differences in the worm’s perception of H and M bacteria, analogous to the qualitative differences by which human choosers distinguish between goods (e.g. colors and flavors of fruits in Figure 1). We cannot, of course, conclude on this basis that the worm’s nervous system actually distinguishes H from M; formally, the neurosensory representations of H and M could be similar. Further evidence on this point is presented below. It is notable that M food releases greater amounts of chemoattractants than H food does, yet is less attractive (Figure 2C, azide+). A possible explanation is that the nematicidal compound released by M food is a repellant that mitigates its potential to attract.

Table 1
Volatile organic compounds released by H and M food.
DesignationCAS#CompoundH food (DA1877)M food (DA1885)
a1534-08-3Methylthioacetate*0.01.0
b624-92-0Dimethyl disulfide*19.438.3
c2432-51-1S-Methyl butanethioate0.04.7
d23747-45-7S-Methyl 3-methylbutanethioate0.02.4
e3658-80-8Dimethyltrisulfide*1.56.4
  1. Compounds were identified by gas chromatography-mass spectrometry of headspace of H and M food and confirmed with known standards. Amounts were inferred from the area under elution peaks, averaged across two replicates, and normalized to the amount of methylthioacetate in DA1885.

  2. *

    Identified chemoattractant; other compounds are uncharacterized in chemotaxis assays.

  3. Vapor is nematicidal.

Figure 2 with 2 supplements see all
Edible bacteria act as goods over which worms form preferences through experience.

(A) Food quality training and preference assays. Filled circles represent patches of bacteria as indicated in the key. Stars indicate worm starting locations. (B). Mean preference at t= 60 min. in the open-field accumulation assay for trained and untrained N2 and ceh-36 mutants. Asterisk, see Table 21. Replicates, Trained, strain(N): N2(8), ceh-36(9). Replicates, Untrained, strain(N): N2(8), ceh-36(8). (C). Mean preference vs. time for trained and untrained N2 worms in T-maze accumulation assays, with and without sodium azide in the food patches. (D). Mean preference index vs. time for trained and untrained cat-2(tm2261) mutants and N2 controls in T-maze accumulation assays. N2 data are from C. (B–D). Error bars, 95% CI. For sample size (N), statistical methods used, and significance level, see Table 2, rows 1-15.

Figure 2—source data 1

Edible bacteria act as goods over which worms form preferences through experience.

https://cdn.elifesciences.org/articles/69779/elife-69779-fig2-data1-v2.xlsx
Figure 2—source data 2

Loss of dopamine signaling does not reduce proportion of time on food.

https://cdn.elifesciences.org/articles/69779/elife-69779-fig2-data2-v2.xlsx

We chose to work with adult worms as they are easier to handle and count than the L1 larvae used in the original food-choice experiments (Shtonda and Avery, 2006). We were initially uncertain whether older worms could learn new food preferences, so we began by investigating the magnitude, neuronal dependence, and mechanisms of food quality learning in the developmental period spanning late L3 to young adulthood. Synchronized, late L3 worms (N2) were transferred to a training plate which contained an equal number of similar sized patches of H and M foods (Figure 2A, Trained). Preference for H versus M food was assessed the following day at the young adult stage on a test plate having a single pair of H and M food patches (henceforth, the open-field accumulation assay). Control worms were transferred to a mock training plate and tested in parallel with trained worms (Figure 2A, Untrained). Preference index I was quantified on a scale such that +1 and –1 represent absolute preference for H and M food, respectively; 0 represents indifference. Note that accumulation assays are not the same as the revealed preference assays used later in this study to investigate utility maximization. In particular, accumulation assays do not allow worms to consume mixtures of the goods (bundles) in the same feeding bout, nor do they challenge worms with different relative food densities (prices).

Trained N2 worms preferred H food to M food more strongly than untrained worms (Figure 2B and N2, Trained vs. Untrained, Table 21;) indicating a significant effect of food quality training. We conclude that worms in the developmental period under study can learn new food preferences; we refer to these as trained preferences. However, untrained N2 worms also preferred H to M food even though they were encountering these foods for the first time (Figure 2B and N2 Untrained, I>0, Table 22). The preference for H food in untrained worms is interesting because hatchlings, which are eating food for the first time, show equal preference for these two foods (Shtonda and Avery, 2006). One possibility is that preferences in untrained worms are the result of learning over the 60 min experiment. Another possibility is that these preferences arise from events that occurred between hatching and testing; we refer to such preferences as latent preferences. To distinguish between these possibilities, we ran accumulation assays with and without the paralytic agent sodium azide in each food patch. The presence of sodium azide captures the preference of worms upon first approach to food. We found that trained and untrained worms preferred H food even when sodium azide was present (Figure 2C, Table 28,9), albeit to a lesser degree than in the absence of sodium azide (Figure 2C, Table 211,12), and that the effect of training was evident in both groups (Figure 2C, Table 27,10). We draw three main conclusions from this experiment: (i) worms do not need to sample both patches before expressing a preference, (ii) training increases preference upon first approach, indicative of a change in olfactory sensitivity, and (iii) latent preferences exist and may contribute to overall preference.

Table 2
Statistics.

Horizontal location of cell entries varies by row.

RowFigureTestEffect or comparison testedUnits of replication or samplingNumber of replicates or samplesStatisticDF 1 or combined DFDF 2pEffect size
12B*t-testTrained N2 vs. Untrained N2Assay platesN=8t2.50142.56E-021.248
22Bt-testN2 Untrained, 60 min mean I>0Assay platesN=8t10.2271.86E-05
32Bt-testceh-36 Untrained, 60 min mean I>0Assay platesN=8t3.5879.01E-03
42Bt-testTrained ceh-36 vs. Untrained N2Assay platesN=8t0.64142.50E-01
52Bt-testUntrained ceh-36 vs. Untrained N2Assay platesN=8t1.87148.22E-02
62Bt-testTrained ceh-36 vs. Untrained ceh-36Assay platesN=8t0.90143.82E-01
72CTwo-factor ANOVA, repeated measures, main effectAzide- Trained vs. Azide- UntrainedAssay platesN≥9 / treatmentF11.281212.98E-030.349
82Ct-testAzide +Trained, 60 min mean I>0Assay platesN=10t6.35108.36E-05
92Ct-testAzide+, Untrained, 60 min mean I>0Assay platesN=10t3.09101.15E-02
102CTwo-factor ANOVA, repeated measures, main effectAzide +Trained vs. Azide +UntrainedAssay platesN=10 / treatmentF10.321204.37E-030.340
112CTwo-factor ANOVA, repeated measures, main effectAzide +Trained, vs. Azide– TrainedAssay platesN≥9 / treatmentF11.171193.43E-030.370
122CTwo-factor ANOVA, repeated measures, main effectAzide +Untrained vs. Azide– UntrainedAssay platesN≥10 / treatmentF38.281223.16E-060.635
132DTwo-factor ANOVA, repeated measures, main effectUntrained N2 vs. Untrained cat-2Assay platesN≥9 / strainF23.251219.14E-050.493
142DTwo-factor ANOVA, repeated measures, main effectTrained N2 vs. Trained cat-2Assay platesN=9 / strainF52.501189.74E-070.207
152DTwo-factor ANOVA, repeated measures, main effectTrained cat-2 vs. Untrained cat-2Assay platesN=9 / treatmentF0.901186.43E-01
164ATwo-factor ANOVA, main effectFamiliar vs. UnfamiliarWormsN≥19 / treatmentF10.461542.10E-030.162
174 A*t-testUnfamiliar, grown in H vs. grown in MWormsN≥6t2.65172.10E-020.876
184Bt-testTrained, f_H>0.5WormsN=19t8.60188.60E-08
194Bt-testUntrained, f_H>0.5WormsN=28t4.35271.70E-04
204B*t-testTrained vs. UntrainedWormsN≥19t2.95445.11E-030.850
214ETwo-factor ANOVAMain effect of optical densityWormsN≥22 / densityF31.5831089.80E-150.467
224FTwo-factor ANOVAMain effect of optical densityWormsN≥22 / densityF3.1031063.00E-020.081
235BTwo-factor ANOVAMain effect of price ratioWormsAvg N=15 / ratioF44.1361957.89E-340.576
245BTwo-factor ANOVAMain effect of trainingWormsAvg N=15 / ratioF36.1611958.82E-090.156
255Bt-testTrained, point a, mean f_H<0.5WormsN=9t6.2282.52E-04
265Bt-testUntrained, point a, mean f_H<0.5WormsN=12t8.29114.66E-06
276ARegression with replication slope testFigure 6A, points abd, Trained slope ≠ 0WormsN≥9 / ratioF118.791471.85E-14
286ARegression with replication slope testFigure 6A, points abd, Untrained slope ≠ 0WormsN≥10 / ratioF28.521394.26E-06
296ARegression with replication slope testFigure 6A, points cef, Trained slope ≠ 0WormsN≥10 / ratioF20.291464.54E-05
306ARegression with replication slope testFigure 6A, points cef, Untrained slope ≠ 0WormsN≥14 / ratioF26.561494.55E-06
316ARegression with replication slope testFigure 6A, points deg, Trained slope ≠ 0WormsN≥6 / ratioF2.341511.32E-01
326ARegression with replication slope testFigure 6A, points deg, Untrained slope ≠ 0WormsN≥7 / ratioF7.821457.56E-03
337ALinear correlationFrequency ratio vs. f_HWormsN=142t6.641416.53E-10
347BLinear correlationDwell time ratio vs. f_HWormsN=203t39.602026.95E-97
357CLinear correlationDwell time ratio vs. mean head angleWormsN=203t35.962022.62E-89
367Dt-testceh-36 Untrained, f_H>0.5WormsN=11t4.20101.84E-03
377DTwo-factor ANOVATreatment ×Strain interactionWormsN≥7 / treatmentF5.031622.85E-020.075
387D*t-testN2, Trained vs. UntrainedWormsN≥20t3.45461.21E-030.186
397Dt-testceh-36, Trained vs. UntrainedWormsN=7 / treatmentt0.58165.83E-01
408BTwo-factor ANOVAMain effect of food typeWormsN≥6 / treatmentF3.561237.20E-02
418DTwo-factor ANOVAMain effect of food typeWormsN≥7 / treatmentF18.421252.00E-040.424
428 C*t-testPeak response, Untrained, H vs. M foodWormsN≥7 / treatmentt2.98121.30E-020.913
438 C×t-testPeak response, Trained, H vs. M foodWormsN≥7 / treatmentt2.29133.96E-021.184
448BTwo-factor ANOVAMain effect of trainingWormsN≥6 / treatmentF0.001239.90E-01
458DTwo-factor ANOVAMain effect of trainingWormsN=7 / treatmentF7.521251.10E-020.883
468D*t-testH food, Trained vs. UntrainedWormsN=7 / treatmentt2.86121.44E-021.528
478Dt-testM food, Trained vs. UntrainedWormsN≥7 / treatmentt0.80134.39E-01
489 A*t-testH → M, peak response, Trained vs. UntrainedWormsN≥14 / treatmentt2.66281.29E-020.972
499At-testM → H, area under the curve, Trained vs. UntrainedWormsN≥15 / treatmentt0.74294.67E-01
519CLinear correlationAWC activation vs. utility, TrainedWormsN≥6 / meant0.1059.27E-01
529CLinear correlationAWC activation vs. utility, UntrainedWormsN≥8 / meant0.1758.75E-01
539DLinear correlationAWC activation vs. preference, TrainedWormsN≥6 / meant1.5751.77E-01
549DLinear correlationAWC activation vs. preference, UntrainedWormsN≥8 / meant0.4456.78E-01
559Ct-testTrained, point e vs. Untrained, point dWormsN≥8 / meant2.14254.23E-020.889
  1. p-values associated with significant results are shown in bold font. Sample size was determined by increasing the number of biological replicates until the coefficient of variation for each means converged. Each experiment was performed once, with the indicated number of biological replicates; the non-stationary nature of the organism precluded technical replicates. No data were censored or excluded.

C. elegans has 12 pairs of anterior chemosensory neurons that respond to bacteria conditioned medium (Zaslaver et al., 2015), acting either as on-cells (activated by onset), or off-cells (activated by offset). As a first step in identifying the locus of food quality learning, we measured food preferences in worms with a loss of function mutation in the Otx homeobox gene ceh-36. This gene is expressed specifically in two food-sensitive chemosensory neuron pairs, AWC and ASE, where it is required for normal expression levels of functionally essential genes, including chemoreceptors and ion channel subunits required for chemotransduction (Lanjuin et al., 2003; Koga and Ohshima, 2004). We found that ceh-36 worms were nevertheless able to distinguish H from M food, as even untrained worms exhibited a marked preference for H food (Figure 2B, ceh-36, Untrained vs. I=0, Table 23). Moreover, this level of preference was indistinguishable from that exhibited by untrained N2 worms (Figure 2B, Trained or Untrained ceh-36 vs. Untrained N2, Table 24,5). In contrast, we were unable to detect an effect of training on food preference in ceh-36 worms (Figure 2B, ceh-36, Trained vs. Untrained, Table 26). The effect size associated with food quality training was reduced relative to wild type (Cohen’s d: N2, 0.21; ceh-36=0.10). This drop was attributable to a reduction in the difference between means (N2, 1.25; ceh-36, 0.45) and an increase in the pooled standard deviation (N2, 0.17; ceh-36, 0.22). We conclude that training effects in ceh-36, if present, are probably weaker than in N2. Taken together, these results show that undiminished ceh-36 function is likely required for food preference acquired through food quality training, implicating AWC and/or ASE in this process; however, full ceh-36 function is dispensable for latent food preferences, suggesting the other neurons may subserve this behavior. Below we present functional imaging data consistent with a role for AWC neurons in mediating the behavior effects of food quality training.

We next considered the mechanism of accumulation in food patches and how it may be altered by food quality training. The number of worms in a food patch depends on between patch entry and exit rates. In a simple experiment to study the effects of entry rate on preference index, we added a fast-acting metabolic poison (sodium azide) to each food patch to prevent worms from leaving (Choi et al., 2016). To increase the resolution of our preference measurements, we used a T-maze baited with H and M foods (Figure 2—figure supplement 1); the maze prevents worms from wandering out of range of food spots.

Trained N2 worms tested in the absence of sodium azide preferred H food to M food more strongly than untrained worms (Figure 2C, Azide –, Trained vs. Untrained, Table 27) indicating a significant effect of food quality training. Preference in both groups continued to rise after the 40-min sample point. This rise could be refinement of preferences as worms go back and forth between patches, additional food-quality learning, or both. In the presence of sodium azide, trained and untrained worms still accumulated more strongly in H food than in M food (Figure 2C: Azide+, Trained and Untrained vs. I=0, Table 28,9). This finding shows that preferences can be established on the basis of entry rate alone. Furthermore, it shows that worms do not have to sample both patches before expressing a preference. This means at least some of the H-food preference seen in untrained worms is independent of sampling experience during the assay.

We also observed a significant effect of training on food preference in the azide condition (Figure 2C, Azide+, Trained vs. Untrained, Table 210), indicating that food quality training increases entry rate. Finally, preference levels were substantially reduced by sodium azide (Figure 2C, Trained, Azide +vs. Azide–; Table 211 and Untrained, Azide +vs. Azide–; Table 212). This result shows that additional mechanisms contribute to differential accumulation in H and M food, mostly likely differences in exit rate, shown previously to contribute to accumulation in open-field accumulation assays (Shtonda and Avery, 2006).

Learning to avoid the odors of pathogenic bacteria is reinforced by serotonin (Zhang et al., 2005), but less is known about how preferences for nonpathogenic foods are reinforced. We found that food preferences in general were reduced in cat-2 mutants, which have substantially reduced levels of dopamine (Lints and Emmons, 1999; Sawin et al., 2000; Calvo et al., 2011). Preference for H food in untrained cat-2 mutants was lower than in untrained N2 (Figure 2D, Untrained, N2 vs. cat-2, Table 213) indicating impaired acquisition of latent preferences. Preference for H food in trained cat-2 mutants was lower than in trained N2 worms (Figure 2D, Trained, N2 vs. cat-2, Table 214), indicating an impairment in trained preferences. Finally, preferences in trained and untrained cat-2 mutants were indistinguishable (Figure 2D cat-2, Trained vs. Untrained, Table 215), another indication that trained preferences were impaired.

What accounts for these impairments? Worms move more slowly when in contact with food particles, an effect caused by mechanical activation of dopaminergic neurons (Sawin et al., 2000; Tanimoto et al., 2016). Slowing is reduced in cat-2 mutants (Sawin et al., 2000; Cermak et al., 2020). During the training procedure, this reduction could cause cat-2 mutants to exit food patches sooner than wild type worms. It is possible, therefore, that food quality learning in cat-2 mutants is impaired simply because they spend less time in the food, hence have less experience of it. However, we found no differences between wild type and cat-2 mutants in the proportion of time on food (Figure 2—figure supplement 2). This finding points to a requirement for dopamine signaling in the acquisition or expression of food memory, in accordance with substantial evidence showing a requirement for dopamine in several forms of associative learning in C. elegans (Hukema et al., 2008; Voglis and Tavernarakis, 2008; Lee et al., 2009; Musselman et al., 2012).

GARP prerequisite (ii): Measurement of the consumption choices

Bacteria are ingested via the worm’s pharynx, a rhythmically active, muscular pump comprising the animal’s throat. Each pharyngeal contraction is called a ‘pump’. To measure the relationship between price and consumption, we developed a system for presenting single worms with a pair of bacteria suspensions while recording the number of pumps the worm ‘spends’ on each (Figure 3). The system is based on a microfluidic chip (called the ‘Y-chip’) originally designed to investigate the neural mechanism of klinotaxis (McCormick et al., 2011), a common form of chemotaxis. C. elegans klinotaxis takes the form of accentuating or attenuating, respectively, locomotory head bends toward or away from attractive tastes and odors, including food (Iino and Yoshida, 2009). The Y-chip restrains the worm at the border between two streams of bacteria suspension (Figure 3A and B), representing contiguous patches of food as might occur in the natural environment (Frézal and Félix, 2015). Restraint is achieved by means of a vacuum clamp that leaves the worm’s head, upper body, and tail free to move. The worm’s head alternates between the two streams, making sinusoidal movements that resemble crawling on a standard agarose substrate in form and frequency (Video 1).

Single-worm food choice assays.

(A) Layout of the Y-chip. Asterisks indicate the position of recording electrodes. Ground electrodes (not shown) were inserted into the food and buffer ports to reduce electrical interference. The chip is shown configured for the experiments in Figures 4B and 5B. (B). Area of detail shown in A. The dashed line is the centerline of chip; the white line within the worm is its centerline. The black arrow connects the middle of the neck where it enters the food channel with anterior end of worm’s centerline. Positive values of head angle (θ) indicate displacement toward H food. Colored arrows show direction of flow. (C). Schematic overview of fluidic system. (D). Typical electropharyngeogram. Each pair of excitation (E) and relaxation (R) spikes constitutes one pharyngeal pump.

Video 1
Foraging behavior in the Y-chip.

Simulated Y-chip experiment. The worm is held at its midsection by a vacuum activated clamp, leaving the head (left) and tail free to move. The both fluid streams contain bacteria-free buffer, flowing to the right to left. Food dye was added to the lower stream to visualize the interface between streams. Bubbles originating at the clamp are formed by air that has been pulled through the PDMS walls of the chip by the vacuum. The worm prefers the dyed stream as it contains potassium sorbate, which acts as a chemoattractant.

Large movements of the worm’s head in the Y-chip made it impractical to count accurately the number of pumps in a feeding bout by optical methods (Fang-Yen et al., 2009; Scholz et al., 2016). Instead, we counted pumps by recording each worm’s electropharyngeogram (Raizen and Avery, 1994) via electrodes inserted into the chip (Faumont et al., 2012). Despite movements of the worm’s body, normal looking EPGs were obtained, with readily identifiable muscle excitation spikes (E) and relaxation spikes (R) (Figure 3D). We quantified consumption of H and M food in terms of the number of pumps that occurred in each food during a 12-min exposure to particular food offerings. This time limit was chosen as compromise between the need acquire reliable preference measures without allowing the worm to feed so long as to allow preferences to changes, for example, by onset of satiety.

We measured the consumption of each food in terms of the fraction of pumps that occurred while the worm’s head was in that food’s stream. In C. elegans feeding decisions, the muscular energy utilized while feeding, can be thought of as the functional equivalent of money, in human budgetary experiments. Following this logic, price P can be defined as the cost incurred by swallowing the amount of bacteria ingested in a single pump. We assume that at equal density, approximately the same number of H and M bacteria cells are ingested per pump. This assumption is based on: (i) the observation that H and M bacteria are similar in size (Avery and Shtonda, 2003), and (ii) the likelihood that pump volume v is approximately constant. We presume pump volume depends mainly on the maximum extent of contraction of pharyngeal muscles, which opens the pharyngeal lumen. This, in turn, should be most strongly influenced by the duration of the pharyngeal action potential, which is constant across the food densities utilized in our study (Lee et al., 2017). Assuming constant pump volume,

(1) cells/pump=ν[nL/pump]d[cells/nL],

where d is the density of bacteria cells. Taking the inverse of cells/pump, and expressing volume in units of the volume of the fully-open pharyngeal lumen (v=1) we can define a measure of price for bacteria X,

(2) PX(dX)=1/dX[pumps/cell].

Equation 2 embodies the intuition that doubling bacteria density reduces the energetic cost of consumption by half.

Finally, consumption, QX, is the number of pumps in food X, nX, times the number of cells/pump (Equation 1),

(3) QX(nX,dX)=nXdX[cells]

Our method of measuring consumption choices differs in operational terms from the method used in many experimental economics GARP studies. Participants in the experiment make instantaneous choices from a set of menu items. This type of experiment abstracts away from the classical revealed preference theory on which these experiments are based (Samuelson, 1938; Houthakker, 1950). In the classical theory, and essentially all economy-wide measurements that rest on it, consumption is defined in terms of the rate at which units of goods are acquired or consumed over time. In our study, we employ this more classical approach. Here, consumption is the product of the number of pumps and food density (Equation 3). The number of pumps is, in effect, the time integral of pumping rate. In other words, it is the integral of consumption rate. As such, it captures a key feature of the classical presentation missed by many in-lab experimental economics studies.

GARP prerequisite (iii): consumption trade-offs

In GARP experiments with human participants, trade-offs between goods within a choice set are established by setting a fixed budget which each bundle must stay within. Given the assumption that more is preferred to less, the budget constraint will be satisfied by establishment of equality between expenditure and budget,

(4) PXQX+PYQY=E[dollars],

where the left hand side is total expenditure and E is the budget. Participants are not made aware of the budget constraint; it remains implicit in the set of available choices. For worms, the analogous equality is

(5) PHQH+PMQM=N[pumps].

where N is the total number of pumps (N=nH+nM). In human experiments the trade-off between consuming more of one good at the expense of less of another is enforced by the budget constraint. In C. elegans experiments, however, imposing a budget constraint is not necessary, as trade-offs are enforced by the Y-chip. The chip contains only two streams, one for H and one for M food, such that for every pump spent on H food, the worm necessarily forgoes a pump spent on M food, and vice versa.

