Broadly speaking, when an animal must choose between options, it can employ one of three different strategies, characterized by different levels of precision: random choice; following a heuristic or rule of thumb; or comparison of outcome value and choice for the highest. Traditional economic theory, exemplified by expected utility theory, assumes (human) decision-makers are rational and perform strict value-based choice (Mankiw, 2011). The now well-established field of behavioural economics has vigorously pushed back against this idea, demonstrating that humans often make decisions which are not fully logical, economically rational, or ‘optimal’ (Camerer et al., 2011; Tversky and Kahneman, 1974), even when actively comparing options.

A major insight lying at the heart of behavioural economics is that value is perceived. This can lead directly to deviations from optimality: between the acquisition of the information and the evaluation of possible outcomes, something gets lost in translation. As has been well established for over a century by the study of pyschophysics, perception is non-linear, usually on a logarithmic scale (Gescheider, 1997). Value perception for humans is likewise non-linear, as famously stated by Kahneman and Tversky, and extensively demonstrated thereafter (Camerer, 2004; Kahneman and Tversky, 1979). Moreover, humans weigh losses more strongly than gains. Finally, value is relative, usually to an expectation or some sort of anchor, see Figure 1.

Figure 1

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The non-linear nature of perceived value results in many behavioural biases, a very prominent one being the bundling vs. segregation effect. Crucial to the current experiment, the perceived value of a compound item or option can be changed by presenting it either as one option (bundling) or as multiple small parts (segregation). Due to diminishing returns, bundling results in a weaker total sensation than segregation – either lower value for positive value options or lower cost for negative value options (see Figure 1). This is because more of the sensation occurs on the shallow part of the curve. This fact is regularly exploited by consumer psychologists and marketing experts, for example by bundling option when selling new cars: when spending €50,000 on a new car, spending €51,000 for the model with included sound system might not be experienced as painfully costly, even if, considered by itself, €1000 might be more than most people are willing to spend on a sound system for a car. Bundling and segregation have been extensively studied by consumer psychologists (Johnson et al., 1999; Naylor and Frank, 2001; Noone and Mattila, 2009).

As in the study of human economics, non-human animals have been treated and modelled as rational economic agents, leading to deep insights into animal behaviour via the optimal foraging theory framework (Davies, 2012; Emlen, 1966; MacArthur and Pianka, 1966; Pyke et al., 1977). However, often inspired directly by behavioural economic research on humans, predictable deviations from optimality and rationality have been described (Zentall, 2015). For example, pigeons, rats, and ants all show a preference for high-effort over low-effort associated options (Clement et al., 2000; Czaczkes et al., 2018a; Lydall et al., 2010), much as humans do (Norton et al., 2012). Similarly, much as in humans, the addition of an irrelevant option in an option set (a ‘decoy’) can change the preference structure in many animals, including birds, cats, bees, and ants (Bateson et al., 2002; Bateson et al., 2003; Parrish et al., 2015a; Sasaki and Pratt, 2011; Scarpi, 2011; Schuck-Paim et al., 2004; Shafir et al., 2002).

Ants and bees also show relative value perception, changing the perceived value of an option depending on their expectations (Bitterman, 1976; Couvillon and Bitterman, 1984; Wendt et al., 2019; Wendt and Czaczkes, 2020). An ant which is trained to expect a very sweet reward, for example, will be more likely to reject a moderate reward than an ant which was expecting a moderate one – a negative contrast. Likewise, ants expecting a very mild reward are more likely to accept a moderate reward than ants which were expecting that quality – a positive contrast (Wendt et al., 2019). These changes are also mirrored in the ants’ deposition of recruitment pheromone: ants deposit more pheromone to resources they perceive as higher quality (Beckers et al., 1993; Jackson and Châline, 2007), and indeed ants deposit more pheromone for moderate rewards if they had been expected poor quality, and less pheromone if they were expecting high quality. This demonstrates that a key aspect of prospect theory – relative value perception – is present in insects as well as in humans.

Crucially for the current experiment, there is evidence that social insects, especially ants, perceive value logarithmically. This is perhaps not surprising, given than logarithmic perception is a key assumption of the well-established Weber-Fechner law (Fechner, 1860; Weber, 1834), which describes the psychophysics of perception. Wendt et al., 2019, demonstrated a faster rise in food acceptance in the lower range of acceptance food qualities (e.g. from 0.1 to 0.3 molar) than in the higher range (e.g. from 0.5 to 1.5 molar). Recently, De Agrò et al., 2021, demonstrated that Lasius niger ants have a strong aversion to risky food sources (i.e. with fluctuating quality), which could be fully explained by logarithmic value perception, as predicted by prospect theory. Ants prefer a certain food source offering 0.55 M sucrose to one which fluctuates between 0.1 and 1.0, but if the options are logarithmically balanced (0.3 M vs. 0.1 or 0.9), ants are completely indifferent.

While the bundling vs. segregation effect is extremely well studied in humans, surprisingly, to our knowledge no attempt has been made to examine it in animals. In a related study, chimps were shown to prefer whole rewards (potato chips) to rewards which were broken into smaller pieces, even when the broken rewards had an higher absolute quantity (Parrish et al., 2015b). However, consumption of the whole and broken rewards took the same amount of time, and rewards were chosen before consumption could begin, so it is likely that both broken and whole rewards were considered as one unitary bundle.

In order to study bundling and segregation in ants, we segregated rewards spatially, using small sucrose drops along a linear runway. However, while this segregates rewards, it also segregates a potential cost – the walking distance to the reward. Thus, we first demonstrate that ants do indeed prefer closer to farther food sources, and thus that food distance is considered a cost. We then train individual ants to two of three treatments: rewards and costs bundled (‘bundled’), rewards and costs segregated (‘segregated all’), and rewards segregated but costs bundled (‘segregated reward’). We record pheromone depositions on the ant’s return from each treatment type, and then ask ants to choose between the pair of treatments they were trained on. We predicted that the ‘segregated reward’ treatment would be the preferred option, as bundling of costs should minimize their impact, and segregation of rewards should boost theirs. As we did not know the relative strength of the rewards and costs, we had no strong a priori predictions about the relative perception of ‘bundled’ and ‘segregated all’. However, as prospect theory predicts that losses are weighted more strongly than gains (Kahneman and Tversky, 1979), we had a weak expectation that ‘bundled’ would be perceived as slightly better than ‘all segregated’.

Bundling and segregation treatment strongly affected the ants’ pheromone deposition, but not their choices. No consistent preference was found in the binary choices of the ants from the main study. While ants significantly preferred the segregated reward over the bundled reward in their second of three trials, we can conceive of no plausible biological or psychological reason for this to be so, and interpret this as a false positive. Thus, there is no evidence that bundling or segregation affect choice.

However, the pattern of pheromone deposition, which correlates strongly with perceived food quality in these and other ants (Beckers et al., 1993; Czaczkes et al., 2018b; Jackson and Châline, 2007; Wendt et al., 2019), was partially in line with our predictions: ants deposited most pheromone when the costs were bundled and rewards segregated, and less in the other two treatments (Figure 4). Our weaker prediction of ‘bundled’ presenting a higher deposition than ‘segregated all’ was also supported. Thus, pheromone deposition seems to be in line with predictions from classical behavioural economic and perception research (Camerer, 2004; Johnson et al., 1999; Kahneman and Tversky, 1979; Naylor and Frank, 2001; Noone and Mattila, 2009). Specifically, we observed more deposition for ‘bundled’ over ‘segregated all’, and for ‘segregated reward’ over ‘segregated all’. By contrast, the preference for ‘segregated reward’ over ‘bundled’ is not significant. This seems counter-intuitive, as the ‘bundled’ and ‘segregated reward’ options only differ in the boosting of a gain. Moreover, the contrast of ‘segregated all’ vs. ‘bundled’ – for which we had no strong a priori prediction as we had no idea how gains and losses are weighted – shows a very clear difference.