As the total number of pumps emitted by individual worms over a fixed observation period was quite variable, and the observation period had to be brief to limit possible consumption changes due to satiety, we found it expedient to express consumption in terms of the proportion of pumps spent on each food, rather than number of pumps spent on each food, with

(6) qH(nH,dH)=nHNdHqM(nM,dM)=nMNdM

where qH and qM represent consumption in proportional terms. The corresponding equality is

(7) PHqH+PMqM=1

Below, in the section Behavioral mechanisms of utility maximization, we show that worms pump at nearly the same rate in H and M food. Therefore, consumption is determined mainly by the fraction of time the worm pumps in each food. Note that by expressing consumption of a food as the fraction of total pumps spent in that food, rather than as the number of pumps spent on that food, the number of pumps N (or equivalently the total time allowed for feeding) cancels out. This has the advantage that we do not have to assume that worms are aware of a pump or time budget.

GARP prerequisite (iv): observation of decision outcomes from intersecting budget lines

By systematically altering the densities of H and M bacteria in the Y-chip, we could alter their relative prices. Changing the density of both foods at the same time allowed us to create changes analogous to increases or decreases in the total consumption budget, which shifts the budget line in or out relative to the origin. This approach allowed us to create a series of intersecting choice sets.

Basic feeding decisions are preserved in Y-chip

A concern at the outset was the possibility that feeding in the Y-chip is not representative of feeding under standard laboratory conditions such as on an agar substrate or in liquid culture. For example, the vacuum clamp likely stimulates the worm mechanically, which can inhibit feeding (Keane and Avery, 2003). It was necessary, therefore, to assess the degree to which feeding behavior in the chip is normal. We did this by comparing the worm’s choices of what to eat and how avidly to eat it on agar plates and in the Y-chip.

Food familiarity effect

C. elegans is reluctant to eat unfamiliar food. It pumps slower in unfamiliar food than in familiar food (Song et al., 2013). This effect is the result of feeding suppression triggered by the taste or smell of unfamiliar bacteria. To test for this effect in the Y-chip, we grew worms on H food or M food until young adulthood and measured pumping rates either in the same (familiar) or the converse (unfamiliar) food. In this experiment, both streams in the chip carried the same food. We found that mean pumping rate for a given type of food was lower when that food was unfamiliar, indicating that the food familiarity effect is intact in the Y-chip (Figure 4A, Familiar food vs. Unfamiliar food, Table 216). Furthermore, we noted that pumping rate on familiar food was the same in the two cases. This allowed us to compare directly the extent to which unfamiliar H and M food suppressed pumping rate. We found that suppression was greater when the unfamiliar food was lower in quality than the familiar food (Figure 4A, Unfamiliar food, grown on H vs. grown on M, Table 217). This result is consistent with a model in which worms are even more reluctant to feed on unfamiliar food when it is worse than what they have eaten in the recent past. A similar result has been seen in the case of food-patch leaving behavior (Shtonda and Avery, 2006).

Validation of the Y-chip for measuring food preferences.

(A) Familiar food effect. Mean pump frequency of worms grown on H or M food and tested on the same or the converse food. Asterisk, see Table 217. Both foods were at OD 1. Pumping was recorded for 12 min. Replicates, Grown on H, tested on (N): Familiar(16), Unfamiliar(6). Replicates, Grown on M, tested on(N): Familiar(23), Unfamiliar(13). Error bars, 95% CI. (B). Food quality learning. Mean fraction of pumps in H food in trained and untrained worms. Asterisk, see Table 220. The dashed line indicates equal preference for H and M food. Both foods were at OD 1. Error bars, 95% CI. (C,D). Time course of pump frequency at four different densities of familiar food. Food enters the chip at t=0 sec. Optical density is indicated next to each trace. The black trace shows pumping in the absence of food. Shading, ± SEM E. Dependence of mean peak pump frequency density of familiar food. (F). Dependence of latency to half-maximal pump frequency on density of familiar food. (E,F). Error bars, 95% CI. For sample size (N), statistical methods used, and significance level, see Table 2, rows 16-000.

Figure 4—source data 1

Validation of the Y-chip for measuring food preferences.

https://cdn.elifesciences.org/articles/69779/elife-69779-fig4-data1-v2.xlsx

The food familiarity effect supports a model in which H and M foods are qualitatively distinct to the worm. In the alternative model, the foods are qualitatively similar but one food generates a more intense perception than the other, perhaps by emitting more of the characteristic compound or compounds by which H and M are detected. Worms familiar with H or M food pump at the same rate in them (Figure 4A, left bars), indicating H and M are not distinct. By the alternative model, this means H and M emit the same amount of the characteristic compounds. In light of this result, the alternative model obviously fails to predict the familiarity effect for, as H and M are indistinguishable, neither of them can be unfamiliar to the worm under the conditions of our experiment. From the fact that worms pump at different rates on H and M food when they are familiar versus unfamiliar, we can conclude that the foods are qualitatively distinct.

Food quality training

We tested groups of trained and untrained worms with H and M food at equal concentrations (OD 1.0) in their respective streams in the Y-chip. Preference, as indicated by the fraction of pumps in H food (fH, see Materials and methods), in trained and untrained worms was greater than 0.5, indicating that both groups preferred H food in the chip, just as they do in accumulation assays (Figure 4B, Table 218,19). Moreover, we found that this preference was enhanced by training, again consistent with accumulation assays (Figure 4B, Trained vs. Untrained, Table 220). We conclude that the effects of food quality training are detectable in the Y-chip.

Effect of food density on pumping rate

Although there appear to be no systematic studies of this effect when worms are feeding on bacteria lawns in petri plates, pumping rate has been shown to increase as a function of food density in liquid culture (Avery and Horvitz, 1990). This effect has also been demonstrated under conditions of mild restraint in microfluidic devices (Scholz et al., 2016; Lee et al., 2017; Weeks et al., 2018). To test for this effect in the Y-chip, we trained worms as in Figure 2A, except that the training plate contained a single food, H or M. During testing, both channels in the Y-chip carried the food on which the animals were trained (H or M) at an OD of 0.1, 0.3, 1.0, or 3.0. Pumping rate in H food was stable whereas pumping rate in M appeared to decline later in the experiment (Figure 4C and D); therefore, we quantified pumping in terms of its peak rate for both food types. Peak pumping rate was comparable to the rate recorded in similar densities of E. coli strain OP50 under mild restraint in microfluidic devices (Scholz et al., 2016; Lee et al., 2017; Weeks et al., 2018), and exhibited the expected increase with food density (Figure 4E; effect of OD, Table 221). We conclude that the density dependence of pumping rate is intact in the Y-chip. This experiment also revealed previously unreported aspects of pumping kinetics. Regardless of food type, pumping rate rose slowly, on the time scale of 100 s of seconds (Figure 4C and D), Additionally, we observed an inverse relationship between the latency to half-maximum pumping rate and concentration (Figure 4F; effect of OD, Table 222). Thus, worms encountering a richer food source eat sooner at higher rates, a coordinated response that is presumably adaptive in natural environments.

Demand curves

We next turned to the question of whether C. elegans feeding behavior is altered by the relative price of food options that vary in quality. Economists identify several different types of goods according to how demand (or equivalently, consumption) is affected by changes in income or price. An ordinary good is one for which there is an inverse relationship between price and demand. To determine whether H and M food behave as ordinary goods in C. elegans feeding ecology, we constructed demand curves, in which consumption was plotted against pricefor H and M food (Figure 5A). We found an inverse relationship between consumption and price, indicating that H and M food act as normal goods and therefore are well suited to a GARP experiment.

Figure 5 with 2 supplements see all
Economic analysis of food choice in C. elegans.

(A) Demand curves. Mean consumption of familiar food versus its price. Consumption is computed as number of pumps times optical density of bacteria. Price is computed by Equation 2. The data are fit by Equation 8 with ϵ=-2.2 for H food and ϵ=-1.9 for M food. H food price(N): 0.33(13), 1.0 (16), 3.3 (21), 10(15). M food price(N): 0.33(9), 1.0 (23), 3.3 (7), 10(10). (B). Price ratio curves. Food preference, measured as fraction of pumps in H food, versus price ratio for Trained and Untrained worms. Horizontal dashed line: indifference between H and M food; vertical dashed line: H and M food at equal price. Data at log price ratio = 0 are replotted from Figure 4B. Replicates, Trained, point(N): a(9), b(14), c(18), d(27), e(20), f(10), g(6). Replicates, Untrained, point(N): a(12), b(17), c(13), d(12), e(28), f(10), g(7). (C). GARP analysis of C. elegans food preferences. Plotted points show mean consumption of M food versus consumption of H food in Trained and Untrained worms. Lines are choice sets as in Figure 1. The x and y intercepts of each line indicate the amounts of H and M food that would have been consumed if the worm spent all its pumps on one or the other food type. Error bars, 95% CI. (D). Predicted consumption of H and M food in Trained and Untrained animals on a widely-used ensemble containing 11 budget lines (Harbaugh et al., 2001). (A–C). Error bars, 95% CI. For sample size (N), statistical methods used, and significance level, see Table 2, rows 23-26.

Figure 5—source data 1

Economic analysis of food choice in C. elegans.

https://cdn.elifesciences.org/articles/69779/elife-69779-fig5-data1-v2.xlsx
Figure 5—source data 2

Distributions of preference values in trained and untrained animals in Figure 5B.

https://cdn.elifesciences.org/articles/69779/elife-69779-fig5-data2-v2.xlsx

More broadly, these results show that C. elegans obeys the classic law of demand, exhibiting the fundamental sensitivity of consumption to price seen in humans. The data of Figure 5A were well fit by

(8) qX(pX)=ApXϵ

where A is a positive constant and ϵ<0. This is the equation for a demand curve in which the percentage change in consumption from a given percentage change in price is constant at all prices, that is, there is constant elasticity of demand (Varian, 1992). We found ϵ-2 for both food types, indicating strong elasticity, a condition that typically arises when substitute goods of similar value are available. Interestingly, this may actually be the case for C. elegans, which grows robustly on approximately 80% of the hundreds of bacteria species in its natural habitat (Samuel et al., 2016). Elasticity is not always the case in foraging animals. Rats exhibit inelastic demand when offered essential commodities such as food pellets and water (Kagel et al., 1975; Kagel et al., 1981).

Integration of preference and price

In a GARP experiment, participants evaluate offerings in the choice sets by taking into account their preferences and the price of various goods. To determine if C. elegans takes preference and price into account, we repeated the experiment of Figure 4B, now for a broad range of relative H and M prices (Figure 5B). To avoid progressive effects of feeding and satiety on food choices, each worm experienced a single choice set, and we allowed worms to feed for only 12 min.

Data were analyzed by plotting preference, the mean fraction of pumps spent on H food, fH, against the log of price ratio log(pM/pH) which, by Equation 2, is equal to log(dH/dM). The data were fit by an exponential sigmoid function of the form

(9) fH(r)=11+10(rr0)/k

where r is log price ratio, r0 is log price ratio at the point of indifference between H and M food (fH(r0)=0.5), and k set dynamic range of the function. We chose an exponential sigmoid because, like fH, it is bounded between 0 and 1. We refer to this mathematical relationship as a price-ratio curve. We found that in trained and untrained groups alike, worms spent more pumps on H food as its relative density rose, that is, as its relative price was reduced (Figure 5B, effect of price ratio, Table 223), showing that worms take relative price into account when choosing food. Training shifted the price-ratio curve (Figure 5B, Trained vs. Untrained, Table 224), such that the inferred indifference point between H and M food (intersection of the fitted curve and the dashed horizontal line) moved leftward. That is, a higher relative concentration of M food was now required to make the two options equally preferred. In other words, training increased the relative preference for H food. Importantly, we also found that worms could be induced to spend the majority of pumps on non-preferred food M if the preferred food H was made sufficiently dilute, i.e., expensive (Figure 5B, point a, Trained and Untrained, fH < 0.5, Table 225,26). Therefore, price can overcome preference. Taken together, these data show that neither food preference nor price is the sole factor determining consumption. Worms appear to take both preference and price into account, as human consumers often do, and as required for a GARP experiment.

Utility maximization

To apply the test for utility maximization to C. elegans food choice, we mapped the data of Figure 5B into the GARP framework by plotting mean consumption of M food against mean consumption of H food at each price ratio (Figure 5C). Under this mapping, the lines in Figure 5C correspond to choice sets like those in Figure 1. There is one line for each combination of price ratio and income. The x and y intercepts of these lines indicate the amount of food (up to a scale factor) that would have been consumed had the worms spent all of their pumps on H or M food, respectively. We found it impractical to standardize the number of pumps to impose a fixed budget on each worm because of individual differences in latency to feed and mean pumping rate during the recordings (Figure 4C–F). We therefore plotted proportional consumption, qH and qM (Equation 6).

Utility maximization was assessed according to the procedure outlined by Varian, 1996. This assessment yields a single number that captures the total degree of consistency of preferences. Using choices averaged over all trials, we found no violations of GARP in either the trained or untrained data set (Figure 5C). Therefore, worms were choosing as if they were maximizing utility on the seven budget lines in our study.

To assess the robustness of our finding of utility maximization, we first considered whether it could be attributed to sampling error. Error bars in Figure 5C show the confidence intervals for mean consumption of H food on each budget line. Given this degree of variability, it is conceivable that one or more violations was missed because of sampling error. We therefore constructed 108 simulated data sets by sampling from the gaussian distributions implied by the means and standard errors of each point. Sampling from gaussian distributions was justified by the form of the distributions of preference values (Figure 5—figure supplement 1). Finding no violations of utility maximization in either the trained or untrained group, we estimated the probability of at least one violation to be less than 10–8. It is therefore unlikely that the absence of violations was an accident of sampling error.

However, it is conceivable that violations might have been observed if we had used a larger ensemble of budget lines. To address this concern, we predicted the choices worms would make on a widely used ensemble (Harbaugh et al., 2001; Camille et al., 2011; Chung et al., 2017), which contains 11 budget lines and covers the choice space more uniformly than our 7-budget ensemble. We first assessed the stringency of the 11-budget ensemble as a test for the utility maximization. This was done by assuming a conservative null hypothesis: that worms choose completely randomly, such that the fraction of pumps in H food, fH, could be modeled by drawing from a flat distribution between 0 and 1 (fraction of pumps in M food was 1fH). Based on 106 random data sets constructed in this way, we estimated the probability of a false positive finding of utility maximization (no violations) in the 11-budget ensemble to be 0.06. The 7-budget ensemble, by comparison, has a false positive probability of 0.87. We conclude that the 11-budget ensemble is considerably more stringent.

To compute how C. elegans would be expected to perform when choosing on the stringent 11-budget ensemble, we used Equation 9 to predict the expected behavior on the budget lines in Figure 5D. There were no violations of GARP. There were also no violations when, instead of Equation 9, we used piecewise linear representations of Figure 5 data. Finally, to take into account the variance about the means in Figure 5B, we created 106 random data sets by sampling from gaussian distributions centered on the means. The standard deviation of the gaussians was set to the highest value of the standard error of the mean in either the trained or untrained data set in Figure 5B. By this procedure, we estimated the probability that worms would exhibit utility maximization in the 11-budget ensemble to be ≥ 0.98, regardless of training state or type of fit (Equation 9 or piecewise linear). We conclude that the worm’s price-ratio curve likely constitutes a robust utility maximization strategy.

Higher order features of utility maximization

Evidence that C. elegans is a utility maximizer (Figure 5C and D), allowed us to investigate several higher order features of utility maximization considered to be properties of human decisions. Ultimately, we succeeded in establishing a utility model describing what may be the underlying valuation process guiding the worm’s choices.

Economic theory distinguishes between two main classes of goods – substitutes versus complements – according to how changes in the price or quantity of one good that a consumer possesses affects consumption of a second good. In the case of substitutes, which are relatively interchangeable from the consumer’s perspective, an increase in the price of one good causes a decrease in the consumption of that good and a compensatory increase in consumption of the substitute. This occurs as consumers trade some of the good whose price increased for more of the alternative good. Pairs of goods that are traded-off at a constant exchange rate, regardless of the amounts of goods on offer, are called perfect substitutes; black and blue pens are an example of perfect substitutes. In the case of complements, which are defined as goods that are more desirable when consumed together rather than separately, an increase in the price of one good causes a decrease in consumption of both goods. Left and right are an example of perfect complements. Wearing only one shoe has essentially zero utility, so increases in the price of left shoes leads to decreased shoe consumption overall. Although worms consistently ate some of both foods in our experiments, we predicted that H and M food should act, to some degree, as substitutes for each other, as each provides nutrition.

To test this prediction, we took advantage of the design of the experiment in Figure 5B. The seven choice sets can be arranged in groups in which the price of one food was held constant while the other food was offered at three different prices. There were two groups in which the price of M food was constant while the price H food changed (points a, b, d, and points c, e, f), and there was one group in which the price of H food as constant while the price of M food changed (points d, e, g); see Supplementary file 1. We analyzed these groups by plotting consumption of the food whose price was constant against the price of the other food (Figure 6A). In five out of six cases, consumption of the constant-price food increased in response to increases in the price of the other food (Figure 6A, non-zero positive slope, Table 227-32). We conclude that H and M food are substitutes for C. elegans as predicted.

Higher order features of utility maximization.

(A) H and M food act as substitutes. Consumption is plotted against price for triplets of cost ratios in which the concentration of one food was constant and the concentration of the other food was variable (see Supplementary file 1). Lower case italic letters: data points in Figure 5B. Capital letters: the food whose density was constant, the consumption of which is plotted on the y-axis. Solid lines: regression slope different from zero (p0.01); dashed lines: slope not different from zero. Error bars, 95% CI. (B). H and M food are not perfect substitutes. Colored contour lines are indifference curves in a perfect substitute model (Equation 10) with β=10/11. Data points from Figure 5C are replotted for comparison, with associated budget lines, according to the conventions of that figure. ‘X’ symbols indicate the point of highest utility on each budget line. (C–D). Best fitting parameterizations of the CES function (Equation 11) for Trained and Untrained animals. Each panel shows the seven the iso-utility lines that are tangent to the budget lines. Goodness of fit can be assessed by observing that the iso-utility lines are tangent to the budget lines at, or near, the data points which indicate mean consumption of H and M food. For sample size (N), statistical methods used, and significance level, see Table 2, rows 27-32.

Further, we can be reasonably certain that the H and M foods used in our experiments are not perfect substitutes. In the case of perfect substitutes, utility is the weighted sum of the consumed amount of each good. This relationship can be described with the equation

(10) U(x,y)=βx+(1β)y

where x and y are the amounts of each good, and β is a weighting factor (0β1). In that case, the exchange rate between the two goods, i.e., the amount of y required to compensate for giving up one unit of x, is a constant, β/(1β). For example, goods that can be substituted on a one-for-one basis have an exchange rate of unity (β=0.5). Equation 10 defines a planar utility surface that lies above the positive x,y plane and passes through the origin. This plane is indicated by the colored contour lines in Figure 6B, which also contains the data of Figure 5C for comparison. The contour lines represent iso-utility lines within the plane. Such lines are called indifference curves, because a chooser would be indifferent between bundles located on the same curve, as these would have the same utility. In the example shown, β=10/11>0.5, meaning that the slope of the plane is steeper in the direction parallel to the axis indicating consumption of good x, that is, H food in the figure. A utility maximizer will therefore choose the points labeled ‘X’ as these have the highest utility available on the associated budget line. Such points are called corner solutions, where the chooser devotes the entire budget to a one of the two options. In this example, the corner solutions are arrayed along the x axis (and a hypothetical worm showing this pattern of perfect substitution would spend all of its pumps eating only the H food); for β<0.5 the corner solutions would be arrayed along the y-axis. Worms in the Y-chip may be incapable of generating perfect corner solutions because they continuously wave their heads, frequently crossing into the opposite stream. We found that they are nevertheless capable of generating close approximations to corner solutions (e.g. point g for trained worms in Figure 5C). Even so, we did not observe a consistent pattern of approximate corner solutions. We conclude that C. elegans does not perceive H and M food as perfect substitutes under our conditions, but rather as imperfect substitutes.

A model of valuation in the worm

In widely used models of choices made by human consumers when offered imperfect substitutes, the exchange rate is not constant, but varies as a function of the amount of each good offered in a particular bundle. In economics this case is often modeled by the Constant Elasticity of Substitution (CES) function. The CES function takes the form

(11) U(qH,qM)=(βqHρ+(1β)qMρ)1/ρ

The exponent ρ0 represents the sensitivity of choosers to the fact that the more of a good they already possess, the less valuable each additional unit of the good becomes; in economics, this is called diminishing marginal utility. This sensitivity is inversely related to ρ. Here, as in Equation 10, β captures the tradeoff between the goods, now after transformation by ρ. The CES utility function is quite flexible in that it can generate indifference curves for perfect substitutes (ρ=1), imperfect substitutes (0.5<ρ<1), and perfect complements (ρ-0.5).

The best fitting parameterizations of the CES function (β,ρ) for the preference data in Figure 5C are shown for trained and untrained worms in Figure 6C and D, respectively. The highest contour reached by any budget line is the one that is tangent to it, and this contour constitutes the CES function’s prediction of the worm’s mean preference in that choice set. The close match between model and behavior for trained and untrained worms indicates that C. elegans food choice conforms to a widely used model of choice behavior in humans. We found that β and ρ increased following training. Therefore, training caused worms value H more and made diminishing marginal utility less relevant to their food valuations.

Behavioral mechanisms of utility maximization

We next asked how utility is maximized at the behavioral level. As noted in above, we defined preference as the fraction of pumps in H food, fH=NH/(NH+NM), where NH and NM are the number of pumps in H and M food, respectively. In one model, the pumping-rate model, the behavioral expression of preference is a higher pumping rate in the preferred option. Alternatively, in the dwell-time model, behavioral expression is increased amount of time spent feeding on the preferred side. Because the number of pumps in a given food type is equal to product of the time spent in that food and the mean pumping frequency in that food, an equivalent expression for preference is

(12) fH=FHtHFHtH+FMtM

where F and t are, respectively, mean pumping frequency and mean total dwell time in the indicated food type. Limiting cases are informative here. If preference depends entirely on pumping frequency, then tH=tM, and Equation 12 reduces to the pumping-rate model

(13) fH=FHFH+FM

in which preference for H food occurs when FH>FM, whereas preference for M food occurs when FM>FH; we refer to Equation 13 as the frequency index. Plotting preference as defined by Equation 13 for each animal against its actual preference, fH, revealed a modest but significant negative correlation (Figure 7A, Table 233). This result indicates a paradoxical but weak tendency to pump more slowly in H food as preference for it increases. The mean frequency index was 0.50±0.004 SEM and the extreme y-values of the linear fit to the data were only about 10% higher or lower. Therefore, we conclude that worms pump at approximately the same frequency in H and M food.

Behavioral mechanisms of utility maximization.

(A) Pumping-rate model of preference. Equation 13 is evaluated for each worm in Figure 5B and the result is plotted against preference in terms of fraction of pumps in H food for the same animal. (B). Dwell-time model of preference. Same as A but using Equation 14. (C). Regression of Equation 14 against mean head angle as defined in Figure 3B. (A–C). Blue lines: regressions on the data. (D). Diminished ceh-36 function eliminates the effect of food quality training on food preference. Asterisk, see Table 238. (H and M) are at OD = 1. N2 data are from Figure 4B. Replicates, Trained, strain(N): N2(20), ceh-36(7). Replicates, Untrained, strain(N): N2(28), ceh-36(11). Error bars, 95% CI. Correlation coefficients are shown ±95% CI. For sample size (N), statistical methods used, and significance level, see Table 2, rows 33-39.

Conversely, if preference depends entirely on time in each food, then FH=FM, and Equation 10 reduces to the dwell-time model

(14) fH=tHtH+tM

in which preference for H food occurs when tH>tM, whereas preference M food occurs when tM>tH; we refere to Equation 14 as the dwell-time index. We found a strong positive correlation preference defined by the well-time index and actual preference, fH (Figure 7B, Table 234). These findings favor the dwell-time model. We propose that once the worm detects the presence of food, pharyngeal pumping is activated at a fairly constant rate and preference is determined by the fraction of time the worm’s head is in H food.

To determine how dwell time is biased toward the preferred food option, we measured mean head angle for each animal in the data set underlying Figure 5B. As expected, we found a strong positive correlation between the dwell-time index and mean head angle in the Y-chip (Figure 7C, Table 235). Calcium imaging suggests that the angle of the worm’s head with respect to the rest of the body is regulated by differential activation of dorsal and ventral neck muscle motor neurons (Hendricks et al., 2012). We propose, therefore, that the function of the neural circuit that maximizes utility is to generate asymmetric activation of these motor neurons during head bends.

Role of chemosensory neurons in utility maximization

ceh-36 is required for the effects of food quality training measured in the Y-chip

In a final series of experiments, we began the search for neuronal representations of utility in C. elegans, beginning with its chemosensory neurons. As shown in Figure 4B, N2 worms preferred H to M food in the Y-chip, and there was a significant effect of training. In the experiment of Figure 7D, we found that whereas untrained ceh-36 worms also preferred H to M food (Figure 7D, ceh-36 Untrained, fH>0.5, Table 236), the effect of food quality training differed between N2 and ceh-36 (Figure 7D, training ×strain, Table 237), such that trained and untrained ceh-36 worms were indistinguishable (Figure 7D, ceh-36 Trained vs. Untrained, Table 239). These findings indicate a requirement for normal function of the ceh-36 expressing neurons AWC and/or ASE in food quality learning.

Characterization of AWC’s response to delivery and removal of bacteria

In perhaps the most likely scenario, the worm’s internal representation of H and M food is distributed across some or all of the 12 pairs of food sensitive chemosensory neurons in this organism. As a first step, we focused on one of these, AWC, because its role in directing chemotaxis to food is particularly well established. Additionally, it is one of the few chemosensory neurons known from optogenetic manipulation to be capable of producing precisely the type of head-angle bias that underlies the expression of utility maximization in C. elegans seen in Figure 7C (Kocabas et al., 2012). The two AWC neurons are designated AWCON and AWCOFF according to differences in gene expression (Wes and Bargmann, 2001). AWCON and AWCOFF generate similar calcium transients to odorants that they both detect (Chalasani et al., 2007); for consistency, we recorded from AWCON (henceforth, ‘AWC’). Calcium imaging shows that AWC is inhibited by bacteria conditioned medium or odorants, such as isoamyl alcohol, that are released by attractive bacteria (Worthy et al., 2018a) but then responds with a robust, positive-going transient when the stimulus is removed; AWC is therefore considered to be a food-off neuron. However, in one case, AWC is known to generate an off-transient when the stimulus is switched from the odor of a preferred food to the odor of a less preferred food (Ha et al., 2010; Lin et al., 2023). This finding indicates that AWC may be sensitive to food preferences.

To test whether AWC activity reflects preferences for the foods used in our study, we stimulated AWC with suspensions of H and M bacteria. We first characterized AWC’s responses to the delivery and removal of H and M food (OD = 1) Such events mimic the experience of an AWC neuron when the worm moves in or out of a food patch, respectively, as in our accumulation assays (e.g. Figure 2B–D). We found, as expected from odorant experiments (Chalasani et al., 2007), that AWC is inhibited by food onset (Figure 8A) and excited by food offset (Figure 8C) regardless of food type, consistent with previously reported off-responses to E. coli (Calhoun et al., 2015).

Figure 8 with 1 supplement see all
Characterization of AWC’s response to delivery and removal of food.

(A) Ensemble averages of relative fluorescence versus time in response to onset of the indicated food in trained and untrained animals. (B). Summary of data in A, showing mean integrated calcium transients. (C). Ensemble averages of relative fluorescence versus time in response to removal of the indicated food in trained and untrained animals. Asterisk: untrained group, mean peak response, H vs. M food, see Table 242. Cross: trained group, mean peak response, H vs. M food, see Table 243. (D). Summary of data in C, showing mean integrated calcium transients Asterisk, see Table 246. (A–D). OD = 1 for H and M food. Shading, ± SEM. Error bars, 95% CI. For sample size (N), statistical methods used, and significance level, see Table 2, rows 40-47.

Figure 8—source data 1

Characterization of AWC's response to delivery and removal of food.

https://cdn.elifesciences.org/articles/69779/elife-69779-fig8-data1-v2.xlsx

Do AWC responses reflect the worm’s overall preference for H? With respect to food onset, the apparently stronger inhibition in response to H than to M food (Figure 8A), when measured in terms of integrated calcium response, did not reach significance (Figure 8B, effect of food type, Table 240). However, with respect to food offset, AWC was more strongly excited by H than M food (Figure 8D, effect of food type, Table 241). At the more fine-grained level of peak responses within training groups, peak H food responses were significantly stronger than peak M food responses (Figure 8C, Untrained, effect of food type, *, Table 242; Figure 8C, Trained, effect of food type, ×, Table 243). Overall, we conclude AWC responds more strongly to removal of H food than M food. Exogenous activation of AWC increases the probability of a bout of reverse locomotion (Gordus et al., 2015). Therefore, AWC’s response to food offset would be expected to increase reversal probability, leading to increased retention food patches. Our imaging data suggest that AWC-mediated retention would be stronger for H than M food, promoting greater preference for H food, as seen in Figure 2B–D.

What is the effect of food-quality training on AWC responses? Training had no effect on integrated response to food onset (Figure 8B, effect of training, Table 244). In the case of food offset, training increased integrated response to H food (Figure 8D, Trained vs. Untrained, Table 245 and H food, Trained vs. Untrained, *, Table 246), but not to M food (Figure 8D, Table 247). Overall, our imaging data suggest that AWC-mediated retention in H food patches would be stronger in trained than untrained animals, promoting greater preference for H food after training, as seen in Figure 2B–D.

AWC’s response to transitions between H and M food

We next asked whether AWC responds to changes in food quality. If AWC were merely a food-off neuron, then switching between H and M food at the same density should produce no response, as food is always present. We found, on the contrary, that AWC was strongly excited by H→M transitions, and peak responses were amplified by food-quality training (Figure 9A, asterisk, Trained vs. Untrained, Table 248). AWC appeared to be inhibited by M→H transitions. The extent of inhibition, quantified as the integrated calcium transient, was insensitive to training (Figure 9A, Table 249). We conclude that AWC is capable of reporting not only the mere presence or absence of food, but also changes in food quality.

Figure 9 with 1 supplement see all
Characterization of AWC’s response to bacterial foods in Y-chip assays.

(A) Ensemble average of relative fluorescence versus time in response to transitions from H to M (H→M) or M to H (M→H) food. Asterisk, see Table 248. Both foods were presented at OD = 1. Food was switched at t = 0. H→M, Trained, N = 16; H→M, Untrained N = 14. M→H, Trained, N = 16; M→H, Untrained, N = 15. Shading,±SEM. (B). Typical fluorescence waveform in response to a series of transitions between H and M food. Notation: F0, baseline fluorescence after sustained exposure to H food (≅ 2 min.); FM, maximum H→M fluorescence; FH, minimum M→H fluorescence. The box delineates the time period of presumptive steady-state responses over which mean response amplitudes AF were computed for each recorded worm. (C–E). AF versus utility, preference, and log price ratio. Lines and curves are, respectively, linear and gaussian fits. Italic letters refer to labeled points in Figure 5B. Replicates, Trained, point(N): a(6), b(10), c(18), d(12), e(19), f(10), g(9). Replicates, Untrained. point(N): a(8), b(11), c(10), d(8), e(12), f(8), g(10). Error bars, 95% CI. For sample size (N), statistical methods used, and significance level, see Table 2, rows 48-55.

Figure 9—source data 1

Characterization of AWC’s response to bacterial foods in Y-chip assays.

https://cdn.elifesciences.org/articles/69779/elife-69779-fig9-data1-v2.xlsx

The fact that normal ceh-36 function is required for food preference in the Y-chip (Figure 7D), and that AWC is sensitive to food quality (Figure 9A), suggests that it could provide sensory input to the worm’s utility maximization circuit. If so, it should respond to changes in food quality on the time scale of individual head bends (seconds). We therefore presented worms with an alternating series of 2 s. presentations of each food. (Figure 9B), which approximate the time to peak calcium responses in Figure 9A. The imaging trace in Figure 9B illustrates a typical fluorescence waveform in the experiment. AWC responded at two distinct time scales. On the longer time scale, it exhibited a positive transient that decayed over tens of seconds, reminiscent of the time course of responses to sustained changes from H to M food (Figure 9A). On the shorter time scale, AWC responded with positive-going transients at each H→M transition, and negative-going transients at each M→H transition. In control experiments, when each fluid channel contained bacteria-free buffer, AWC did not respond (Figure 9—figure supplement 1), making it unlikely that pressure artifacts associated with valve activation contributed to fluorescence transients. We conclude that AWC is capable of responding to changes in food quality on the time scale of individual head bends.

Exogenous activation of AWC truncates head bends (Kocabas et al., 2012). The fact that positive transients occurred at the H→M transitions is consistent with AWC having a role in truncating head bends into the non-preferred food, as a means of biasing mean head angle toward the preferred side (Figure 7C). The waveforms we obtained closely resemble the response to alternating presentations of plain buffer and buffer containing a food-related odor sensed by AWC (Kato et al., 2013), suggesting the AWC perceives the transition to lower food quality as being similar to the transition to food-free medium.

Representational content of AWC’s responses

To investigate a possible role of AWC in utility maximization, we mapped its response function across the seven price ratios used in the GARP analysis of Figure 5C. We assumed that the steady-state region of the imaging trace is a reasonably accurate representation of AWC activity throughout the 12 min. behavioral recordings in the Y-chip (Figure 5B). We defined the amplitude of the calcium transients at steady-state as the mean fractional change in fluorescence between the peak at the end of an M step and its preceding trough at the end of an H step (AΔF=(FMFH)/F0). In perhaps the simplest model of utility maximization, individual chemosensory neurons like AWC report changes in the utility of the local environment. In that case, AWC activation would be well correlated with the utility of the chosen mixture of H and M food at each price ratio in Figure 5B. However, plotting AF against the utility values predicted by fits of utility functions to the preference data in Figure 6C and D showed no such relationship (Figure 9C, Table 250, 51). We conclude that AWC is not representing the utility of chosen food. A similar analysis showed AWC activation was also not correlated with preference for H food (Figure 9D, Table 252,53).

Given that AWC represents neither to chosen utility nor to preference, perhaps it represents some other economic quantity. Plotting AF against price ratio revealed an inverted U-shaped response function (Figure 9E). Such response functions have been observed in primate orbitofrontal cortex (Padoa-Schioppa and Assad, 2006) in plots of mean firing rate (analogous to our AF measure) against the ratio of offered amounts of two desirable juice rewards (analogous to price ratio in our study). By regressing mean firing rate against a wide range of value-related economic quantities, it was found that these neurons represent the relative value of the chosen juice, termed chosen value.

We therefore sought correlations between AF and offered food value (H or M), chosen food value, and 15 additional quantities that depend on them (Supplementary file 2). Food value, referenced to M food, was computed as

(15) VM=dMVH=wTdHorwUdH,

where wT and wU specify the number of units of M food that are equivalent to one unit of H food assuming a linear valuation function in the vicinity of the indifference point (where fH=0.5), in trained and untrained animals, respectively. These quantities were computed as 1/r0 from the fit of Equation 9 to the preference data in Figure 5B. To test whether AWC represents any of these quantities, we computed correlation coefficients between AF each quantity, in trained and untrained animals. We found no significant correlations (Supplementary file 3). In a separate analysis, we also considered offered utility and change in chosen utility, again finding no significant correlations. We conclude that AWC represents neither the value of food nor utility.

A potential clue to the function of AWC in food choice stems from the observation that the peak of its response function lies at or near the point on the price-ratio axis where the two foods are presented at the same density. This is the point where foraging decisions are the most difficult, as food density is no longer available as cue to identify the better option. Moreover, food quality training greatly increased the height of the function’s peak (Figure 9E, effect of training, Table 254), improving AWC’s ability to make such distinctions. Accordingly, we propose that AWC’s role is to report changes in relative food quality as defined by prior experience.

Discussion

There is substantial evidence that C. elegans is capable of several forms of valuation. These include valuations inherent in cost-benefit decisions, transitivity of binary preferences, and independence of irrelevant alternatives (Barrios et al., 2008; Bendesky et al., 2011; Shinkai et al., 2011; Ghosh et al., 2016; Cohen et al., 2019; Iwanir et al., 2019). The present work establishes a new reference point in the study of valuation in C. elegans in four key respects. (i) C. elegans food choices obey the classic law of supply and demand (Figure 5A). This law has been shown to apply not just to humans but to a variety of model organisms (Kagel et al., 1975; Kagel et al., 1995; Bickel et al., 1995), but none as simple as C. elegans. (i) C. elegans behaves as if maximizing utility (Figure 5C). When challenged with multiple trade-offs between food quality and price, its choices satisfy the necessary and sufficient conditions for utility maximization. An organism that maximizes utility also maximizes subjective value, for it is reasonable to maximize only what is valued. We believe this may be the first demonstration of value-based decision making according to GARP in an invertebrate. (iii) C. elegans food-consumption decisions are well fit by the CES utility function (Figure 6C and D). This function is widely used to model human consumers, but the extent to which it applies to other species remains an open question (Fréchette, 2016). Here, we show that the CES function accurately models consumption decisions in an organism that diverged from the line leading to humans 600 million years ago (Raible and Arendt, 2004; Figure 6C and D), which provides new evidence of the function’s universality. (iv) In addition to demonstrating utility maximization in C. elegans, we have outlined a plausible mechanism for it. The C. elegans price-ratio curve is monotonic-increasing (Figure 5B). Below we offer a proof that monotonicity of the price-ratio curve guarantees adherence to GARP (Figure 10). Importantly, such a price-ratio curve seems simple to implement at the neuronal level, requiring only that chemosensory neurons are able to regulate the amplitude of locomotory head-bends as they occur, and to do so monotonically in response to differences in food value on either side of the body.

Price ratio curves and utility maximization.

(A) A pair of intersecting budget lines wherein choices a and b are governed by a price-ratio curve (not shown) that is monotonic-increasing. To support a direct violation of GARP, a must be to the right of the intersection of lines A and B, and b must be to the left of it. However, by price-ratio monotonicity, b must lie to the right of a, for reasons described in the text. This constraint precludes direct violations of GARP. (B). Choice data from a human participant in a GARP experiment (Camille et al., 2011). The data are consistent with utility maximization. Inset, price ratio data inferred from the experiment. Log price ratios for points a-k are calculated as logXZ/YZ, where XZ and YZ are, respectively, the x and y intercepts of budget line Z. The fraction of total budget spent on good X is computed as xZ/XZ, where xZ is the amount of good X chosen on line Z.

A key challenge in the present study was to develop the methodology for presenting worms with choices that can be analyzed using revealed preference theory. This meant finding a method of offering worms qualitatively distinct goods whose prices could be varied systemically under the constraint of an explicit trade-off between them. It also meant finding a way to measure consumption of each good. We chose species of high- and medium-quality bacteria as goods. We showed that these species have different olfactory fingerprints, making it conceivable that they are qualitatively distinct (Table 1). Furthermore, we showed that worms feed differently on these species in a way that can only be explained by a model in which the foods are indeed qualitatively distinct (Figure 4A). Price differences were modeled as differences in bacteria density under the assumption that doubling food density reduces by half the number of pharyngeal pumps required to ingest a given mass of food. In human experiments, trade-offs are established by means of a budget constraint ensuring that choosing more of one good means getting less of the other. That is the only purpose of the budget constraint, and participants need not and are not made aware of it. In the case of C. elegans, it was not necessary to impose a budget constraint because trade-offs could be established simply by the geometry of the microfluidic device, which ensured that more a pump spent in one food is a pump not spent in the other food (Figure 3). Finally, to measure relative consumption of the two bacteria, we computed the fraction of pumps emitted in each food stream (Figure 5B). Overall, this methodology results in decision-making paradigm that is formally analogous to GARP experiments in humans.

There are several possible objections to this methodology. (i) There is the concern that revealed preference theory, created to model human consumers, is unnecessarily complex for modeling worm behavior. However, our study uses this framework not as a model but as litmus test for utility maximization. (ii) We have not shown that qualitative distinctions between bacteria (Table 1, Figure 4A) are mirrored by distinct representations in the worm’s nervous system, as is presumably the case in the human nervous system. However, revealed preference theory makes no such stipulation as to how utility maximization physically occurs, including neural representations of goods. In worms, cells other neurons, such as gut cells, could be part of the representation without violating theoretical assumptions. (iii) Finally, there is the concern that that conscious awareness of the budget constraint is a necessary condition for application of the theory. However, revealed preference theory merely requires the ability to choose between different bundles of goods. There is no requirement that that these choices be made consciously after considering prices and income and calculating the range of possible choices. The budget constraint can instead be imposed physically, as in this experiment.

Our study has several experimental limitations. (i) There was a high probability of a false-positive finding of utility maximization in Figure 5C. A contributing factor to this problem is the comparatively small number of budget lines in our budget ensemble. Another factor is the somewhat uneven coverage of choice space, with two budget lines close to the y axis (a and b). We included these budget lines to make a stronger case for complex decision making in the worm by demonstrating preference reversals (Figure 5B, point a); this required presenting H food at very low density. We were able to address this limitation by showing that the price-ratio curve of Figure 5B predicted the absence of transitivity violations in a larger budget ensemble that covered choice space completely (Figure 5D). Moreover, we show below that the absence of violations in the larger ensemble is essentially guaranteed by the monotonic form of the worm’s price-ratio curve. (ii) In the calcium imaging experiment of Figure 9B–E, dwell times in the two foods were equal (2 s). This stimulus pattern is somewhat unrealistic because in the behavioral experiments to measure food preference in the Y-chip, dwell times were rarely equal (Figure 7B). We nevertheless used equal dwell times because we were primarily interested in the question of whether AWC is capable of reporting food utility via its inherent sensitivity to the food quality, that is, without the complicating factor of dwell time, which is behaviorally determined and can increase or decrease peak calcium responses. (iii) Our demonstration of utility maximization is currently limited to the klinotaxis component of C. elegans foraging behavior. It does not necessary extend to other components, such as klinokinesis (biased random walk Pierce-Shimomura et al., 1999) and orthokinesis (slowing in the presence food Sawin et al., 2000). (iv) Finally, it will now be important to test whether utility maximization is observed in choices between other pairs of bacteria strains.

Distinctions between GARP and binary transitivity

Assessment of utility maximization by GARP involves demonstration of internally consistent preferences. This means non-violation of transitivity relationships inherent in directly revealed preferences, as well as those revealed indirectly through sequences of directly revealed preferences. The scientific literature on transitive choice in animals is extensive, encompassing a wide range of vertebrates: primates (Addessi et al., 2008), birds (Mazur and Coe, 1987; Sumpter et al., 1999; Schuck-Paim and Kacelnik, 2002), and fish (Dechaume-Moncharmont et al., 2013). Many invertebrates also exhibit transitivity: bees (Shafir, 1994), fruit flies (Arbuthnott et al., 2017), nematodes (Cohen et al., 2019; Iwanir et al., 2019), and even slime molds (Latty and Beekman, 2011). However, these studies have focused almost entirely on binary transitivity, meaning either-or decisions between pairs of items. Transitivity in this sense can be impressive, even in simple organisms. Choices of male fruit flies presented with pairs of genetically distinct females drawn from 10 divergent inbred strains form a transitive hierarchy of order 10 (Arbuthnott et al., 2017). Such examples notwithstanding, binary transitivity is not a sufficient condition for utility maximization. That is because in binary choices there is no notion of amount. It is therefore impossible to assess whether choices between different goods are consistent with the rule ‘more is better’ which, as illustrated in Figure 1A, is a necessary condition for utility maximization. Here, we have demonstrated a form of transitivity in which not only the quality of goods but also their offered amount (hence price) is taken into account by the organism. The full set of transitivity relationships exhibited by worms in our study is illustrated in Figure 5—figure supplement 1.

What is being maximized?

Utility maximization raises the ineluctable question of what is being maximized. Revealed preference theory, including GARP, cannot answer this question. At present, it is easier to identify what is not being maximized. Three ethologically plausible maximization targets can be ruled out by simple inspection of Figure 5C. (i) It is unlikely that the worm is maximizing the amount of high quality food consumed, as that would have resulted in corner solutions. (ii) It is also unlikely that the worm is maximizing the overall amount of food consumed. That would have resulted in feeding exclusively in whichever of the two streams carried denser food, again yielding corner solutions (except at point e, where densities are equal and so the worm would be indifferent, which is was not). (iii) Finally, and perhaps surprisingly, the worm is probably not maximizing its potential for growth, at least in terms of a simple model in which this potential is the product the characteristic growth rates of worm in H or M food, 0.50 and 0.43 days–10, respectively (Shtonda, 2004), and the densities of those foods. The growth-potential model fails to explain our data because H and M growth rates are not sufficiently different to make the less dense food preferred under any of the price ratios tested. It predicts an outcome similar to maximizing amount of food consumed (except at point e, where instead of indifference, it predicts that H food would be preferred). Together, considerations (i)-(iii) imply that the worm is not maximizing fitness, at least in terms of food consumption. It is conceivable that the worm is maximizing some combination of fitness-related quantities which, in addition to food consumption, might include knowledge about the local food environment (Calhoun et al., 2014), food safety (Song et al., 2013), and the foraging benefits of continuous locomotion while feeding (Shtonda and Avery, 2006), but we have no evidence of these as yet.