The observed result suggests two, non-mutually exclusive, interpretations: Either ants experience a strong segregation effect for losses, and a very mild one, if any, for gains; or our treatment failed to segregate rewards effectively. If the first interpretation is true, the ‘bundled’ and the ‘segregated reward’ treatments will be perceived as almost identical. In the contrast between ‘segregated all’ and ‘bundled’, the higher number of depositions for bundled makes sense, as the segregation of losses drives the preference completely. The higher deposition for ‘segregated reward’ over ‘segregated all’ remains equally clear, as the two options only differ in the realm of losses. If our second interpretation is correct, the three sucrose solution drops, especially in the ‘segregated reward’ condition, are still considered by the animal as a single (i.e. bundled) reward. In the ‘segregated all’ condition the separation between rewards seems more believable, however the results observed strongly suggest that the reward segregation have a very low effect on the perceived value, being overridden by the segregation of losses. It is impossible to disentangle these two options from the current data.

However, the pattern is somewhat more complicated, as we saw large differences in pheromone deposition for the same treatment, depending on the treatments they were paired with. For example, while ants encountering the ‘segregated rewards’ deposit twice as much pheromone as ‘segregated all’ when they are paired, for ‘segregated rewards’ they deposit much less than when paired with the ‘bundled’ treatment (see Figure 4). A similar pattern is seen with ‘bundled’, where more pheromone is deposited when paired with ‘segregated all’ and less when paired with ‘segregated reward’. One possibility is that these differences arise due to a series of contrast effects. This pattern is further complicated by a strong effect of first encountered treatment (see Figure 5). In every condition the effects strengthen when the preferred option is presented first, and drops to chance level when presented second. This suggest that the bias generated through the bundling process has a similar strength to the bias for the first experienced odour (Oberhauser, 2019), and thus they appear to counterbalance each other.

Bundling and segregation of options to modify perceived value in insects may have ecological implications, especially in plant-pollinator interactions. If, by segregation, the perceived value of a reward can be increased, plants may be selected to split rewards amongst multiple smaller flowers in an inflorescence, or flowers on a plant. Similarly, they may be selected to attempt to bundle costs, favouring multi-flower inflorescences, allowing insects to walk between flowers, over multiple small, separate flowers.

The finding that bundling and segregation affect ant value perception adds this behavioural economic effect to several others which have also been shown to affect perceived value in insects, including decoy effects (Sasaki and Pratt, 2011; Shafir et al., 2002; Tan et al., 2015), invested effort increasing perceived value (Czaczkes et al., 2018a), relative value perception (Bitterman, 1976; Couvillon and Bitterman, 1984; Wendt et al., 2019), and labelling effects (Hemingway and Muth, 2022; Wendt and Czaczkes, 2020). It is becoming clear that the underlying patterns driving value perception in insects are in many ways parallel to those of humans. This implies either an extremely early evolutionary origin of shared perceptual mechanisms resulting in shared psychophysical laws or convergent evolution on similarly effective systems. The finding of a bundling and segregation effect, alongside the way in which insects respond to differences between experienced and expected rewards, strongly implies that insects share the same broad value function shape as humans (see Figure 1). Thus, we would predict that any other behavioural economic effects in humans, which arise from this value function, to also be present in insects. Still missing is a demonstration of an inflection point – that is, like in humans, losses loom larger than gains for insects. That our results imply bundling to more strongly influence losses than gain (see above) suggests this is the case, but formal testing will be required.

The absence of a significant preference in the Y-maze test, contrasted with the clear effect appreciable in the pheromone deposition, is puzzling. We have to consider the possibility that processes often assumed to be tightly linked to each other are instead separate. In this specific case, choice in the Y-maze depends on memory formation, as the choice is made by mentally comparing two options previously experienced. Pheromone deposition instead happens immediately after experience, and does not require any mental comparison to be expressed.

It is possible that ants have simply failed to associate each odour with the reward treatment, and thus chooses randomly in the Y-maze. This seems highly unlikely, as many examples of similar experiments on the same species are available in the literature, where ants are demonstrated to be extremely capable learners, learning even complex multimodal associations with fewer exposures than used in the current study (Czaczkes and Kumar, 2020; De Agrò et al., 2020).

The most likely explanation to us is that while a difference in the value of options is perceived, the same difference is not recorded during memory formation. Scalar utility theory (Kacelnik and Brito e Abreu, 1998; Rosenström et al., 2016) is an influential framework that has been developed to describe decision making under uncertainty. This theory postulates that encoding neurons, responsible for the internal representation of values (i.e. quantity, quality, delay, etc.), have logarithmically spaced sensitivities and specificities. Prospect theory (see Introduction) also assumes a process based on a logarithmic function. Thus, both make very similar behavioural predictions, even though one concentrates on value perception, and the other on memory acquisition. However, they do not have to be identical. Most experiments recording both pheromone deposition and subsequent choice use food quality as the measured unit (De Agrò et al., 2021; Oberhauser and Czaczkes, 2018; Wendt et al., 2019). Logarithmic perception of quality is probably the reason a mismatch between choice and instantaneous value perception has eluded discovery. We believe that the mismatch produced in this experiment has to do with the type of cost chosen as treatment: distance travelled. As previously mentioned, our treatment seemed unable to produce a segregation effect for the reward, while showing a strong segregation effect for losses, that is, the travelled distance. It is reasonable to assume that ants perceive value logarithmically, in accordance with prospect theory (De Agrò et al., 2021). In other words, the overall perception of the experience is affected by the artefacts of a log curve, segregation effect included (see Figure 1). Being produced instantaneously, pheromone deposition is likely linked to this information stream. However, when registering distances in memory ants need to be extremely precise. They possess an internal step counter and a visual odometer, which allows them to judge distances and return successfully to the nest (Narendra, 2007; Wittlinger et al., 2006). Encoding steps logarithmically would be absolutely insufficient for accurate homing, given the need to already cope with errors introduced in the path integration process (Merkle et al., 2006; Merkle and Wehner, 2010; Müller and Wehner, 1988; Schwarz et al., 2011). For this, a linear, 1:1 correspondence is required. It is possible that distance is memorized linearly and in a separated stream from the value perception. When asked to choose, the ant can only compare the two memories of distances, which due to their linear nature are immune to the segregation effect (Figure 6). If the ant odometer truly is a rare example of linear perception, it would be an invaluable system for investigating information processing in insects, as it allows the roles of perception and post-perceptual processing to be disentangled.

Figure 6

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The dissociation between immediate reaction and subsequent choice could also be explained by a separation between ‘liking’ and ‘wanting’. The duality between ‘liking’ and ‘wanting’, first described in rats (Berridge et al., 1989) and then confirmed extensively in humans (Brauer and De Wit, 1997; Leyton et al., 2002; Pool et al., 2015), distinguishes two aspects of reward. ‘Liking’ refers to acutely perceived hedonic reactions, while ‘wanting’ refers to motivation and desire for a goal. While ‘liking’ and ‘wanting’ usually co-vary, these are neurologically separate processes, and can, in vertebrates, be separately inactivated (Berridge et al., 1989) or enhanced (Berridge and Valenstein, 1991; Leyton et al., 2002; Treit and Berridge, 1990). A dedicated network for ‘wanting’ has been recently discovered in insects as well (Garcia and Dyer, 2022; Huang et al., 2022), making it very likely to be present in L. niger ants as well. Under this perspective, the immediate reaction to experiencing the reward (i.e. the pheromone deposited) may correspond to how much the animal ‘liked’ each option. The choice of which reward to head for in the Y-maze task may reflect how much ‘wants’ either option. However, neurological evidence would be required to support this speculation. Moreover, further experiments should test whether pheromone deposition and binary choice are indeed appropriate proxies of ‘liking’ and ‘wanting’, respectively.