The worm’s preference for non-corner solutions, called ‘interior solutions’, is consistent with at least two hypotheses concerning what is being maximized. The worm might be maximizing something having to do with mixtures of the two foods, reminiscent of ‘a taste for variety’ in economics (Senior, 1836; Jevons, 1871). This would be an appropriate strategy if, for example, the two foods had unique essential nutrients, but we currently have no evidence for or against this. A second hypothesis is that interior solutions arise because the worm is balancing the benefit of consuming the better food option against the cost of forgoing the possibility of the sudden appearance of an even better option on the other side; this hypothesis mirrors an exploitation-exploration trade-off. Alternatively, neuromechanical constraints such as chemosensory transduction delays coupled with behavioral momentum (inability to reverse the current head bend).

Establishment of subjective value assignments

It is well established that learning alters food preferences in C. elegans (Ardiel and Rankin, 2010). We extended these findings by showing that worms are capable of food quality learning for palatable foods at least as late as larval stage L4 (Figure 2) and that this process requires intact dopamine signaling. A requirement for dopamine signaling in C. elegans has also been demonstrated in the formation of enhanced preferences for salt ions that were paired with cocaine or methamphetamine, drugs that increase the amount of dopamine in the synaptic cleft (Musselman et al., 2012). Furthermore, pairing these drugs with a particular food increases preference for it. These findings are consistent with model in which trained preferences arise by a form of classical conditioning that is driven by the rewarding properties of food. However, our data do not exclude possible non-associative effects during training, such as sensitization and habituation to H and M food, respectively. Studying untrained worms, we found evidence for acquisition of latent food preferences that occurred in the absence of direct experience of the newly preferred foods. The fact that acquisition of latent preferences also requires intact dopamine signaling (Figure 2D) is consistent with this process being reward-driven, but developmental effects cannot be ruled out on the basis of the available data.

Training and the latent effects of food experience may be dissociable at the circuit level in that training effects, but not latent effects, exhibit a requirement for ceh-36 (Figure 2B). In one simple model, at least one of two chemosensory neurons, AWC or ASE, is a locus of food memories implanted by sampling both foods repeatedly over time, whereas some or all of the other chemosensory neurons mediate latent preferences. In partial support of this model, AWC’s response to removal of H food (Figure 8C) and to H→M transitions (Figure 9A and E), is strongly enhanced by training. It will now be important to determine whether food responses in ASE neurons are also modified by training, and whether the responses of other chemosensory neurons are exhibit latent effects.

The fact that in cat-2 mutants training has no effect on food preferences (Figure 2D) implicates dopamine signaling in the acquisition or expression of food quality memories. One hypothesis is that during training, dopamine neuron activity in C. elegans signals reward, as it does in many other organisms. In support of this model, cat-2 is required for learned associations between salt cues and drugs of abuse that co-opt the reward systems, such as cocaine and methamphetamine (Musselman et al., 2012) as well acquisition of alcohol preference (Lee et al., 2009). Similarly, the C. elegans gene asic-1, a member of the degenerin/epithelial sodium channel family that is mainly expressed at presynaptic terminals of dopaminergic neurons, is required for learned associations between tastes or odors and the presence of food (Voglis and Tavernarakis, 2008).

Monotonic-increasing price-ratio curves guarantee adherence to GARP

The preference values fH, plotted against price ratio r=dH/dM (Figure 5B), were well fit by smooth curves that are monotonic-increasing (strictly, non-decreasing; Equation 9). Here we offer a proof that a monotonic-increasing price-ratio curve precludes GARP violations. In Figure 10A, Point a represents any location on A such that ba could be revealed directly (meaning a is between the A-B intersection and the x axis; see Figure 1A). Point b, on the other hand, represents any location on B that is consistent with monotonicity, conditional on the location of a. By Equation 6, the x coordinates of points a and b, representing the consumed quanties of H, are

(16) ha=fH(rA)dH(A)hb=fH(rB)dH(B)

Budget line A has the steeper slope of the two lines which means that dM(A)/dH(A) > dM(B)/dH(B). These ratios are the inverse of price ratio. Therefore, rB>rA and, by monotonicity,

(17) fH(rB)>fH(rA)

Furthermore, by construction,

(18) dH(B)>dH(A)

Given these inequalities, hb>ha, meaning that point b must always lie to the right of a. Therefore, b can never reside to the left of the A-B intersection, as needed to generate a direct violation. Monotonicity of the price-ratio curve thereby precludes direct violations of GARP. Furthermore, for indirect violations to occur, there must be at least one direct violation (Rose, 1958; Heufer, 2009). Therefore, we can conclude that monotonic price-ratio curves guarantee adherence to GARP. This conclusion explains our finding that when modeling C. elegans food choice by the worm’s price-ratio curve, the probability of finding utility maximization in the 11-budget ensemble was ≥0.98 (the exceptions being due to sampling noise). Although monotonic-increasing price-ratio curves guarantee utility maximization, they are not necessary for it. Figure 10B shows data from a human subject who exhibited no utility violations, yet whose price-ratio curve was clearly non-monotonic. Thus, in relying upon monotonic price-ratio curves, the worm’s choice strategy may be an adaptation for utility maximization under the constraint of limited computational capacity.

A neuronal mechanism of utility maximization

The following simple model illustrates how a monotonic price-ratio curve, and thus utility maximization, could be achieved by the C. elegans klinotaxis circuit. The food-sensitive chemosensory off-cells (AWC, ASER, AWB, ASH, ASK) and on-cells (ASEL, AFD, AWA, ASJ, BAG, ASI, ADF) activate, respectively, when the cell’s preferred stimulus is removed or delivered (Zaslaver et al., 2015). The off-cells AWC and ASER are known to truncate head bends when exogenously activated (Kocabas et al., 2012). The model assumes that other off-cells do likewise, whereas on-cells extend head bends. Provided that summed activations of all off-cells and on-cells are, respectively, monotonic functions of price ratio, the amplitude of head-bend truncations and extensions will also be monotonic with respect to price ratio. Given the sinusoidal kinematics of C. elegans locomotion, this relationship necessarily extends to relative dwell time on the side of the preferred food option, thereby increasing the fraction of pumps on that side. The non-monotonic activation function of AWC (Figure 9E) could be compensated by activations of other chemosensory neurons at price ratios greater than unity. This model can now be tested by recording and stimulating neurons in the klinotaxis circuit during choices of the type studied here.

Conclusion

All animals forage to obtain sufficient food at minimal cost. Omnivores like humans, C. elegans, and other species face the additional challenge of reconciling trade-offs between food quality and a variety of costs, such as energy, time (lost opportunity), and risk. Our findings expand the scope of comparative studies already in progress in ethology, behavioral ecology, and neuroeconomics to probe the limits of classical economic theory in explaining such fundamental trade-offs (Kalenscher and van Wingerden, 2011; Pearson et al., 2014). Is the classical theory universally applicable to animal behavior? To what extent can this theory be grounded in neurophysiology? The small size and unequalled annotation of the C. elegans nervous system (White et al., 1986; Jarrell et al., 2012; Hammarlund et al., 2018; Cook et al., 2019; Brittin et al., 2021; Hobert, 2021), coupled with recent advances in brain wide imaging in this organism (Kato et al., 2015; Nguyen et al., 2016; Venkatachalam et al., 2016) offer unique advantages in answering these questions.

Materials and methods

Key resources table
Reagent type (species) or resourceDesignationSource or referenceIdentifiersAdditional information
Strain, strain background (E. coli)OP50CGC (C. elegans Genetic Center)RRID:WB-STRAIN:WBStrain00041969
Strain, strain background (Comamonas sp.)DA1877CGCRRID:WB-STRAIN:WBStrain00040995
Strain, strain background (Bacillus simplex)DA1885CGCRRID:WB-STRAIN:WBStrain00040997
Genetic reagent (C. elegans)N2, BristolCGCRRID:WB-STRAIN:WBStrain00000001
Genetic reagent (C. elegans)CX5893CGCRRID:WB-Strain00005275
Genetic reagent (C. elegans)JP5651National Resource Project (Japan)Nonecat-2(tm2261)
Genetic reagent (C. elegans)MT15620CGCRRID:WB-Strain00027527cat-2(n4547)
Genetic reagent (C. elegans)CB1112Stern et al., 2017; PMID:29198526RRID:WB-Strain00004246cat-2(e1112)
Genetic reagent (C. elegans)XL322Lockery labNonentIs1703[str-2::GCaMP6s-wcherry; unc-122::dsred2]
Recombinant DNA reagentGCaMP-6s::wCherryZhen labNone
Software, algorithmIgor ProWavemetrics https://www.wavemetrics.com/Version 9.01

Worm strains

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The following C. elegans genotypes were used:

ExperimentFigureGenotype
Wild type decision making2, 4–9N2
Requirement for AWC/ASE neurons2B, 7Dceh-36(ky646)
Requirement for dopamine signaling2Dcat-2(tm2261)
Calcium imaging from AWC neurons9ntIs1703[str-2::GCamp6s-wcherry; unc-122::dsred2]
Proportion of time on food2 (suppl.)cat-2(n4547), cat-2(e1112)

Bacteria strains and suspensions

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Streptomycin-resistant strains of three species were used: E. coli (OP50 DA 837) representing standard laboratory food, Comamonas sp. (DA1877) representing high-quality food (H), and Bacillus simplex (DA1885), representing mediumquality food (M). To culture bacteria, a small scraping of frozen stock was transferred to 400 mL of LB broth in a 500 mL flask to which streptomycin (50 μg/mL) added to inhibit competitive bacterial growth. Cultures were grown overnight in on a shaker at 35 C. Bacteria cultured as described above were washed three times by centrifugation and resuspension of the pellet in 10–20 mL minimal buffer which contained (in mM): 1 MgSO4, 10 HEPES adjusted 350–360 mOsm (glycerol). The final wash pellet was resuspended in a smaller volume of buffer to create a stock suspension whose bacteria density was greater than the desired value. The density of the stock suspension was measured by dilution of a small sample into the linear range of the densitometer (0–1 OD600). The final suspension at the desired density d was obtained by dilution of the stock suspension.

Identification of volatile organic compounds released by bacteria

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Bacteria were prepared for Thermal Desorption Gas Chromatography-Mass Spectrometry (TD-GC-MS) analysis in a similar method as described (Worthy et al., 2018a; Worthy et al., 2018b) Bacteria were grown overnight in LB with 50 mg/mL streptomycin at 37 °C, centrifuged, and then resuspended at an OD600=10. Two peptone-free NGM plates were prepared each with 9 spots of 25 μL of bacterial suspension. For the controls, 25 μL of LB media without bacteria was spotted on NGM plate. Plates were incubated for 1 hr at 20 °C. Then 18 squares of the NGM agar with 25 μL bacteria suspension were placed in a GC-MS glass vial for 24 hr. Samples were analyzed by Thermal Desorption (TD) GC-MS using the Agilent 6890 GC System equipped with a Markes Unity II Thermal Desorption System on the GC inlet, a Restek, Rtx-5 column, and Agilent 5973 Mass Selective Detector. The temperature program was: hold 8 min at 35 °C, increased to 130 °C at a rate of 10 °C/min, hold 5 min at 130 °C then increased to 300 °C at a rate of 15 °C/min, and hold at 300 °C for 1 min. MS ranged from 30 to 550 in full scan mode. VOCs were identified with the NIST 11 (National Institute of Standards and Technology) mass spectral library and pure chemical standards run following the same parameters as for bacterial samples. Samples were prepared for analysis in duplicate from a single stock of each bacteria and LB control samples were run immediately before or after each bacterial sample.

Worm cultivation and training

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Worms were synchronized by isolating eggs from 10 gravid adults allowed to lay eggs for five hours. Progeny were cultivated until late larval stage L3 at 20 °C on 50 cm plates containing low-density nematode growth medium (NGM; Brenner, 1974) seeded with standard laboratory food (E. coli OP50). In experiments involving food quality training, worms were washed three times in M9 buffer, pelleted by sedimentation, then transferred in a 2 μL aliquot (~150 worms) to a training plate (50 mm diam.) filled with bactopeptone-free NGM containing 200 μg/mL streptomycin. Training plates were prepared one day in advance by spotting them with eight patches each of H and M food. Patches were formed by pipetting 10 μL aliquots of bacteria culture, suspended in LB broth at OD = 10, in a 4×4 grid with 10 mm between patch centers (Figure 2A). Control plates were spotted with patches of OP50 in the same pattern. Worms resided on training plates for 18–24 hr before testing. In experiments involving the food familiarity effect, training plates contained 16 patches of either H or M food prepared in the same way.

Behavioral assays

Accumulation assays

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In open-field assays, NGM test plates (50 mm diameter) were spotted with one patch each of H and M food (100 μL, OD = 10) separated by 25 mm. In T-maze assays, a mask was formed by laser cutting 2-mm-thick ethylene-vinyl acetate foam sheets (Figure 2—figure supplement 1; Supplemental CAD file 1). The mask was placed on the NGM surface and the maze was baited with the same amounts of H and M food, which were placed within the maze on the agar surface at the end of each arm. After training, worms were washed and transferred as above to the plate center or the starting point in the T-maze. Accumulation was scored for 60 min at 15 min. intervals. At each time point, preference I was computed as (NHNM)/(NH+NM), where N is the number of worms in contact with the food-type indicated by the subscript; worms not in contact with food, and small numbers of escaped worms (~5%), were not counted. Worms were counted by eye with the aid of a tally counter; the experimenter was blind to condition.

Food dwell-time assays

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Dwell-time on food patches was measured as described previously (Cermak et al., 2020). Assay plates were standard 10 cm diameter petri dishes filled with low-peptone (0.2 g/L) nematode growth medium, seeded with 200 mL E. coli OP50. Low-peptone medium ensured thin bacterial lawns for improved tracking optics. Roughly circular lawns were created with a spreader, and plates were left to dry overnight before use. For recordings, a single 72 hr old adult animal was picked to an assay plate, allowed to accommodate for 10 min, and then tracked for approximately six hours at 20 fps using the described automated tracking microscope. Prior to tracking, the lawn boundary was annotated by manually circumscribing it with the microscope. This procedure enabled post-hoc determination of when the worm was on or off the lawn.

System for recording food choice in semi-restrained worms

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The system comprised (1) a food delivery system, (2) instrumentation for electrophysiological recording, and (3) a video camera for recording behavior (Figure 3).

(1) Food delivery system. Bacteria suspensions, and bacteria-free buffer, were held in 20 mL reservoirs (syringes with plungers removed) fitted with stopcocks. Reservoirs were suspended 50 cm above the chip and connected to it via polyethylene tubing (PE-9) fitted with 1.5 mm diameter × 12.5 mm stainless steel nipples (17 Ga, × 0.500”, New England Small Tube, Litchfield, New Hampshire). To minimize settling of bacteria, a miniature magnetic stir bar in each reservoir was agitated periodically during experiments by moving a small hand-held magnet. The layout of the Y-chip was similar in all main respects to a previous design (McCormick et al., 2011); feature height was 55 μm. Flow rate in the chip was regulated by a peristaltic pump (model 426-2000, Labconco, Kansas City, MO, USA) attached to chip’s outlet port.

(2) Electrophysiology. Electropharyngeograms were recorded by means of electrodes (stainless steel nipples, see above) inserted into the worm port and fluid outlet. In this configuration they were used to measure the voltage differences that occur between the worm’s head and tail during pharyngeal muscle action potentials. The vacuum clamp accentuates these voltage differences by increasing the electrical resistance between head and tail. Voltage differences between electrodes were amplified by a differential amplifier (model 1700, AM Systems, Sequim, Washington) and digitized (2 kHz) for later analysis (USB-9215A, National Instruments, Austin, Texas). Digitized recordings were bandpass filtered between 5 and 200 Hz. E and R spikes were detected offline by a manually adjusted threshold in custom data analysis software. Instantaneous pumping rate was computed using a 5 sec. sliding window average (forward looking).

(3) Videography. The worm was imaged using a stereomicroscope (Wild M3C, Leica, Buffalo Grove, Illinois) with a 1.5× objective, and a video camera (VE-CCDTX, DATG MTI, Michigan City, Illinois) with a frame rate of 30 Hz. Individual frames were analyzed by MATLAB scripts (Mathworks, Natick, MA) to extract head angle of the worm as previously described (McCormick et al., 2011). First, each frame was thresholded to identify the worm’s head and neck region, which was then skeletonized to obtain its centerline (white line, Figure 3B) and head angle (θ) was defined as described Figure 3B. Values of head angle when the worm was exhibiting presumptive reversal behavior (Faumont and Lockery, 2006) where excluded manually, without knowledge of experimental condition.

Single-worm food choice assays

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Bacteria cultured as described above (late stationary phase) were washed three times by centrifugation and resuspension in ~5 mL minimal buffer; the buffer contained (in mM): 1 MgSO4, 10 HEPES adjusted 350–360 mOsm (glycerol). After resuspension of the final wash, bacteria cell density d was measured by diluting a sample of known volume by a factor 1/a such that the optical density of the sample, ODs, was in in the linear range relative to cell density, that is, ODs <1 unit (Stevenson et al., 2016). We computed d as a× ODs; typical values of d were 4–6 units. The final resuspension was then diluted to the desired density for each experiment. We found that OD = 1 corresponds to approximately 2.35×109 and 2.00×109 colony forming units/mL of Comamonas and Simplex, respectively.

After training, worms were washed and transferred to foodless plates for 1–2 hr of food deprivation. At the start of the assay, the Y-chip was filled with bacteria-free buffer solution and a worm was inserted into the chip by liquid transfer using a syringe fitting with PE tubing and a steel nipple. During a 2 min. accommodation period, both streams carried bacteria-free buffer and the video and electrophysiological recordings were initiated. After accommodation, both streams were switched to particular food types and food densities according to the design of the experiment. In food-familiarity (Figure 4A) and food-density experiments (Figure 4C–D) channels 1 and 4 carried the same food (H or M). In food quality learning (Figure 4B) and integration of preference and price (Figure 5B), channel 1 carried H food and channel 4 carried M food at optical densities given in the legends or indicated in the figures. Feeding was recorded for 12 min after food onset. Mean pumping frequency was computed as the number of pumps (paired E and R spikes) divided by total observation time. Preference fH was defined as the fraction of pumps emitted when the tip of the worm’s head, where the mouth is located, was in H food, as detected in the synchronized video recording. Specifically, fH=NH/NH+NM, where NH and NM are the number of pumps in H and M food, respectively; on this scale, fH=0.5 constitutes equal preference for the two foods or, in economic terms, indifference between the two options. No animals were censored.

Fitting utility functions to preference data

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To fit the CES function (Equation 11) to the choice data in Figure 6C and D, we estimated the parameters β and ρ using two-limit tobit maximum likelihood. Values of the error term were drawn from identical and independent normal distributions (Andreoni and Miller, 2002).

System for calcium imaging of neuronal activity

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For recording from AWC neurons, the genetically encoded calcium indicator GCaMP6s was expressed under control of the str-2 promoter. Late L4 or early adult worms were immobilized in a newly designed microfluidic imaging chip (Figure 8—figure supplement 1; Supplemental CAD file 2) based on a previous device in which the worm’s nose protrudes into a switchable stimulus stream (Chronis et al., 2007). Chip feature-height was 30 μm. The chip was adapted for rapid switching. The switching time constant in a microfluidic chip that is driven by a constant current source (e.g. a syringe pump) is equal to the product of the system’s compliance (C) and fluidic resistance of the chip (R). To reduce compliance we used rigid inlet tubing and to reduce resistance we greatly enlarged the food-carrying channels. An additional advantage of reduced resistance is a reduction in mechanical switching artifacts. Although edible bacteria were perfused through the chip, worms did not feed while being imaged, presumably as a result of being tightly constrained in the chip.

To improve stimulus stability, fluid flow was driven by a syringe pump rather than gravity or pressure. Two of the four syringes in the pump were filled with H food and two with M food, prepared in the same was as for single-worm food choice assays. Syringes were connected to the chip such that if all four channels were flowing into the chip, the cross-sectional flow at the point of confluence near the worm would be H2 H1 M1 M2. Stimulus presentation was automated utilizing a microprocessor to control a pair of two-way solenoid valves (LFAA1201610H, The Lee Company, Westbrook, Connecticut) in series with the syringes H1 and M1; the outer channels H2 and M2 flowed continuously. To present H food, the stimulus pattern was H2 H1 M1; to present M food the pattern was H1 M1 M2. As all channels flowed at the same rate, each occupied 1/3 of the cross-sectional flow at the worm’s position with the result that small fluctuations in the position of fluidic interfaces were kept far from the worm’s nose.

A Hamamatsu CCD camera (model C11254) controlled by HCImage was used to capture stacks of TIFF images at 10 frames/sec. Images were analyzed by manually drawing a region of interest (ROI) comprising a tightly cropped segment of the neurite connecting the cilium and soma. Mean background fluorescence was estimated from a 2-pixel thick margin situated 2 pixels outside the ROI in each frame. Absolute neuronal fluorescence was quantified as the mean of the 200 brightest pixels in the ROI, minus mean background. Finally, fluorescence values were expressed as fractional change relative to pre-stimulus baseline absolute fluorescence. Traces shown were not bleach-corrected.

Microfabrication

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Devices were fabricated using standard soft lithography (Xia and Whitesides, 1998; Xia, 2008). Silicon-wafer masters were created by exposing a layer of SU-8 2025 resist (Microchem, Newton, MA) through a transparency mask and developing the master in a bath of glycol monomethyl ether acetate (PGMEA). CAD files for the Y-chip and the imaging chip are provided in Supplemental CAD file 2 and 3. Masters were treated with tridecafluoro-1,1,2,2-tetrahydrooctyl trichlorosilane (Gelest, Morrisville, Pennsylvania) vapor to facilitate release. Devices were formed by casting polydimethylsiloxane pre-polymer (PDMS Sylgard 184, Dow Corning, Corning, NY) against masters. After curing and mold release, holes for external connections (fluidic inlets and outlets, worm injection, and electrodes) were formed using a 1.5 diameter punch. Devices were exposed to an air plasma then bonded to glass slides (Y-chip) or coverslips (calcium imaging chip).

Statistics

The following statistical tests were employed according to experimental design. We used t-tests to determine whether the mean differed from a specific value, and to compare means from two samples or experimental groups (strains, treatments, optical densities, and price ratios). When the number of experimental groups exceeded two we used a two-factor analysis of variance. When the number of experimental groups exceeded two and individuals within groups were measured successively over time, we used a two-factor analysis of variance with repeated measures. For all comparisons, the center of distributions were their arithmetic mean. For dispersion measures, we used 95% confidence intervals, except in the case of time-series data where we used standard errors of the mean. None of the experimental designs required correction for multiple comparisons. Statistical details for each test (statistical test, effect or comparison tested, definition of units of replication, number of replicates, statistic value, degrees of freedom, p-value, and effect size) are compiled in Table 2. These details are cited by the notation “Table 2, where n is the row number in the table. Because all assays were novel, sample sizes were determined empirically, by noting how variance changed as a function of number of replicates. All replicates were biological replicates. In the case of ‘assay plates’, a replicate is unique cohort of worms on an assay plate. In the case of ‘worms’, a replicate is a unique animal tested once. No outliers were excluded.

Data availability

Data of Figures 2, 4, 5-9 are available as source data files associated with this publication.

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Decision letter

  1. Manuel Zimmer
    Reviewing Editor; University of Vienna, Austria
  2. Piali Sengupta
    Senior Editor; Brandeis University, United States
  3. Doug Portman
    Reviewer

Our editorial process produces two outputs: (i) public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.

Decision letter after peer review:

Thank you for submitting your article "The nematode worm C. elegans chooses between bacterial foods exactly as if maximizing economic utility" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Ronald Calabrese as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Doug Portman (Reviewer #2).

All reviewers are excited about the manuscript, however, reviewer #2 raises a major technical concern and the main comments by reviewers #1 and #3 are at a conceptual level. They have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

Reviewer #1 (Recommendations for the authors):

1) The authors developed a clever experimental design that allows to precisely monitor the food consumption of worms presented with two streams of different bacterial strains of different nutritious value, H(igh) vs M(medium), and at varying concentrations. Previous work showed that worms prefer H bacteria. Animals are clamped into a microfluidic device where they are free to choose between the two streams by positioning their heads in either one of them; they can also modulate the rate of food ingestion by varying the rate of pharyngeal pumping. Under the assumption that the two types of bacteria are equally bite-sized, the "price" of food is directly related to the dilution of the bacterial suspension. I.e., the more diluted the food is the more pumps need to be invested to intake the same amount. A central finding of the study is presented in Figure 5B, showing that the intake of H monotonically increases with the price ratio of the H and M streams. The authors claim that this finding precludes violations of GARP and therefore strongly supports utility maximization within this GARP framework. However, I wonder how comparable the experimental design is to the GARP experiment shown in Figure 1. Here, subjects are presented with choosing between two option bundles of qualitatively different goods (apples and oranges); humans are consciously aware of their limited budget and the trade-off between the two goods. I don't think that worms are faced with the same task in the present experimental design. (1) there is no evidence that C. elegans worms qualitatively distinguish H and M bacteria, i.e. we do not know whether in their brains H and M are represented as qualitatively different objects, like humans perceive apples and oranges. Most likely H produces more of an attractive odorant X; therefore, worms likely are sensitive to the concentration difference of X between the two streams. The AWC imaging experiments are supporting this; they were shown previously to be sensitive to food-borne odorant concentrations in a gradual manner. Thus, AWC neuronal activity does not represent H and M as qualitatively different objects (see Figure 8). Therefore, unlike in Figure 1, worms do not make a trade-off between H and M, they more likely detect high and low concentrations of X. This simple mechanism is sufficient to explain the data in Figure 5B. This would lead also to consistent choices that maximize utility, i.e. foraging in areas that contain more of X which is likely to increase welfare in form of more nutritious food intake. The experiment in Figure 5B could be done using just H bacteria with different dilution. (2) In the experiments, worms are not faced with a binary choice among two bundles of goods that they can take home. They rather continuously forage the two streams by varying pumping rate and waving their heads. This means they are free to choose of how much they can intake from the H and M streams. Worms are also not aware of the duration of the experiment. This means there is no fixed budget, and their choices are not on a fixed budget line. I am therefore not convinced that the statement in lines 531-532: " Under this mapping, the lines in Figure 5C correspond to choice sets like those in Figure 1." is correct.

These (1-2) major differences to the GARP experimental design in Figure 1 largely confuse me and I wonder how useful for understanding neuronal mechanisms is it to rigidly analyse the data with the mathematical tools of this framework. Vice versa, a reader from the field of economic decision making might find the explanations in (1) too trivial and must be similarly concerned of how much the experimental design fits into the GARP framework. The authors spend a good amount of effort justifying the various GARP requisites. I think they should also discuss these obvious differences and provide clear justification why their experimental design is a good worm equivalent to what is shown in Figure 1.

2) The animals show a baseline preference for H bacteria, which is interpreted by the authors as "latent learning". There is no evidence that this preference is due to a latent learning mechanism, it could be just an innate preference. This is also not important for the major conclusions of the paper, so I recommend to avoid this terminology and leave it only to the final discussion.

3) The authors use the term "explicit" learning for the enhanced H preference after training. Explicit learning and explicit memory are differently understood in the field, like abilities or events that humans consciously acquire or remember. I strongly suggest to avoid this term as this could cause some confusion.

Note -> (2-3) was also raised by reviewers #2-3

4) The behavioural defect of cat-2 is interesting but on its own it does not help much to better understand the mechanism that establishes food preference. Since the paper is quite complex already, I would recommend the authors keep these results for future mechanistic studies. – just a recommendation.

5) line 434: you cannot conclude that food quality learning is intact in the Y-chip, since the animals never learned in the chip; acquired food preference upon learning can robustly be measured under Y-chip conditions.

6) Line 461: text abruptly terminates and some important explanatory text to understand the law of demand is missing.

7) Figure 4C-D: what is t=0? Switching from buffer to food streams? What is the time course of pump frequency when no food (OD 0.0) is supplied?

8) Figure 4: I suggest to add legend for colour code in C-F, green = H food, yellow = M food.

9) Line 536: you mean Figure 4?

10) Ca++ imaging experiments lack negative controls. Since switches in microfluidic devices unavoidably come with pressure profiles, proper control experiments should be included.

11) do worms pump/feed in Ca++ imaging assays? Please discuss.

12) Line 964: since worm locomotion needs to perform dorsal to ventral bending patterns under unconstrained conditions, they have a strong internal drive to keep undulating their heads. They just can't keep still. Here, they cannot leave and crawl out of the position in the device. I think the constraints in the device thus could be a major explanation why you don't see corner solutions (see also reviewer #2).

13) line 167: aren't oranges in A double the price of apples?

14) Figure 2 panel B does not show what is described in main text and Figure caption

Reviewer #2 (Recommendations for the authors):

1. Bacterial concentration: precision and accuracy in the measurement of bacterial concentration is critical to essentially all analyses carried out here. One of the most fundamental variables in the model, price, is a simple function of this. Exactly how bacterial suspensions of different concentrations/densities are prepared is not clear, but the authors repeatedly use OD600 as a measurement of bacterial concentration (this is explicitly stated in lines 341-2). This has the potential to be a significant concern, as OD600 has a linear relationship with bacterial density only in very narrow range of relatively low density -- above this (certainly ODs of 1 or 3, which are used regularly here) there can be vast deviations from linearity. As noted by one of the references this paper cites (Stevenson et al. 2016), OD600 can even have a parabolic relationship to concentration in some density regimes because of the complexities of light scattering by bacteria. It's hard to tell whether this has been accounted for here – it seems that the authors are assuming, for example, that a suspension of OD 3 has 30x as much food as one of OD 0.1, which almost certainly not case. Further, when considering how this applies to H vs. M food, the authors calculate the difference in mass/OD ratio between H and M food at OD = 1, but this ratio seems very unlikely to hold at different ODs. If bacterial concentration has been mis-estimated because of these problems, it's possible that errors in price would propagate through all of the subsequent analyses. If the authors have indeed accounted for these complications, that's great – in this case, they'd need provide additional details about how this was done. If not, however, additional work will have to be done to figure this out.

2. In Figure 9, the authors provide evidence that AWC physiology does not encode a simple economic quantity like value. I have a few comments/concerns about this analysis. First, if bacterial concentrations are being mis-estimated as described above, it may be the case that the conclusions here will change, possibly dramatically. Second, it looks to me like the red line in 9D indicates a clear relationship between preference and ∆F in trained animals. The statistics might not bear this out because of the limited power of the analysis, but I'm surprised that the authors don't find this at least suggestive of what's going on. Third, authors make an argument for calculating ∆F from its steady state responses, but it would seem that the initial responses might be informative too – this is when relative values are first being assessed. Also, the presentation of the two stimuli with equal times for each doesn't really mimic the steady-state situation when an animal has a strong preference for one of them (in this case, the nose would be exposed to the preferred stimulus for most of the time). Maybe it would be useful to examine AWC responses with different stimulus patterns? Fourth, in rationalizing 9E, authors say that they asked whether AWC might encode "some other economic quantity". How many such quantities were examined? Is this a case where correction for multiple comparisons would be appropriate?

Reviewer #3 (Recommendations for the authors):

Introduction: GARP applies to consumer's choices, and importantly, assumes rational agents. The leap to nematodes is huge. Can the authors comment on this?

Line 102: Citation that can potentially be added: Ghosh et al., 2016, Neuron, PMID: 27866800 (for risk assessment).

Line 120: "it is reasonable to expect that C. elegans food choices maximize fitness"◊ The notion that an organism's food choices maximize fitness is directly related to the Optimal Foraging Theory. Among the major criticisms this notion has received, is that it relies on the assumption that natural selection and evolution have somehow resulted in a decision-making process that maximizes fitness. However, natural selection has not necessarily led to such a result when it comes to the feeding strategy or food choices of an organism, because it is a process of selection and not a mechanism that produces optimal results, e.g., behaviors. Therefore, it is debatable whether C. elegans food choices maximize fitness.

Reviewer #1 and #3 discussed and reviewer #3 recommends to rephrase, e.g. "promote fitness" instead of "maximize".

Line 145: redundant word: during

Line 146: bends, should be plural

Line 150: a period is missing at the end of the sentence.

Line 154: "GARP for worms": although this is the title of this Results section, the section itself is about explaining in detail how utility maximization and its violations can be manifested in graphic representation of bundle choices in experiments with human subjects. This section is not about C. elegans and GARP. I suggest revising the title. It is also unclear why this section is part of the Results, since there is practically no result presented.

Line 167: it seems to me that the opposite is inferred from the text (and from Figure 1 legend): apples are half the price of oranges. Is this a typo? - see also reviewer #1

What is the budget of a C. elegans nematode? In line 535 and onward authors state that "We found it impractical to standardize the number of pumps to impose a fixed energy budget on each worm because […]", and then they explain that they have been plotting the fractional consumption and equation 5. Does this mean that the budget changes depending on the food source? Can the authors elaborate on this? Are worms' budget units consistent with the goods' prices units? -> see also reviewer #1

Why do the authors consider the abundance of a bacterial strain equivalent to price? In human experiments, the ratio of, e.g., oranges vs apples is one of the variables (amount of fruit per weight), and the dollars per unit is another.

Line 236: Worms were cultured on E. coli OP50 before the H/M training took place. What is the nutritional value of this food source compared to H and to M?

Line 253: "If H food smells to the worm more like E. coli than M food does, this preference might be explained by the so-called food familiarity effect (Song et al., 2013), in which worms eat familiar food more readily than novel food." In this case, worms do not prefer H food based on its "quality" but based on its similarity to the food source they have been used to. In this case, maybe the sequence of preference choices does not constitute a violation of the utility maximization. In this case, worms do not choose driven by an urge to maximize their fitness, but rather by a tendency to maintain a familiar environment. How does this fit with the authors claims and assumption?

Figure 2B: The caption reads "Mean preference versus time for trained and untrained ceh-36 mutants and N2 controls in open-field accumulation assays", however, I am not sure that this is what the figure shows, given also that the y axis is labeled as "fraction of pumps". Please explain. -> see also reviewer #1

Given the issue with Figure 2B, it is hard to tell, at this point, which plot represents the open field assay and which the maze choice assay, therefore it is hard to compare the two or evaluate the findings in a combined way.

Line 298: "The decision to accumulate in a particular food can be made, at least in part, before the animal enters the patch." ◊ I think that, for the sake of accuracy, the decision in question is not about deciding to accumulate; a worm does not decide to accumulate, but rather to approach or reach or forage on food H or M. How do the authors comment on this?

Have the Authors performed the open-field accumulation assay in the presence of sodium azide?

The authors speak about latent learning (=a type of learning which is not apparent in the learner's behavior at the time of learning, but which manifests later when a suitable motivation and circumstances appear) in case of the non-trained animals, and about explicit learning (=a more conscious process where the individual makes and tests hypotheses in a deliberate search for answers) in case of the trained animals. This implies a dipole scheme of latent vs explicit. However, the authors do not justify the use of these two terms, nor do they provide evidence that in non-trained animals the learning is latent; in addition, there is no justification for the use of the term explicit in the second case. The worms have been simply conditioned or not conditioned, respectively. Even in lines 307-309 when they cite two papers by Worthy et al., stating that "Explicit food quality learning in C. elegans is formally equivalent to a type of classical conditioning in which an association is formed between the mélange of odors characteristic of particular bacteria species (Worthy, Haynes, et al., 2018; Worthy, Rojas, et al., 2018)", this is perplexing, because I am not sure that these papers claim or demonstrate that explicit learning in C. elegans is equivalent to classical conditioning. Despite that, the authors state that they are trying to find the locus of explicit food quality learning (line 259). I think the use of the two terms, explicit and latent, should be better justified or other terms should be used instead. -> see also reviewers #1/2

In relation to that, in lines 323-333, it is implied that food learning occurs while the animals forage on the food patches. What is it exactly that worms learn? Is this some form of non-associative learning? In addition, the effect on their preference developed as they forage on a specific food patch is something that should be present in both trained and non-trained animals. The authors state that "It is possible, therefore, that food quality learning in cat-2 mutants is impaired simply because they spend less time in the food, hence have less experience of it", line 321. Does this mean the authors believe that food quality learning occurs during the worms' stay on the food patch during the open field or maze assay and not during training?

Have the authors tested only two types of food, i.e., two bacterial strains characterized as medium and high quality? If so, then the reported results could be due to other properties of the bacteria and not their nutritional value (case-specific results). Note that the nutritional value (energy, joules) is what the authors take into account in equation 1. Wouldn't their findings be stronger if the observed preferences were repeated for other pairs of food choices, i.e., by testing other/more bacterial strains?

Figure 4C and 4D: what is the difference between the two? Do they refer to M and H?

Similarly for 4E and 4F: do different colors (green and gold) represent different foods e.g., H and M? Please clarify.

Line 524: Maybe these data should be shown, as they constitute an important link in the authors' train of thought.

Line 550: Can the authors explain why this is expected to be a gaussian distribution?

Line 551-554: Is there a plot/figure to illustrate this?

Line 561: I don't think this is a particularly conservative null hypothesis; in most cases in behavioral assays the null hypothesis is exactly this: that animals choose randomly, i.e., that the treatment has no effect.

Lines 604-606 and Figure 6A: I do not understand why e and d are grouped both in the group in which H changes and in the one H stays constant. Can the authors please explain?

Line 673: "worms require more of it to be satisfied": How do the authors define or measure satisfaction in this case? Without a definition this sentence is misleading.

Line 700: eliminate or support?

Line 766-767, and the entire paragraph: Authors say that "As exogenous activation of AWC produces a bout of reverse locomotion (Gordus et al., 2015), its response to food offset promotes reversals, leading to increased retention patches. Our imaging data suggest that AWC-mediated retention would be stronger for H than M food, promoting greater preference for H food, as seen in Figure 2B-D." The authors rely on their finding that AWC was more strongly excited by H than M food, to jump to the conclusion that "AWC-mediated retention would be stronger for H than M food, promoting greater preference for H food". In my view, this last claim could constitute a well-defined hypothesis to be tested, and not a conclusion based on their findings, even in combination to Gordus et al. In fact, it is Gordus and colleagues who highlight in their 2015 paper that although the activation pattern of AWC is deterministic ("highly reliable"), the resulting reversing behavior is, by contrast, probabilistic: "The AWC calcium response, which is likely correlated with depolarization, is highly reliable from trial to trial, even after dozens of odor presentations (Larsch et al., 2013). By contrast, the reversal response is probabilistic. Even under well-controlled conditions, animals may or may not reverse on individual trials, regardless of the strength of the AWC calcium response (Larsch et al., 2013)" and that "Thus, the variability in the behavioral response results from variable transmission of information from the AWC sensory neuron to AVA command neurons." Based on the above, I do not understand the authors' claim. Maybe they can run an experiment to show that the claim is valid? The results presented in Figure 2, although they show increased retention, they do not allow the conclusion that the animals with stronger AWC activation are the ones that present increased retention. That individuality in the response is, in my view, what Gordus et al. indicate in their work.

Similarly, in the following paragraph, based only on the strength of AWC activation, they conclude that "retention in H food patches would be stronger in trained than untrained animals, promoting greater preference for H food after training". However, stronger activation of AWC does not mean stronger retention (behavioral outcome), based on Gordus et al.

Line 1114: The mask was baited or the maze-shaped NGM area? Where there any escaping animals? Where there any animals that did not choose either of the two (e.g., not reached neither H or M in the allowed time)? How long were the worms allowed to make a decision inside the maze? Were there any animals censored, and if so, does this affect the results? Did the authors alternate the position of H/M food in the two maze arms to eliminate any side preference effect?

Line 914: what do the authors mean by "infra-human species"? Maybe non-human?

Line 919: "literally guarantees", and elsewhere in the text: the authors tend to express their claims using absolute language (see also title, "exactly as"). I feel that it might be more appropriate if the language used is firm and confident, as the authors see fit, but milder.

Lines 914-922, and elsewhere in the text: The authors are trying to convince the reader that C. elegans makes consumption decisions in the same way that a human consumer does. What's more, they claim that such a human-conforming behavior can be captured in nematodes by just mapping the neuronal circuit that steers head bending. This is in the core of the paper, and in my view, it is problematic in many ways. The axioms of the revealed preference theory are justified by the assumption that humans are rational agents. This means that they make rational decisions. Do the authors claim the same for C. elegans nematodes? In parallel, the fact that C. elegans feed on two different food sources and they choose one over the other in a way that the goods qualify as substitutes, is a finding presented as of extreme importance. This is indeed an interesting conclusion, well supported by the data. It becomes more interesting because of the untangling of the neuronal circuit involved. At the same time, this is really not an unexpected result, although providing evidence for it is definitely useful. Any animal that feeds on multiple food sources would alternate between two of them, based on their availability, the effort required, the nutrition provided. Indeed, the authors themselves do not claim that this is unexpected. However, they claim that they "break grounds" because worms' behavior appears to conform with utility maximization principles and can be described with human-centered terms of substitute goods. This is misleading, first, because of the agent rationality assumed, which we have no basis for, and second, because identifying two goods as a substitutes pair is not ground-breaking on its own. Behavioral economics labels pairs of goods as such in order to move on with more complicated claims, theorems and analyses. The authors are interpreting C. elegans feeding behavior using behavioral economics terms that sound extravagant when speaking of nematodes, but in reality, their findings are not extravagant and certainly do not need to be dressed as such in order to be significant. In this reviewer's view, the findings presented in the manuscript are interesting and they constitute a significant contribution. Attempting to attribute to them a dimension disproportionate to their real depth, dampens the initial enthusiasm in an unnecessary way.

Line 979: What are the worms maximizing? This is a question that the authors admit comes up inevitably, but interestingly (and honestly, of course) at the same time they state that they do not have a plausible answer to it. Therefore, even the notion of utility (which is supposed to be maximized) remains obscure. In my understanding, this confirms the fundamental problem with the way this study is presented. The authors are not working toward testing a stated hypothesis (e.g., nematodes' behavior is such that maximizes x), but they rather quantify a nematode behavior in a way that fits the equations used in behavioral economics. What they don't take into account is that, sometimes, even if phenomenon A can be phenomenologically described by a set of equations that has been developed to describe (part of) phenomenon B, this does not mean that A is explained by the same physical or biological principles that steer phenomenon B. This is even more prominent if the organism involved in A is so very different regarding its brain faculties and societal construct than organism B. And even more so if the researchers fail to provide a satisfactory answer for the biological (in lack of maybe a psychological, societal or other) explanation for this behavior.

Finally, a few thoughts, which the authors are not requested to address, neither in the revised manuscript, nor in their rebuttal letter: Any scientific paper creates, upon its publication, new premises. Hence, even if the authors do not continue this work, there will be others who will, one way or another. I wonder what the premises of the present manuscript are/will be. What is the precedent created here? That C. elegans is a valid system to test behavioral economics hypotheses and apply axioms? That C. elegans can be used as a model system to understand, and maybe predict, human economic decisions? To establish C. elegans as an experimental system for behavioral economics? To what extend and to what end? The authors state in the introduction, "A positive result [of this study] would establish a simple experimental system in which neuronal activity correlated with utility could be manipulated both physiologically and genetically to establish behavioral causality. Such a finding would also be interesting from a comparative perspective, extending the domain of utility-based decision making far beyond the boundaries of organisms that are generally considered to have cognition." Do they envision their work as the precursor for manipulating or directing human decision making? I truly appreciate that the authors made me reflect on all these (and many more) issues, and I trust that this work, when published, will instigate a lot of interesting discussions. The way we do research and the questions we choose to pose and answer can have a lot of impact, that goes beyond the citations a paper might receive. To conclude, I would like to share with the authors a note by Claude Shannon, the founder of Information Theory, written back in 1956: https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1056774. He comments on the attempt to apply information theory to more distant fields, like biology, psychology, physics, etc. The term information theory can potentially be substituted with other terms with interdisciplinary appeal, such as game theory, behavioral economics, microeconomics, etc.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "The nematode worm C. elegans chooses between bacterial foods as if maximizing economic utility" for further consideration by eLife. Your revised article has been evaluated by Piali Sengupta (Senior Editor) and a Reviewing Editor.

The revised manuscript has undergone extensive discussion among the reviewers. While reviewers #1 and #2 are enthusiastic about publishing it in eLife, reviewer #3 has raised a strong concern that the Y-chip configuration precludes a GARP conclusion. We are excited that your study is thought-provoking and will likely spark a debate among eLife readers. However, it is essential that major concerns about the appropriateness of your approach be addressed before publication.

Please find below excerpts from the reviewers' comments that we request be addressed in a revised version of the main text. We are aware of the time pressure you have communicated to us and will do our best to expedite the process once we receive a revision, along with a point-by-point response.

Reviewer #1 (Recommendations for the authors):

The authors have made substantial efforts in addressing my previous comments. They show that H and M bacteria release different volatile odorant profiles, indicating that worms potentially sense them as distinct olfactory objects, also supported by the pharyngeal pumping experiments using the food familiarity paradigm. Moreover, they improved the discussion to address some of my conceptual concerns when comparing their assay design with the human apple-orange experiment. However, the data are just indicative and to fully address my concern they would need to show, both with neuronal activity measurements, (I) that worms perceive H & M as distinct odorant objects in the Y-chip and (II) that worms calculate utility based on the relative abundance of H and M. I did not mean to say in my previous comment that (I) and (II) have to be conscious processes (like in humans), but they should have explicit neuronal representations. I think the alternative and simpler model of detecting concentration differences between odorant X in the Y-chip is still a possibility. I understand that addressing this would be out of the scope of the current manuscript and could be interesting for future experiments. At the current stage, I find the here reported approach applied to C. elegans creative, novel, and thought-provoking and since I cannot detect (within my expertise) any technical problems in how the framework is implemented, I would enthusiastically support publication in eLife.

Reviewer #2 (Recommendations for the authors):

The authors have nicely addressed my previous concerns, which were primarily technical. I find the paper to be a fascinating, rigorous, and creative approach to understanding decision neuroscience using C. elegans.

Reviewer #3 (Recommendations for the authors):

The authors have extensively revised large parts of the manuscript, especially in the Results and Discussion sections. The revised manuscript also includes updated figures and captions, new supplementary figures, etc. The manuscript is in much better shape, and much more information is provided, information that is critical to evaluate the results, their interpretation, and the final conclusions. The addition of new authors and expertise, as well as the change in the title are very welcome, too. Many of my concerns were addressed, and I appreciate the detailed explanations provided in some of the authors' responses. My understanding of their work is now much better. Nevertheless, the work continues to present fundamental problems. These are reflected mainly in comments #1, #5, and #11, which can be considered my major concerns. The rest of the comments can be considered minor or easier to answer.

1. Comment 1 of first revision and response 3.1:

The authors write in their rebuttal letter that they adopt the stance that if the agents' behavior adheres to the GARP, then they are rational (and not that rationality is a prerequisite). In their response, the authors list 3 papers to support the stance they claim to adopt, and all three of them have to do with humans, and the work reported has to do with reduced or altered observed rationality because of trauma, aging, etc. Displaying reduced rationality is fundamentally different than potentially lacking the very ability to be rational. I still feel that the issue of rationality needs to be addressed clearly in the manuscript. I explain:

In the revised manuscript, apart from two references to published work on C. elegans observed occasional rationality with many exceptions (lines 106-110), the only important part that addresses rationality is the new text in lines 228-234. Here, the authors mention (line 228) that "tests of adherence to GARP have been utilized to assess the degree to which decision-making agents are rational in the economic sense", and later in the paper, they claim that nematodes adhere to GARP. The authors need to make clear whether they claim rationality for C. elegans, based on their findings, and if so, how is this rationality defined. And in addition, they need to make clear that whatever rationality is claimed for worms, it is not to be confused with what is broadly understood as rationality but is rather a term to describe a mathematically defined concept, the criteria for which are met by nematodes. If this is not absolutely clear, then the reader can be easily misled.

5. Line 301 (related also to response 3.18): " [The preference of naïve worms] could be the result of prior experience or developmental maturation": I do not understand this. What kind of prior experience? If I understand correctly, the worms have been grown in the lab for their entire life, and for a number of prior generations. Have they been fed anything else than E. coli during some part of their life? Have they been exposed to H or M food before? Have their ancestors been exposed to H or M food? If not, then the "prior experience" argument cannot possibly apply. If yes, then this should be mentioned, as it would dramatically change the perspective. As for developmental maturation: If the authors believe this is true, then assessing worms ranging from L3 to Day 1 is obscuring, and distinct age cohorts should be assayed separately (L3, L4, Day 1). Moreover, if this were true, it would mean that older or younger animals prefer, for example, H. Therefore, the ratio of younger/older animals in the tested population could skew the results this way or the other. How do the authors comment on that? As for the trained worms, acquiring a preference because of sampling the two foods during the 60 min training assay seems the most reasonable thing to assume. However, the authors claim that this scenario does not apply, because of the findings of the familiarity experiments in the Y chip, but it is not clear to me why this is the case. Besides, the conclusion in line 522 that the foods are qualitatively distinct, would explain the development of a preference during the 60 min of the assay.

11. The new information provided in the revised manuscript on the budget constraint and the price of goods H and M, and how the budget constraint is imposed because of the Y-chip design, allowed me to get a new perspective of the Y-chip experiments. In consequence, several concerns arise. The process is as follows, roughly: A worm is placed in the chip, and two streams, one of H and one of M food, are provided. The preference is revealed by the worm bending its head toward the M or the H stream, and by performing pumps. The combination of pumps of H or M food is the preferred bundle. The whole process lasts for 12 mins. Therefore, it takes 12 min for the worms to behave in a way that reveals their preference. During these 12 mins, the preference is revealed through a sequential decision-making process, in which the worms sample the goods.

i) The sequential nature of this process is fundamentally different than the one-time decision made by human subjects in analogous experiments. In those, humans select the bundle of preference in a single decision. Nematodes, however, make many decisions, sequentially, that define the preferred bundle. How do the authors believe that this affects the interpretation of the results, with respect to adhering to the GARP prerequisites? I posit that this difference can have many implications as someone is trying to determine whether nematodes meet the same prerequisites that humans meet but while under very different experimental conditions. Some additional methodological concerns are listed below.

ii) During the sequential sampling, the worm needs to bend its body toward this or the other side, in order to perform a pump. Consequently, switching between sides, therefore foods, has a cost for the worm (note that bending just the head does not allow for switching between the two flows, as evident in Video 1). How do we know that this cost does not affect its decision-making with respect to switching between foods? In addition, even though the authors say that the body bending while in the chip resembles the body bending during the sinusoidal locomotion on a GNM plate, in Video 1 we can clearly see the worm bending multiple times toward one side before switching to the other side. This is not what happens during regular locomotion. This can be related to the worm preferring to feed on one food, but also to the cost of the effort required in order to bend to the other side. Given the constraint along the mid-body, this effort seems not to be negligible.

iii) How do we know that the worm is not biased by the content of the first few pumps? Is there a correlation between the first few pumps and the final preferred bundle?

iv) The initial body orientation of the worm is not controlled, as I would guess. How do we know that it does introduce a bias with respect to the initial conditions of the system?

The fact that the worm develops a preference over the course of 12 min, as it is tasting (sampling) the two foods, cannot be overlooked. According to the literature, this can be enough time, for worm standards, to develop behavioral plasticity. How could this affect the "revealed preference" and the adherence of the worm to the GARP prerequisites? Especially since human subjects, who participate in carefully controlled experiments, do not undergo a similar (sequential) process.

v) The (iv) relates to the development of a preference during training in a plate with patches, for the accumulation assay, see comment #5. The authors are reluctant to admit that worms can develop a preference because of sampling the two foods during the 60min training assay. They attempt to justify this reluctance based on the results of the familiarity experiments on the Y-chip. As mentioned in comment #5, I am not sure how the familiarity experiments lead to the conclusion that worms do not develop a preference during training. Does this have to do with the authors not acknowledging that worms might be developing a preference during the Y-chip experiments?

All the above (i-iv) leave the key claim "Overall, this methodology results in decision-making paradigm that is formally analogous to GARP experiments in humans", line 1054, unsupported.

To conclude: the revised manuscript is in much better shape than the original draft, and I recognize the authors' efforts to respond to the reviewers' many comments. The amount of work performed is impressive. However, this paper still presents fundamental problems. These are reflected mainly in comments #1, #5, and #11. Worm's adherence to GARP prerequisites is proposed to be the case, but the methodologies through which this conclusion is drawn and the interpretation of some of the findings are problematic. Trying to adjust human GARP behavioral experiments so that they can be run with nematodes does not seem to work, in this reviewer's opinion. Many of the parameters that experimenters are trying to control when studying humans, in order for them to be able to reliably claim adherence to GARP, are not controlled in the nematode experiments presented here (comment #11), something that can dramatically affect the interpretation of the results. Furthermore, important clarifications need to be made so that the reader is not misled (comment #1), and some explanations the authors provide for some of the observed behaviors are inadequately substantiated (comment #5).

In light of the above, even if the authors addressed everything else satisfactorily, with concern #11 unresolved, I do not see how the main claim can be sufficiently supported and how this paper can be published in eLife. The claims that the authors are making are such that their substantiation should be above any ambiguity.

Sequential decision-making in the Y-chip is a fundamental concern. Here is why: The main claim the authors are making is that C. elegans' behavior abides by the GARP requirements. They claim so, based on their interpretation of experimental findings. By implementing a certain experimental design, they experimentally pose a question to the system, and the system (nematode consumers) responds by demonstrating a certain behavior, and this behavior is interpreted as GARP behavior because presumably, it is similar to the behavior displayed by the human counterparts. As a reference, when behavioral economists run experiments with human subjects, they apply a certain experimental design, they experimentally pose a question to the system (human consumers), and the system responds by demonstrating a certain behavior, and this behavior is defined as GARP behavior. Note that the experimental design followed by behavioral economists is very strictly controlled, to make sure that no undesired variables interfere with the results. However, the Y-chip experiments pose a different question to nematodes, than the question posed to human consumers: the Y-chip asks what the outcome is of a sequential decision-making process, whereas the GARP-defining human experiments ask what is the outcome of a one-time decision-making process. In other words, the problem is that Katzen et al. introduce a variable that is not present in the experimental design used in behavioral economics to decide whether the subject behaves as GARP: the variable of time. The worms display sequential decision-making, but GARP is supposed to explain a one-time decision-making behavior, not a sequential one. This discrepancy, ignoring the extra variable in the Katzen et al. experiment, is problematic and potentially very misleading.

I am particularly concerned because of the potential impact of the claim that authors make: nematodes make economic decisions that can be described by the same set of principles that describe human economic decisions. For such a huge claim to stand, it has to be supported in a concrete way, without gaps in the thought process.

Bottom line: I understand that the experimental design is what it is and that there is no way the Y-chip experiments are performed differently so that the worms could make a one-time decision. Therefore, I see two options: (A) In the current version of the manuscript, because of this discrepancy, the claim is weak and is not adequately supported, in my view. Therefore, I cannot suggest the manuscript be published in eLife. (B) The authors update the manuscript to admit the discrepancy, and they make it absolutely clear to the reader that the nematode system makes its decision according to a process very different than the one that human systems make their decision, in corresponding reference experiments that decide the subjects' GARP behavior. If the authors do that, then everything will be transparent, and the readers can decide for themselves whether the claim stands or not. In such a case, I am fine with publishing the work in eLife, if such is the suggestion made by everyone else.

https://doi.org/10.7554/eLife.69779.sa1

Author response

Reviewer #1 (Recommendations for the authors):

1) The authors developed a clever experimental design that allows to precisely monitor the food consumption of worms presented with two streams of different bacterial strains of different nutritious value, H(igh) vs M(medium), and at varying concentrations. Previous work showed that worms prefer H bacteria. Animals are clamped into a microfluidic device where they are free to choose between the two streams by positioning their heads in either one of them; they can also modulate the rate of food ingestion by varying the rate of pharyngeal pumping. Under the assumption that the two types of bacteria are equally bite-sized, the "price" of food is directly related to the dilution of the bacterial suspension. I.e., the more diluted the food is the more pumps need to be invested to intake the same amount. A central finding of the study is presented in Figure 5B, showing that the intake of H monotonically increases with the price ratio of the H and M streams. The authors claim that this finding precludes violations of GARP and therefore strongly supports utility maximization within this GARP framework. However, I wonder how comparable the experimental design is to the GARP experiment shown in Figure 1. Here, subjects are presented with choosing between two option bundles of qualitatively different goods (apples and oranges); (a) humans are consciously aware of their limited budget and the trade-off between the two goods. I don't think that worms are faced with the same task in the present experimental design. (b) (1) there is no evidence that C. elegans worms qualitatively distinguish H and M bacteria, i.e. (c) we do not know whether in their brains H and M are represented as qualitatively different objects, like humans perceive apples and oranges. (d) Most likely H produces more of an attractive odorant X; therefore, worms likely are sensitive to the concentration difference of X between the two streams. (e) The AWC imaging experiments are supporting this; they were shown previously to be sensitive to food-borne odorant concentrations in a gradual manner. Thus, AWC neuronal activity does not represent H and M as qualitatively different objects (see Figure 8).

1.1.a. Economists do not regard conscious awareness of the budget as a prerequisite for testing adherence to GARP. In fact, human participants are not informed of the budget constraint in GARP tests (Harbaugh, Krause and Berry, 2001; Camille et al., 2011). That is because the purpose of this constraint is solely to ensure that every option in a choice set cost the same amount, thereby establishing trade-offs between goods. This point is now explicitly made in the text, “Participants need not be made aware of the budget constraint; it can remain implicit in the set of available choices presented.”

1.1.b. The experiment of Figure 4A provides evidence for a model in which worms do qualitatively distinguish H from M bacteria. According to the alternative model (see d), the foods are qualitatively similar but one food generates a more intense perception than the other, perhaps by emitting more of the main compound (X) by which H and M are detected. Worms familiar with H or M food pump at the same rate in them (Figure 4A, left bars), indicating H and M are not perceptually distinct, which means they emit the same amount of X. In light of this result, the alternative model obviously fails to predict the familiarity effect for, as H and M are indistinguishable, neither of them can be unfamiliar to the worm. From the fact that worms pump at different rates on H and M when cross-cultured on the other food, we can conclude they are qualitatively distinct. The text has been edited to make this point, “The food familiarity effect supports a model in which H and M foods are qualitatively distinct to the worm. According to the alternative model, the foods are qualitatively similar…”.

1.1.c. The nature of the physical representations underlying the distinct perceptions is at present unknown, although neuronal representations are the obvious candidate. Nevertheless, this question is irrelevant to conclusions drawn from adherence to GARP as GARP makes no assumptions about choice mechanisms.

1.1.d. The manuscript now includes new data showing a chemical analysis of the volatile organic compounds emitted by the H and M bacteria used in our study (Table 1). Each of these bacteria emit many such compounds. This finding provides the olfactory substrate for qualitative differences in the worm’s perception of H and M bacteria, similar to the qualitative differences by which people distinguish between goods (e.g., colors and flavors of fruits in Figure 1). Three of the five main released compounds have been identified as chemoattracts in C. elegans; the others have yet to be tested. Surprisingly, M releases more of each attractant than H. Therefore, if worms choose based solely on odors, M should be more attractive than H.

1.1.e. We did not mean to imply that the neuronal representation of H and M food is restricted to a single chemosensory neuron class. In particular, we stated, “C. elegans has 12 pairs of anterior chemosensory neurons that respond to bacteria conditioned medium (Zaslaver et al., 2015).” This complexity provides the substrate for population-code representations of H and M, which could make C. elegans an effective modal for investigating population codes in decision making. We now state, “In perhaps the most likely scenario, the worm’s internal representation of H and M food is distributed across some or all of the 12 pairs of foods sensitive chemosensory neurons in this organism. As a first step, we focused on one of these, AWC…”

Therefore, unlike in Figure 1, (f) worms do not make a trade-off between H and M, they more likely detect high and low concentrations of X. This simple mechanism is sufficient to explain the data in Figure 5B. (g) This would lead also to consistent choices that maximize utility, i.e. foraging in areas that contain more of X which is likely to increase welfare in form of more nutritious food intake. (h) The experiment in Figure 5B could be done using just H bacteria with different dilution. (2) (i) In the experiments, worms are not faced with a binary choice among two bundles of goods that they can take home. They rather continuously forage the two streams by varying pumping rate and waving their heads. This means they are free to choose of how much they can intake from the H and M streams. (j) Worms are also not aware of the duration of the experiment. (k) This means there is no fixed budget, and their choices are not on a fixed budget line. I am therefore not convinced that the statement in lines 531-532: " Under this mapping, the lines in Figure 5C correspond to choice sets like those in Figure 1." is correct.

1.1.f. Please see response 1.1.b.

1.1.g. We have argued above that the single-odor model is inconsistent with the familiar food effect (Figure 4A) and is not supported by our chemical analysis of released compounds. Furthermore, whereas efficient foraging generally increases food intake, it does not necessarily maximize utility. In economics, utility maximization has a specific technical meaning: that the individual’s choices over distinct commodities are consistent and transitive across a range of price-budget structures, i.e., choice sets. The proposed foraging example does not allow for this type of decision making because it entails neither price nor budget.

1.1.h. Doing the experiment of Figure 5B with a single species of bacteria would be interesting, but that would be very different paper, one that might fit with the probability matching literature (the matching law), whereas the present paper is concerned with rational choice between different goods.

1.1.i. We agree worms were free to eat as much as desired. This would be a potential concern relative to establishing a fixed budget only if a fixed budget were required in order to ensure that trade-offs occur. But in our study, trade-offs were introduced by the geometry of the Y-chip. A conventional budget constraint was not required.

1.1.j. We agree that worms are not aware of the duration of the experiment. Not only is time awareness an inappropriate assumption for nematodes, awareness of time is not necessary in order to establish the required trade-off between H and M food. That is because the trade-off is established by the geometry of the Y-chip.

1.1.k. The purpose of the budget constraint in human experiments is to ensure that there are trade-offs between goods in each choice set. In our experiments, however, trade-offs are ensured by the geometry of the Y-chip. As the two fluid streams are in contact and completely fill the food channel, the worm is always feeding in one stream or the other. Therefore, for every second spent pumping in H food, the worm forgoes a second pumping in M food, and vice versa. Therefore, there are trade-offs in the experiment and, because of these, all possible choices lie one of the budget lines. In human experiments the trade-off between consuming more of one good at the expense of less of another is enforced by the budget constraint. In C. elegans experiments, however, imposing a budget constraint is not necessary, as trade-offs are enforced by the Y-chip. The chip contains only two streams, one for H and one for M food, such that for every pump spent on H food, the worm necessarily forgoes a pump spent on M food, and vice versa.

These (1-2) major differences to the GARP experimental design in Figure 1 largely confuse me and I wonder how useful for understanding neuronal mechanisms is it to rigidly analyse the data with the mathematical tools of this framework. Vice versa, a reader from the field of economic decision making might find the explanations in (1) too trivial and must be similarly concerned of how much the experimental design fits into the GARP framework. The authors spend a good amount of effort justifying the various GARP requisites. I think they should also discuss these obvious differences and provide clear justification why their experimental design is a good worm equivalent to what is shown in Figure 1.

1.1.l. We have added such a paragraph to the Discussion.

2) (a) The animals show a baseline preference for H bacteria, which is interpreted by the authors as "latent learning". There is no evidence that this preference is due to a latent learning mechanism, it could be just an innate preference. This is also not important for the major conclusions of the paper, so I recommend to avoid this terminology and leave it only to the final discussion.

3) The authors use the term "explicit" learning for the enhanced H preference after training. (b) Explicit learning and explicit memory are differently understood in the field, like abilities or events that humans consciously acquire or remember. I strongly suggest to avoid this term as this could cause some confusion.

1.2.a. We agree that referring to the acquisition of baseline preference for H bacteria as latent learning overstates what is known. As originally stated, hatchlings do not prefer H bacteria over others (Shtonda, 2006), so the baseline preference for H cannot be called innate. However, we do not know whether the acquisition of this baseline preference during development is the result of learning about standard laboratory food (strain OP50) that then generalizes to H food, or simply the result for developmental changes in the nervous system. We have replaced the term latent learning with acquisition of latent preferences.

1.2.b. We now refer to preferences acquired through food quality training as trained preferences, thereby eliminating the confusing term explicit.

4) The behavioural defect of cat-2 is interesting but on its own it does not help much to better understand the mechanism that establishes food preference. Since the paper is quite complex already, I would recommend the authors keep these results for future mechanistic studies. – just a recommendation.

1.4. We propose to keep this result as it supports the hypothesis that food quality can be learned by adults.

5) line 434: you cannot conclude that food quality learning is intact in the Y-chip, since the animals never learned in the chip; acquired food preference upon learning can robustly be measured under Y-chip conditions.

1.5. Good point; we agree completely. We now conclude that the effects of food quality training are detectable in the Y-chip.

6) Line 461: text abruptly terminates and some important explanatory text to understand the law of demand is missing.

1.6. Apologies. the missing text has been inserted.

7) (a)Figure 4C-D: what is t=0? Switching from buffer to food streams? (b) What is the time course of pump frequency when no food (OD 0.0) is supplied?

1.7.a. Legend has been revised to define t = 0.

1.7.b. The OD 0 trace has been added.

8) Figure 4: I suggest to add legend for colour code in C-F, green = H food, yellow = M food.

1.8. Done.

9) Line 536: you mean Figure 4?

1.9. Fixed.

10) Ca++ imaging experiments lack negative controls. Since switches in microfluidic devices unavoidably come with pressure profiles, proper control experiments should be included.

1.10. A typical buffer-only control imaging trace has been added (Figure 9—figure supplement 1).

11) Do worms pump/feed in Ca++ imaging assays? Please discuss.

1.11. They do not. We now say this in the methods section.

12) Line 964: since worm locomotion needs to perform dorsal to ventral bending patterns under unconstrained conditions, they have a strong internal drive to keep undulating their heads. They just can't keep still. Here, they cannot leave and crawl out of the position in the device. I think the constraints in the device thus could be a major explanation why you don't see corner solutions (see also reviewer #2).

1.12. We agree worms are probably incapable of generating perfect corner solutions, for the reason the reviewer suggests. However, they are capable of generating close approximations to corner solutions. See for example point g for trained worms in Figure 5C, where H food is ten times denser than M food; the worm’s choice here is a close approximation to a corner solution. Accordingly, the device is not a limiting factor in observing corner solutions. This point has been added to the text.

13) line 167: aren't oranges in A double the price of apples?

1.13. Silly mistake, thanks for catching it.

14) Figure 2 panel B does not show what is described in main text and Figure caption

1.14. Fixed.

Reviewer #2 (Recommendations for the authors):

1. Bacterial concentration: precision and accuracy in the measurement of bacterial concentration is critical to essentially all analyses carried out here. One of the most fundamental variables in the model, price, is a simple function of this. Exactly how bacterial suspensions of different concentrations/densities are prepared is not clear, but the authors repeatedly use OD600 as a measurement of bacterial concentration (this is explicitly stated in lines 341-2). This has the potential to be a significant concern, as OD600 has a linear relationship with bacterial density only in very narrow range of relatively low density -- above this (certainly ODs of 1 or 3, which are used regularly here) there can be vast deviations from linearity. As noted by one of the references this paper cites (Stevenson et al. 2016), OD600 can even have a parabolic relationship to concentration in some density regimes because of the complexities of light scattering by bacteria. It's hard to tell whether this has been accounted for here – it seems that the authors are assuming, for example, that a suspension of OD 3 has 30x as much food as one of OD 0.1, which almost certainly not case. Further, when considering how this applies to H vs. M food, the authors calculate the difference in mass/OD ratio between H and M food at OD = 1, but this ratio seems very unlikely to hold at different ODs. If bacterial concentration has been mis-estimated because of these problems, it's possible that errors in price would propagate through all of the subsequent analyses. If the authors have indeed accounted for these complications, that's great – in this case, they'd need provide additional details about how this was done. If not, however, additional work will have to be done to figure this out.

2.1. Bacteria cell density in food suspensions was always measured in the linear range of OD relative to cell density (OD < 1). For suspensions outside this range, OD was measured in diluted samples. The Materials and methods section has been revised accordingly.

2. In Figure 9, the authors provide evidence that AWC physiology does not encode a simple economic quantity like value. I have a few comments/concerns about this analysis.

a) First, if bacterial concentrations are being mis-estimated as described above, it may be the case that the conclusions here will change, possibly dramatically.

2.2.a. Please see response 2.1.

b) Second, it looks to me like the red line in 9D indicates a clear relationship between preference and ∆F in trained animals. The statistics might not bear this out because of the limited power of the analysis, but I'm surprised that the authors don't find this at least suggestive of what's going on.

2.2.b. As the p-value for this correlation is 0.177, we prefer to be conservative and leave the text as it stands.

c) Third, authors make an argument for calculating ∆F from its steady state responses, but it would seem that the initial responses might be informative too – this is when relative values are first being assessed.

2.2.c. The initial transients died out in 1 min or less, well before most animals had begun to feed. As feeding is almost certainly required to assess value, at least in the case of untrained animals, we believe these transients are likely irrelevant.

d) Also, the presentation of the two stimuli with equal times for each doesn't really mimic the steady-state situation when an animal has a strong preference for one of them (in this case, the nose would be exposed to the preferred stimulus for most of the time). Maybe it would be useful to examine AWC responses with different stimulus patterns?

2.2.d. We agree that it would be interesting to image under conditions of asymmetric dwell times, as these occur in Y-chip experiments. However, in considering whether to implement asymmetric or equal dwell times in the imaging experiments, we chose the latter because we were primarily interested in the question of whether AWC is capable of reporting food utility via its inherent sensitivity to each food, that is, before the rest of the worm acts on this information; in other words, without the confound of the feedback loop between stimulus and behavior. We now explain this reasoning more in the Discussion.

e) Fourth, in rationalizing 9E, authors say that they asked whether AWC might encode "some other economic quantity". How many such quantities were examined? Is this a case where correction for multiple comparisons would be appropriate?

2.2.e. We tested 18 other economic quantities (please see Supplementary file 3). None showed a significant correlation with AWC activation. This means there are no positive findings requiring correction for multiple comparisons.

Reviewer #3 (Recommendations for the authors):

Introduction: GARP applies to consumer's choices, and importantly, assumes rational agents. The leap to nematodes is huge. Can the authors comment on this?

3.1. The implications of revealed preference theory can be viewed from two distance stances. The reviewer appears to adopt the first stance, “If an agent is rational, then his/her preferences will be consistent and transitive, they will satisfy GARP.” The second stance derives from the fact that having preferences that satisfy GARP is the necessary and sufficient condition for rationality. The force of necessity and sufficiency here is that GARP, can be used as a test for rationality, “If an agent’s preferences satisfy GARP, then he/her is rational.” Our study takes this second stance. We use GARP as, literally, a litmus test for utility maximization, one among many forms of rationality (Kacelnik, 2006). We use it solely for this limited purpose, following precedents set by other experimentalists (Camille et al., 2011; Chung, Tymula and Glimcher, 2017; Pastor-Bernier, Stasiak and Schultz, 2019)

Line 102: Citation that can potentially be added: Ghosh et al., 2016, Neuron, PMID: 27866800 (for risk assessment).

3.2. Added.

Line 120: "it is reasonable to expect that C. elegans food choices maximize fitness"◊ The notion that an organism's food choices maximize fitness is directly related to the Optimal Foraging Theory. Among the major criticisms this notion has received, is that it relies on the assumption that natural selection and evolution have somehow resulted in a decision-making process that maximizes fitness. However, natural selection has not necessarily led to such a result when it comes to the feeding strategy or food choices of an organism, because it is a process of selection and not a mechanism that produces optimal results, e.g., behaviors. Therefore, it is debatable whether C. elegans food choices maximize fitness.

Reviewer #1 and #3 discussed and reviewer #3 recommends to rephrase, e.g. "promote fitness" instead of "maximize".

3.3. Satisfaction of GARP indicates that there exists at least one utility function that renders the observed behavior perfectly maximizing. One of the limits of this approach is that we don’t get an exact specification of the utility function. This is true in two different respects. First, in mathematical terms, there can be a variety of different utility functions that fit the choice data equally well. Second, in mechanistic terms (psychological, biological), the units of the z-axis of the utility function remain obscure. One of the exciting aspects of the neuroeconomics approach, here and in general, is that by identifying the neural correlates of utility representations we can gain insights into the physical units of utility.

Line 145: redundant word: during

Line 146: bends, should be plural

Line 150: a period is missing at the end of the sentence.

3.4-3.7. All fixed.

Line 154: "GARP for worms": although this is the title of this Results section, the section itself is about explaining in detail how utility maximization and its violations can be manifested in graphic representation of bundle choices in experiments with human subjects. This section is not about C. elegans and GARP. I suggest revising the title. It is also unclear why this section is part of the Results, since there is practically no result presented.

3.8. We renamed this section “Revealed preference theory.”

Line 167: it seems to me that the opposite is inferred from the text (and from Figure 1 legend): apples are half the price of oranges. Is this a typo? -> see also reviewer #1

3.9. Silly mistake, thanks for catching it.

What is the budget of a C. elegans nematode? In line 535 and onward authors state that "We found it impractical to standardize the number of pumps to impose a fixed energy budget on each worm because […]", and then they explain that they have been plotting the fractional consumption and equation 5. Does this mean that the budget changes depending on the food source? Can the authors elaborate on this? Are worms' budget units consistent with the goods' prices units? -> see also reviewer #1

3.10. The sole purpose of the budget constraint in a human GARP experiment is to establish a trade-off between offered goods. There was no budget in our C. elegans experiments. That is because the trade-off was established by the geometry of the Y-chip.

Why do the authors consider the abundance of a bacterial strain equivalent to price? In human experiments, the ratio of, e.g., oranges vs apples is one of the variables (amount of fruit per weight), and the dollars per unit is another.

3.11. Actually, as stated in the original manuscript, we model price as the inverse of abundance, i.e., the inverse of density. This model is based on the intuition that food that is twice as dilute takes twice as much energy to consume per unit mass of food; the model views energy as cost. This point is now made explicitly in the text.

Line 236: Worms were cultured on E. coli OP50 before the H/M training took place. What is the nutritional value of this food source compared to H and to M?

3.12. This is an interesting question. In the original (and only) study of comparative food quality (Avery and Shtonda, 2003; Shtonda, 2004), quality was defined in terms of growth rate, computed as the inverse of the number of days to reach adulthood. Growth rates ranged from 0.28 day-1 to 0.50 day-1 (Shtonda, 2004). The H and M foods in our study, DA1877 and DA1885, have growth rates of 0.50 and 0.43, respectively. OP50 was not included in that study, but a derivative of OP50, DA837, has a growth rate of 0.45. By this measure, OP50 is a medium quality food, slightly better than our M food (DA1885).

Line 253: "If H food smells to the worm more like E. coli than M food does, this preference might be explained by the so-called food familiarity effect (Song et al., 2013), in which worms eat familiar food more readily than novel food." In this case, worms do not prefer H food based on its "quality" but based on its similarity to the food source they have been used to. In this case, maybe the sequence of preference choices does not constitute a violation of the utility maximization. In this case, worms do not choose driven by an urge to maximize their fitness, but rather by a tendency to maintain a familiar environment. How does this fit with the authors claims and assumption?

3.13. We do not claim that worms maximize fitness, at lease in the simple sense of optimizing food consumption. We claim that worms maximize utility or, in other terms, welfare, defined as fulfillment of their subjective preferences. Subjective preferences can be aligned with fitness, but they can also diverge from that norm. In humans, for example, drugs of abuse cause divergent preferences. In worms, the preference for familiar food even when it is lower in quality than other foods can be seen as a divergent preference. Adherence to GARP means only that preferences are internally consistent, regardless of whether they are aligned with or divergent from fitness. Therefore, we see no contradiction in our claims. Comments on fitness maximization have been added to the discussion.

Figure 2B: The caption reads "Mean preference versus time for trained and untrained ceh-36 mutants and N2 controls in open-field accumulation assays", however, I am not sure that this is what the figure shows, given also that the y axis is labeled as "fraction of pumps". Please explain. - see also reviewer #1

3.14. Apologies for this error, now corrected.

Given the issue with Figure 2B, it is hard to tell, at this point, which plot represents the open field assay and which the maze choice assay, therefore it is hard to compare the two or evaluate the findings in a combined way.

3.15. Caption now contains this information.

Line 298: "The decision to accumulate in a particular food can be made, at least in part, before the animal enters the patch." ◊ I think that, for the sake of accuracy, the decision in question is not about deciding to accumulate; a worm does not decide to accumulate, but rather to approach or reach or forage on food H or M. How do the authors comment on this?

3.16. We replaced decision to accumulate with decision to approach.

Have the Authors performed the open-field accumulation assay in the presence of sodium azide?

3.17. Yes. Please see Figure 4C.

The authors speak about latent learning (=a type of learning which is not apparent in the learner's behavior at the time of learning, but which manifests later when a suitable motivation and circumstances appear) in case of the non-trained animals, and about explicit learning (=a more conscious process where the individual makes and tests hypotheses in a deliberate search for answers) in case of the trained animals. This implies a dipole scheme of latent vs explicit. However, the authors do not justify the use of these two terms, nor do they provide evidence that in non-trained animals the learning is latent; in addition, there is no justification for the use of the term explicit in the second case. The worms have been simply conditioned or not conditioned, respectively. Even in lines 307-309 when they cite two papers by Worthy et al., stating that "Explicit food quality learning in C. elegans is formally equivalent to a type of classical conditioning in which an association is formed between the mélange of odors characteristic of particular bacteria species (Worthy, Haynes, et al., 2018; Worthy, Rojas, et al., 2018)", this is perplexing, because I am not sure that these papers claim or demonstrate that explicit learning in C. elegans is equivalent to classical conditioning. Despite that, the authors state that they are trying to find the locus of explicit food quality learning (line 259). I think the use of the two terms, explicit and latent, should be better justified or other terms should be used instead. -> see also reviewers #1/2

3.18. We have the terms latent and explicit learning. We now refer to preferences acquired through food quality training as trained preferences and preferences acquired in the absence of prior exposure to a particular food as latent preferences. Regarding the latter, we make it clear that latent preferences do not necessarily reflect learning; they could be developmental in origin.

In relation to that, in lines 323-333, it is implied that food learning occurs while the animals forage on the food patches. What is it exactly that worms learn?

3.19. The learning we observe is an increase in the normal bias to accumulate in H vs. M food (Figure 2B-D), and also increased consumption of H vs. M food (Figure 5B). In other words, trained worms learn to prefer H food more strongly than untrained worms.

Is this some form of non-associative learning?

3.20. We understand non-associative learning to be a process in which an organism’s behavior in response to a specific stimulus changes over time in the absence of any evident link to (or association with) consequences or other stimuli that would induce such change. In a simple non-associative model, increased bias for H could be the result of sensitization to H food, habituation/adaptation to M food, or both. In an associative model (e.g., classical conditioning), odors specifically emitted by H and M food would serve as conditioned stimuli, CS1 and CS2. The unconditioned stimulus is the presumptive reinforcing effects of consuming H or M food. At present, we cannot definitively distinguish between these two possibilities. The section “Establishment of subjective value assignments” in the Discussion now includes these points.

In addition, the effect on their preference developed as they forage on a specific food patch is something that should be present in both trained and non-trained animals. The authors state that "It is possible, therefore, that food quality learning in cat-2 mutants is impaired simply because they spend less time in the food, hence have less experience of it", line 321. Does this mean the authors believe that food quality learning occurs during the worms' stay on the food patch during the open field or maze assay and not during training?

3.21. We believe that the majority of the change in food preference occurs during the training phase, which lasts 18-24 hours as opposed to the testing phase, which lasts only 1 hr.

Have the authors tested only two types of food, i.e., two bacterial strains characterized as medium and high quality?

3.22. Yes, in these laborious experiments, we have tested only one pair of food. This limitation of our study is now pointed out in the Discussion.

If so, then the reported results could be due to other properties of the bacteria and not their nutritional value (case-specific results).

3.23. In the original manuscript, we noted that although adherence to GARP does not reveal what is being maximized, we were able to identify three aspects of bacterial food that are not being maximized: amount of high quality food consumed, overall amount of food consumed, and potential for rapid growth. So, we agree with the reviewer: the reported results are likely due to phenomena other than nutritional value. This point is now made in the text.

Note that the nutritional value (energy, joules) is what the authors take into account in equation 1.

3.24. There seems to be some confusion here. In the original manuscript, the term in equation 1 representing energy refers to energy required to swallow food, not the energy gained by swallowing food. That being said, equation 1 in the revised manuscript no longer includes an energy term.

Wouldn't their findings be stronger if the observed preferences were repeated for other pairs of food choices, i.e., by testing other/more bacterial strains?

3.25. Please see our response to 3.22.

Figure 4C and 4D: what is the difference between the two? Do they refer to M and H?

Similarly for 4E and 4F: do different colors (green and gold) represent different foods e.g., H and M? Please clarify.

3.26. Thanks. We have altered the figure to remove this ambiguity.

Line 524: Maybe these data should be shown, as they constitute an important link in the authors' train of thought.

3.27. These data appear in Figure 5B in the original and revised manuscript. The accompanying paragraph has been edited for clarity.

Line 550: Can the authors explain why this is expected to be a gaussian distribution?

Line 551-554: Is there a plot/figure to illustrate this?

3.28. The distributions of preference values in contributing to the means in Figure 5C were well fit by gaussians. See new Figure 5—figure supplement 1.

Line 561: I don't think this is a particularly conservative null hypothesis; in most cases in behavioral assays the null hypothesis is exactly this: that animals choose randomly, i.e., that the treatment has no effect.

3.29. We are a bit confused here, as simulated worms did choose randomly. We stated, “… the fraction of pumps in H food is drawn from a flat distribution between 0 and 1.” Nevertheless, we have eliminated the qualifying adjective, “highly.”

Lines 604-606 and Figure 6A: I do not understand why e and d are grouped both in the group in which H changes and in the one H stays constant. Can the authors please explain?

3.30. We have added a table that clarifies the design of this analysis (Supplementary file 1).

Line 673: "worms require more of it to be satisfied": How do the authors define or measure satisfaction in this case? Without a definition this sentence is misleading.

3.31. We agree. We eliminated “satisfaction.” We now say, “Thus, not only did training make H food more valuable, it also made diminishing marginal utility less relevant to valuation.”

Line 700: eliminate or support?

3.32. Typo. Text now states, “Together, these findings strongly favor the dwell-time model over the frequency model.”

Line 766-767, and the entire paragraph: Authors say that "As exogenous activation of AWC produces a bout of reverse locomotion (Gordus et al., 2015), its response to food offset promotes reversals, leading to increased retention patches. Our imaging data suggest that AWC-mediated retention would be stronger for H than M food, promoting greater preference for H food, as seen in Figure 2B-D." The authors rely on their finding that AWC was more strongly excited by H than M food, to jump to the conclusion that "AWC-mediated retention would be stronger for H than M food, promoting greater preference for H food". In my view, this last claim could constitute a well-defined hypothesis to be tested, and not a conclusion based on their findings, even in combination to Gordus et al. In fact, it is Gordus and colleagues who highlight in their 2015 paper that although the activation pattern of AWC is deterministic ("highly reliable"), the resulting reversing behavior is, by contrast, probabilistic: "The AWC calcium response, which is likely correlated with depolarization, is highly reliable from trial to trial, even after dozens of odor presentations (Larsch et al., 2013). By contrast, the reversal response is probabilistic. Even under well-controlled conditions, animals may or may not reverse on individual trials, regardless of the strength of the AWC calcium response (Larsch et al., 2013)" and that "Thus, the variability in the behavioral response results from variable transmission of information from the AWC sensory neuron to AVA command neurons." Based on the above, I do not understand the authors' claim. Maybe they can run an experiment to show that the claim is valid? The results presented in Figure 2, although they show increased retention, they do not allow the conclusion that the animals with stronger AWC activation are the ones that present increased retention. That individuality in the response is, in my view, what Gordus et al. indicate in their work.

Similarly, in the following paragraph, based only on the strength of AWC activation, they conclude that "retention in H food patches would be stronger in trained than untrained animals, promoting greater preference for H food after training". However, stronger activation of AWC does not mean stronger retention (behavioral outcome), based on Gordus et al.

3.33. We should have made it more clear that our argument is probabilistic in nature. Our model is that greater activation of AWC upon removal of H food is consistent with a higher probability of being retained in H vs. M food patches. The text has been revised to emphasize the fact that our argument is probabilistic.

Line 1114: The mask was baited or the maze-shaped NGM area?

3.34.a. The latter. Methods section now states, “The mask was placed on the NGM surface and the maze was baited with the same amounts of H and M food, which were placed on the agar surface at the end of each arm.”

Where there any escaping animals? Where there any animals that did not choose either of the two (e.g., not reached neither H or M in the allowed time)?

3.34.b. Methods now states, “Preference at each time point was computed as (NHNM)/(NH+ NM), where N is the number of worms in contact with the food-type indicated by the subscript; worms not in contact with food, and the small number of escaped worms (~5%), were not counted.”

How long were the worms allowed to make a decision inside the maze?

3.34c. In open-field and maze experiments, worms were allowed to reveal their food preferences for 60 min as indicated in original versions of (Figure 2C,D). methods section now includes this information … “Accumulation was scored for 60 min. at 15 min. intervals”

Were there any animals censored, and if so, does this affect the results?

3.34.d. No animals were censored. Text now states this this.

Did the authors alternate the position of H/M food in the two maze arms to eliminate any side preference effect?

3.34.e. We did not alternate the position of H/M food. The consistent differences between trained and untrained animals across manipulations (azide and cat-2) testify to the fact that worms were responding to food rather than extraneous stimuli.

Line 914: what do the authors mean by "infra-human species"? Maybe non-human?

3.35. “Infra-human” removed.

Line 919: "literally guarantees", and elsewhere in the text: the authors tend to express their claims using absolute language (see also title, "exactly as"). I feel that it might be more appropriate if the language used is firm and confident, as the authors see fit, but milder.

3.36. “Literally” and “exactly” have been removed.

Lines 914-922, and elsewhere in the text:

a. The authors are trying to convince the reader that C. elegans makes consumption decisions in the same way that a human consumer does. What's more, they claim that such a human-conforming behavior can be captured in nematodes by just mapping the neuronal circuit that steers head bending. This is in the core of the paper, and in my view, it is problematic in many ways. The axioms of the revealed preference theory are justified by the assumption that humans are rational agents. This means that they make rational decisions. Do the authors claim the same for C. elegans nematodes?

3.37.a. This concern seems similar to point 3.1. As noted there, we are using revealed preference theory as a litmus test for utility maximization. In doing so, we are following well-established precedents cited in the original manuscript. A litmus test for utility maximization does not assume utility maximization or any form of rationality. On the contrary, it is a test for utility maximization.

b. In parallel, the fact that C. elegans feed on two different food sources and they choose one over the other in a way that the goods qualify as substitutes, is a finding presented as of extreme importance. This is indeed an interesting conclusion, well supported by the data. It becomes more interesting because of the untangling of the neuronal circuit involved. At the same time, this is really not an unexpected result, although providing evidence for it is definitely useful. Any animal that feeds on multiple food sources would alternate between two of them, based on their availability, the effort required, the nutrition provided. Indeed, the authors themselves do not claim that this is unexpected. However, they claim that they "break grounds" because worms' behavior appears to conform with utility maximization principles and can be described with human-centered terms of substitute goods. This is misleading, first, because of the agent rationality assumed, which we have no basis for, and second, because identifying two goods as a substitutes pair is not ground-breaking on its own. Behavioral economics labels pairs of goods as such in order to move on with more complicated claims, theorems and analyses.

3.37.b. We wish to emphasize, as noted in 3.37.a and also in 3.1 that our approach does not assume rationality; rather, it tests whether C. elegans choice behavior is consistent with a particular model of rational choice, namely utility maximization. As stated in the Discussion, from our perspective the most prominent aspects of our study are (1) C. elegans food choices obey the classic law of supply and demand; (2) C. elegans behaves as if maximizing utility; (3) C. elegans food-consumption decisions are well fit by the CES utility function; (4) A plausible mechanism for utility maximization has been identified. We have replaced “breaks new ground” with “establishes a new reference point.”

c. The authors are interpreting C. elegans feeding behavior using behavioral economics terms that sound extravagant when speaking of nematodes, but in reality, their findings are not extravagant and certainly do not need to be dressed as such in order to be significant. In this reviewer's view, the findings presented in the manuscript are interesting and they constitute a significant contribution. Attempting to attribute to them a dimension disproportionate to their real depth, dampens the initial enthusiasm in an unnecessary way.

3.37c. We wish to disagree, respectfully, with the concern that we are applying revealed preference theory inappropriately (“extravagantly”). On the contrary, we have taken revealed preference theory at its word, and applied it to a remarkably simple organism that nevertheless passes the test for utility maximization. This finding is significant not only for what reveals about the sophistication of C. elegans behavior, but also for our understanding of revealed preference theory itself. Economists will almost certainly be prompted to reexamine the perceived view that revealed preference decisions require awareness and cognition.

Line 979: What are the worms maximizing? This is a question that the authors admit comes up inevitably, but interestingly (and honestly, of course) at the same time they state that they do not have a plausible answer to it. Therefore, even the notion of utility (which is supposed to be maximized) remains obscure. In my understanding, this confirms the fundamental problem with the way this study is presented. The authors are not working toward testing a stated hypothesis (e.g., nematodes' behavior is such that maximizes x), but they rather quantify a nematode behavior in a way that fits the equations used in behavioral economics. What they don't take into account is that, sometimes, even if phenomenon A can be phenomenologically described by a set of equations that has been developed to describe (part of) phenomenon B, this does not mean that A is explained by the same physical or biological principles that steer phenomenon B. This is even more prominent if the organism involved in A is so very different regarding its brain faculties and societal construct than organism B. And even more so if the researchers fail to provide a satisfactory answer for the biological (in lack of maybe a psychological, societal or other) explanation for this behavior.

3.38. We wish to disagree, respectfully, with the reviewer in couple of respects. (i) “The authors are not working toward testing a stated hypothesis.” On the contrary, we have tested the hypothesis that C. elegans decision behavior satisfies the necessary and sufficient conditions for utility maximization. In other words, we tested the hypothesis that C. elegans choices maximize something. (ii) Although we have established that C. elegans choices satisfy the behavioral conditions for utility maximization we do not, on this basis, conclude anything about the biological mechanisms of this phenomenon. To do otherwise would be to misunderstand the limitations of revealed preference theory, which by design is not concerned with mechanism. Nevertheless, our finding of utility maximization in one of the most experimentally tractable organisms in contemporary neuroscience has potentially significant implications. It sets the stage for discovering how at least one nervous system implements this extraordinarily important behavior.

References

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Camille, N. et al. (2011) ‘Ventromedial frontal lobe damage disrupts value maximization in humans’, Journal of Neuroscience. doi: 10.1523/JNEUROSCI.6527-10.2011.

Chung, H.-K., Tymula, A. and Glimcher, P. (2017) ‘The Reduction of Ventrolateral Prefrontal Cortex Gray Matter Volume Correlates with Loss of Economic Rationality in Aging’. doi: 10.1523/JNEUROSCI.1171-17.2017.

Gordus, A. et al. (2015) ‘Feedback from network states generates variability in a probabilistic olfactory circuit’, Cell, 161(2), pp. 215–227. doi: 10.1016/j.cell.2015.02.018.

Harbaugh, W. T., Krause, K. and Berry, T. R. (2001) ‘GARP for Kids’, The American Economic Review, 91(5), pp. 1539–1545.

Kacelnik, A. (2006) ‘Meanings of rationality’, in Hurley, S. L. and Nudds, M. (eds) Rational Animals? Oxford: Oxford University Press, pp. 87–106.

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Niacaris, T. and Avery, L. (2003) ‘Serotonin regulates repolarization of the C. elegans pharyngeal muscle’, Journal of Experimental Biology, 206(2), pp. 223–231. doi: 10.1242/jeb.00101.

Pastor-Bernier, A., Stasiak, A. and Schultz, W. (2019) ‘Orbitofrontal signals for two-component choice options comply with indifference curves of Revealed Preference Theory’, Nature Communications, 10(1). doi: 10.1038/s41467-019-12792-4.

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Shtonda, B. B. (2004) ELECTROPHYSIOLOGICAL AND BEHAVIORAL MECHANISMS OF Caenorhabditis elegans FEEDING. University of Texas Southwestern Medical Center.

Shtonda, B. B. (2006) ‘Dietary choice behavior in Caenorhabditis elegans’, Journal of Experimental Biology. doi: 10.1242/jeb.01955.

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Worthy, Soleil E. et al. (2018) ‘Identification of attractive odorants released by preferred bacterial food found in the natural habitats of C. elegans’, PLoS ONE, 13(7), pp. 1–14. doi: 10.1371/journal.pone.0201158.

Worthy, Soleil E et al. (2018) ‘Identification of Odor Blend Used by Caenorhabditis elegans for Pathogen Recognition’, Chemical Senses, 43(January), pp. 169–180. doi: 10.1093/chemse/bjy001.

Zaslaver, A. et al. (2015) ‘Hierarchical sparse coding in the sensory system of Caenorhabditis elegans’, Proceedings of the National Academy of Sciences of the United States of America, 112(4), pp. 1185–1189. doi: 10.1073/pnas.1423656112.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Reviewer #3 (Recommendations for the authors):

The authors have extensively revised large parts of the manuscript, especially in the Results and Discussion sections. The revised manuscript also includes updated figures and captions, new supplementary figures, etc. The manuscript is in much better shape, and much more information is provided, information that is critical to evaluate the results, their interpretation, and the final conclusions. The addition of new authors and expertise, as well as the change in the title are very welcome, too. Many of my concerns were addressed, and I appreciate the detailed explanations provided in some of the authors' responses. My understanding of their work is now much better. Nevertheless, the work continues to present fundamental problems. These are reflected mainly in comments #1, #5, and #11, which can be considered my major concerns. The rest of the comments can be considered minor or easier to answer.

1. Comment 1 of first revision and response 3.1:

The authors write in their rebuttal letter that they adopt the stance that if the agents' behavior adheres to the GARP, then they are rational (and not that rationality is a prerequisite). In their response, the authors list 3 papers to support the stance they claim to adopt, and all three of them have to do with humans, and the work reported has to do with reduced or altered observed rationality because of trauma, aging, etc. Displaying reduced rationality is fundamentally different than potentially lacking the very ability to be rational. I still feel that the issue of rationality needs to be addressed clearly in the manuscript. I explain:

In the revised manuscript, apart from two references to published work on C. elegans observed occasional rationality with many exceptions (lines 106-110), the only important part that addresses rationality is the new text in lines 228-234. Here, the authors mention (line 228) that "tests of adherence to GARP have been utilized to assess the degree to which decision-making agents are rational in the economic sense", and later in the paper, they claim that nematodes adhere to GARP. The authors need to make clear whether they claim rationality for C. elegans, based on their findings, and if so, how is this rationality defined. And in addition, they need to make clear that whatever rationality is claimed for worms, it is not to be confused with what is broadly understood as rationality but is rather a term to describe a mathematically defined concept, the criteria for which are met by nematodes. If this is not absolutely clear, then the reader can be easily misled.

We have added a paragraph that makes clear that GARP establishes a limited type of rationality, which we refer to as technical rationality. We state that technical rationality neither presupposes nor establishes rationality in the psychological sense of awareness and reasoning (lines 222-230).

5. Line 301 (related also to response 3.18): " [The preference of naïve worms] could be the result of prior experience or developmental maturation": I do not understand this. What kind of prior experience? If I understand correctly, the worms have been grown in the lab for their entire life, and for a number of prior generations. Have they been fed anything else than E. coli during some part of their life? Have they been exposed to H or M food before? Have their ancestors been exposed to H or M food? If not, then the "prior experience" argument cannot possibly apply. If yes, then this should be mentioned, as it would dramatically change the perspective. As for developmental maturation: If the authors believe this is true, then assessing worms ranging from L3 to Day 1 is obscuring, and distinct age cohorts should be assayed separately (L3, L4, Day 1). Moreover, if this were true, it would mean that older or younger animals prefer, for example, H. Therefore, the ratio of younger/older animals in the tested population could skew the results this way or the other. How do the authors comment on that? As for the trained worms, acquiring a preference because of sampling the two foods during the 60 min training assay seems the most reasonable thing to assume. However, the authors claim that this scenario does not apply, because of the findings of the familiarity experiments in the Y chip, but it is not clear to me why this is the case. Besides, the conclusion in line 522 that the foods are qualitatively distinct, would explain the development of a preference during the 60 min of the assay.

We have deleted the sentence quoted above.

11. The new information provided in the revised manuscript on the budget constraint and the price of goods H and M, and how the budget constraint is imposed because of the Y-chip design, allowed me to get a new perspective of the Y-chip experiments. In consequence, several concerns arise. The process is as follows, roughly: A worm is placed in the chip, and two streams, one of H and one of M food, are provided. The preference is revealed by the worm bending its head toward the M or the H stream, and by performing pumps. The combination of pumps of H or M food is the preferred bundle. The whole process lasts for 12 mins. Therefore, it takes 12 min for the worms to behave in a way that reveals their preference. During these 12 mins, the preference is revealed through a sequential decision-making process, in which the worms sample the goods.

i) The sequential nature of this process is fundamentally different than the one-time decision made by human subjects in analogous experiments. In those, humans select the bundle of preference in a single decision. Nematodes, however, make many decisions, sequentially, that define the preferred bundle. How do the authors believe that this affects the interpretation of the results, with respect to adhering to the GARP prerequisites? I posit that this difference can have many implications as someone is trying to determine whether nematodes meet the same prerequisites that humans meet but while under very different experimental conditions. Some additional methodological concerns are listed below.

The reviewer makes an important point here. Yes, the worm can be said to make a series of decisions during the 12 min. testing period, whereas GARP tests on humans involve one-shot decisions. This could be confusing to readers. However, the history of GARP and its relation to behavioral economics is illuminating here. As the reviewer will know, GARP is a refinement of the Strong Axiom of Revealed Preference (SARP) which, in turn is a refinement of Samuelson’s 19381 Weak Axiom of Revealed Preference (WARP). In that work, which launched revealed preference theory, consumption is amount purchased per unit time:

“I assume in the beginning as known, i.e., empirically determinable under ideal conditions, the amounts of n economic goods which will be purchased per unit time by an individual faced with the prices of these goods and with a given total expenditure.”

Clearly, Samuelson had in mind the accumulation of goods over time and, therefore, a series of consumption decisions. Later, revealed preference theory was used to build models of ‘lifetime consumption,’ 2–4 including retirement spending. As this type of spending also occurs over time, it too implicitly involves a series of consumption decisions.

As our consumption metric integrates the rates of consumption of H and M foods over a fixed time, it is consistent with Samuelson’s original theory. Our definition of preference includes whatever micro-decisions are made during that time. This situation is akin to defining consumption in humans, as economists do, in terms of what is in the grocery cart as a consumer leaves the store. Placing items in the cart is a sequential process (one orange at time, so to speak), and initial biases and non-stationary preferences are irrelevant. Of course, by changing the definition of preference one could take those phenomena into account, but revealed preference theory does not require this.

It was not until the studies of Andreoni, Glimcher, Harbaugh, and Kariv that the classical theory of revealed preference was realized in terms of one-shot decisions. The one-shot decision framework was adopted purely for experimental purposes. Therefore, GARP can be investigated either way: in terms of sequential decisions over time, or in terms of one-shot decisions.

We have added to the manuscript a paragraph that explains why sequential decisions are consistent with revealed preference theory (lines 222-230).

ii) During the sequential sampling, the worm needs to bend its body toward this or the other side, in order to perform a pump. Consequently, switching between sides, therefore foods, has a cost for the worm (note that bending just the head does not allow for switching between the two flows, as evident in Video 1). How do we know that this cost does not affect its decision-making with respect to switching between foods? In addition, even though the authors say that the body bending while in the chip resembles the body bending during the sinusoidal locomotion on a GNM plate, in Video 1 we can clearly see the worm bending multiple times toward one side before switching to the other side. This is not what happens during regular locomotion. This can be related to the worm preferring to feed on one food, but also to the cost of the effort required in order to bend to the other side. Given the constraint along the mid-body, this effort seems not to be negligible.

We agree that, in theory, there could be energetic costs for switching sides. There could also be opportunity costs. And, during sequential decision making, these costs may contribute to relative preference for each food, in a process akin to effort discounting. But revealed preference theory by design is blind to underlying factors contributing to preferences. Therefore, costs, if they do occur, do not undermine our finding of utility maximization. One could argue that costs might be different in a differently shaped chip and, therefore, that relative preferences might be different as well. But we do not claim that our methodology measures the worm’s preferences independent of testing conditions. Nor would such a claim be a necessary condition for utility maximization.

iii) How do we know that the worm is not biased by the content of the first few pumps? Is there a correlation between the first few pumps and the final preferred bundle?

This is an interesting question. Our study does not have the statistical resolution to answer it, but we believe this question is not relevant to our finding of utility maximization. That’s because the food first eaten in the chip can be assimilated to the individualized history of the worm, its accumulated experience over its lifetime, including during testing. This history is part of what makes preferences subjective. And, as noted above, revealed preference theory is blind to underlying factors contributing to individual preferences.

It is also worth noting that the type of bias the reviewer imagines does not necessarily have an effect on population-level preference. Here’s the proof.

Let’s assume that worm is biased by the content of the first few pumps, such that it strongly prefers what it first ate. As stated in Materials and methods, worms are accommodated to the Y-chip in food-free buffer. After accommodation, foods are introduced. We can reasonably assume that the initial pumps will be left-right randomized, according to posture of the worm when food first reaches it. This situation can be modeled as

fHH= nH+xH(nH+xH)+(nMxH)
fHM=nHxM(nHxM)+(nM+xM)

where fHH is the preference of worms the that first ate H food, and fHM is the preference of worms the first ate M food. The variables xH and xM represent, respectively, the extra pumps that occurred in H or M food. The expected preference across the population is

FH=12(fHH+fHM)

Substituting for fHH and fHM and combining terms gives

FH=nHnH+nM+xHxM2(nH+nM)

In the simple case where the number of extra pumps on either side is equal (xH=xM), the right hand term in the above equation is zero, meaning there is no effect of food first eaten. In the extreme case of complete bias toward the food first eaten, xH=nM and xM=nH, and FH = 0.5. This scenario does not match our data, as preferences much greater or much less than 0.5 were observed (Figure 5B). For xHxM, FH can take a range of values greater or less than the baseline preference of FH=nH(nH+nM). Thus, the initial experience of each worm in the chip could be a factor that shapes preference. But, as noted above (lines 223-225) revealed preference theory is blind to underlying factors contributing to preferences.

iv) The initial body orientation of the worm is not controlled, as I would guess. How do we know that it does introduce a bias with respect to the initial conditions of the system?

This concern seems analogous to (iii). Initial posture can be assimilated to the worm’s subjective history, with no implications for the applicability of revealed preference theory.

iv) The fact that the worm develops a preference over the course of 12 min, as it is tasting (sampling) the two foods, cannot be overlooked. According to the literature, this can be enough time, for worm standards, to develop behavioral plasticity. How could this affect the "revealed preference" and the adherence of the worm to the GARP prerequisites? Especially since human subjects, who participate in carefully controlled experiments, do not undergo a similar (sequential) process.

As point of clarification, it is not a fact that preference “develops” during the 12 min. testing period. At this point, we don’t know whether or not this happens because, again, our data do not have the required statistical resolution. But, even if preference is modulated by experience in the chip, that experience can be assimilated to the worm’s subjective history, with no implications for the applicability of revealed preference theory.

v) The (iv) relates to the development of a preference during training in a plate with patches, for the accumulation assay, see comment #5. The authors are reluctant to admit that worms can develop a preference because of sampling the two foods during the 60min training assay. (1) They attempt to justify this reluctance based on the results of the familiarity experiments on the Y-chip. As mentioned in comment #5, I am not sure how the familiarity experiments lead to the conclusion that worms do not develop a preference during training. (2) Does this have to do with the authors not acknowledging that worms might be developing a preference during the Y-chip experiments?

1. It is conceivable that learning-through-sampling occurs during the 60 min food-preference assays. We now say this in the text (lines 302-303). But whether or not learning occurs during this assay has no bearing on the main conclusion of the paper – that the worm behaves as if maximizing utility – because that conclusion is based a different assay.

2. We agree that the logic behind the statement that familiarity experiments argue against preference acquisition during the Y-chip assay was unclear; it has been deleted.

All the above (i-iv) leave the key claim "Overall, this methodology results in decision-making paradigm that is formally analogous to GARP experiments in humans", line 1054, unsupported.

To conclude: the revised manuscript is in much better shape than the original draft, and I recognize the authors' efforts to respond to the reviewers' many comments. The amount of work performed is impressive. However, this paper still presents fundamental problems. These are reflected mainly in comments #1, #5, and #11. Worm's adherence to GARP prerequisites is proposed to be the case, but the methodologies through which this conclusion is drawn and the interpretation of some of the findings are problematic. Trying to adjust human GARP behavioral experiments so that they can be run with nematodes does not seem to work, in this reviewer's opinion. Many of the parameters that experimenters are trying to control when studying humans, in order for them to be able to reliably claim adherence to GARP, are not controlled in the nematode experiments presented here (comment #11), something that can dramatically affect the interpretation of the results. Furthermore, important clarifications need to be made so that the reader is not misled (comment #1), and some explanations the authors provide for some of the observed behaviors are inadequately substantiated (comment #5).

In light of the above, even if the authors addressed everything else satisfactorily, with concern #11 unresolved, I do not see how the main claim can be sufficiently supported and how this paper can be published in eLife. The claims that the authors are making are such that their substantiation should be above any ambiguity.

Reviewer #3's additional comments from the consultation session:

Sequential decision-making in the Y-chip is a fundamental concern. Here is why: The main claim the authors are making is that C. elegans' behavior abides by the GARP requirements. They claim so, based on their interpretation of experimental findings. By implementing a certain experimental design, they experimentally pose a question to the system, and the system (nematode consumers) responds by demonstrating a certain behavior, and this behavior is interpreted as GARP behavior because presumably, it is similar to the behavior displayed by the human counterparts. As a reference, when behavioral economists run experiments with human subjects, they apply a certain experimental design, they experimentally pose a question to the system (human consumers), and the system responds by demonstrating a certain behavior, and this behavior is defined as GARP behavior. Note that the experimental design followed by behavioral economists is very strictly controlled, to make sure that no undesired variables interfere with the results. However, the Y-chip experiments pose a different question to nematodes, than the question posed to human consumers: the Y-chip asks what the outcome is of a sequential decision-making process, whereas the GARP-defining human experiments ask what is the outcome of a one-time decision-making process. In other words, the problem is that Katzen et al. introduce a variable that is not present in the experimental design used in behavioral economics to decide whether the subject behaves as GARP: the variable of time. The worms display sequential decision-making, but GARP is supposed to explain a one-time decision-making behavior, not a sequential one. This discrepancy, ignoring the extra variable in the Katzen et al. experiment, is problematic and potentially very misleading.

I am particularly concerned because of the potential impact of the claim that authors make: nematodes make economic decisions that can be described by the same set of principles that describe human economic decisions. For such a huge claim to stand, it has to be supported in a concrete way, without gaps in the thought process.

Bottom line: I understand that the experimental design is what it is and that there is no way the Y-chip experiments are performed differently so that the worms could make a one-time decision. Therefore, I see two options: (A) In the current version of the manuscript, because of this discrepancy, the claim is weak and is not adequately supported, in my view. Therefore, I cannot suggest the manuscript be published in eLife. (B) The authors update the manuscript to admit the discrepancy, and they make it absolutely clear to the reader that the nematode system makes its decision according to a process very different than the one that human systems make their decision, in corresponding reference experiments that decide the subjects' GARP behavior. If the authors do that, then everything will be transparent, and the readers can decide for themselves whether the claim stands or not. In such a case, I am fine with publishing the work in eLife, if such is the suggestion made by everyone else.

We understand the distinction the reviewer has made and the confusion it could cause, and we are grateful to the reviewer for pointing this out to us. However, as described above (lines 173-207), quantification of consumption over time (sequential decisions), is consistent with classical revealed preference theory. Accordingly, relative to (A), the use of this method does not in any way weaken the claim of utility maximization in C. elegans and, regarding (B) there is no discrepancy to admit.

That said, we agree that the manuscript could be improved by clarifying the relationship between one-shot decisions and sequential decisions relative to classical revealed preference theory. We have added such a paragraph (lines 457-466).

References

1. Samuelson, P. A. A note on the pure theory of consumer’s behaviour. Economica 51, 61–71 (1938).

2. Ghez, G. R. & Becker, G. S. The Allocation of Time and Goods over the Life Cycle. (NBER, 1974).

3. Friedman, M. A Theory of the Consumption Function. (Princeton Universitiy Press, 1957).

4. Deaton, A. Understanding Consumption. (Clarendon Press).

https://doi.org/10.7554/eLife.69779.sa2

Article and author information

Author details

  1. Abraham Katzen

    Institute of Neuroscience, University of Oregon, Eugene, United States
    Contribution
    Software, Investigation, Methodology, Writing – original draft
    Competing interests
    No competing interests declared
  2. Hui-Kuan Chung

    1. Center for Neural Science, New York University, New York, United States
    2. Neuroscience Institute, New York University School of Medicine, New York, United States
    Contribution
    Software, Methodology, Writing – review and editing
    Contributed equally with
    William T Harbaugh
    Competing interests
    No competing interests declared
  3. William T Harbaugh

    Department of Economics, University of Oregon, Eugene, United States
    Contribution
    Formal analysis, Methodology, Writing – review and editing
    Contributed equally with
    Hui-Kuan Chung
    Competing interests
    No competing interests declared
  4. Christina Della Iacono

    Institute of Neuroscience, University of Oregon, Eugene, United States
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  5. Nicholas Jackson

    Institute of Neuroscience, University of Oregon, Eugene, United States
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  6. Elizabeth E Glater

    Department of Neuroscience, Pomona College, Claremont, United States
    Contribution
    Analysis of volatile organic compounds
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-0205-8209
  7. Charles J Taylor

    Department of Chemistry, Pomona College, Claremont, United States
    Contribution
    Analysis of volatile organic compounds
    Competing interests
    No competing interests declared
  8. Stephanie K Yu

    Picower Institute for Learning and Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, United States
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  9. Steven W Flavell

    Picower Institute for Learning and Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, United States
    Contribution
    Supervision, Investigation
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-9464-1877
  10. Paul W Glimcher

    1. Center for Neural Science, New York University, New York, United States
    2. Neuroscience Institute, New York University School of Medicine, New York, United States
    Contribution
    Supervision, Investigation, Writing – review and editing
    Competing interests
    No competing interests declared
  11. James Andreoni

    Department of Economics, University of California, San Diego, La Jolla, United States
    Contribution
    Formal analysis
    Competing interests
    No competing interests declared
  12. Shawn R Lockery

    Institute of Neuroscience, University of Oregon, Eugene, United States
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Methodology, Writing – original draft, Writing – review and editing
    For correspondence
    shawn.lockery@nemametrix.com
    Competing interests
    is co-founder and Chief Technology Officer of InVivo Biosystems, Inc, which manufactures instrumentation for recording electropharyngeograms
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8535-7989

Funding

National Institute of Mental Health (MH051383)

  • Shawn R Lockery

National Institute of General Medical Sciences (GM129576)

  • Shawn R Lockery

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This research was supported by MH051383 and GM129576 from the National Institutes of Health (SRL). We thank Mei Zhen for the GCaMP-6s::wCherry probe used in imaging experiments, Jonathan Millet for assistance, and Anastasia Levichev for comments on the manuscript.

Senior Editor

  1. Piali Sengupta, Brandeis University, United States

Reviewing Editor

  1. Manuel Zimmer, University of Vienna, Austria

Reviewer

  1. Doug Portman

Version history

  1. Preprint posted: April 26, 2021 (view preprint)
  2. Received: April 26, 2021
  3. Accepted: April 19, 2023
  4. Accepted Manuscript published: April 25, 2023 (version 1)
  5. Version of Record published: May 31, 2023 (version 2)

Copyright

© 2023, Katzen et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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  1. Abraham Katzen
  2. Hui-Kuan Chung
  3. William T Harbaugh
  4. Christina Della Iacono
  5. Nicholas Jackson
  6. Elizabeth E Glater
  7. Charles J Taylor
  8. Stephanie K Yu
  9. Steven W Flavell
  10. Paul W Glimcher
  11. James Andreoni
  12. Shawn R Lockery
(2023)
The nematode worm C. elegans chooses between bacterial foods as if maximizing economic utility
eLife 12:e69779.
https://doi.org/10.7554/eLife.69779

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https://doi.org/10.7554/eLife.69779

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