Our work also demonstrates empirically that individual ants prefer near to distant food sources. Such a preference have been previously observed in nature (Frank and Linsenmair, 2017; Nyamukondiwa and Addison, 2014) but never directly tested. Ants also recruited significantly more to closer food source, as reported in this and other ant species as well (Devigne and Detrain, 2006; Fewell et al., 1992).

This study adds the bundling and segregation effect to the collection of value-distorting effects from behavioural economics which also affect animal value perception. Critically, by finding this effect in an invertebrate, we demonstrate that the complexities of the vertebrate brain are not required for these effects to manifest. Animal behaviour, much like human behaviour, can often be modelled as a value-maximizing system. However, deviations for strict economic rationality, such as the one demonstrated here, may play important roles in the animals’ ecology, especially in their foraging behaviour and biotic interactions.

Raw data collected in the experiments and used for the analysis are available in Source data 1.

1. 1. Bateson M
   2. Healy SD
   3. Hurly TA

   (2002) Irrational choices in hummingbird foraging behaviour

   Animal Behaviour 63:587–596.

   https://doi.org/10.1006/anbe.2001.1925

   • Google Scholar
2. 1. Bateson M
   2. Healy SD
   3. Hurly TA

   (2003) Context-Dependent foraging decisions in rufous hummingbirds

   Proceedings. Biological Sciences 270:1271–1276.

   https://doi.org/10.1098/rspb.2003.2365

   • PubMed
   • Google Scholar
3. 1. Beckers R
   2. Deneubourg JL
   3. Goss S

   (1992) Trails and U-turns in the selection of a path by the ant Lasius niger

   Journal of Theoretical Biology 159:397–415.

   https://doi.org/10.1016/S0022-5193(05)80686-1

   • Google Scholar
4. 1. Beckers R
   2. Deneubourg JL
   3. Goss S

   (1993) Modulation of TRAIL laying in the antlasius niger (Hymenoptera: Formicidae) and its role in the collective selection of a food source

   Journal of Insect Behavior 6:751–759.

   https://doi.org/10.1007/BF01201674

   • Google Scholar
5. 1. Ben-Shachar MS
   2. Lüdecke D
   3. Makowski D

   (2020) Effectsize: estimation of effect size indices and standardized parameters

   Journal of Open Source Software 5:2815.

   https://doi.org/10.21105/joss.02815

   • Google Scholar
6. 1. Berridge KC
   2. Venier IL
   3. Robinson TE

   (1989) Taste reactivity analysis of 6-hydroxydopamine-induced aphagia: implications for arousal and anhedonia hypotheses of dopamine function

   Behavioral Neuroscience 103:36–45.

   https://doi.org/10.1037//0735-7044.103.1.36

   • PubMed
   • Google Scholar
7. 1. Berridge KC
   2. Valenstein ES

   (1991) What psychological process mediates feeding evoked by electrical stimulation of the lateral hypothalamus?

   Behavioral Neuroscience 105:3–14.

   https://doi.org/10.1037//0735-7044.105.1.3

   • PubMed
   • Google Scholar
8. 1. Bitterman ME

   (1976) Incentive contrast in honey bees

   Science 192:380–382.

   https://doi.org/10.1126/science.1257773

   • PubMed
   • Google Scholar
9. 1. Brauer LH
   2. De Wit H

   (1997) High dose pimozide does not block amphetamine-induced euphoria in normal volunteers

   Pharmacology, Biochemistry, and Behavior 56:265–272.

   https://doi.org/10.1016/s0091-3057(96)00240-7

   • PubMed
   • Google Scholar
10. 1. Brooks M
    2. Kristensen K
    3. Benthem K
    4. Magnusson A
    5. Berg C
    6. Nielsen A
    7. Skaug H
    8. Mächler M
    9. Bolker B

    (2017) GlmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling

    The R Journal 9:378.

    https://doi.org/10.32614/RJ-2017-066

    • Google Scholar
11. 1. Camerer CF

    (2004)

    Advances in Behavioral Economics, The Roundtable Series in Behavioral Economics

    148–161, Prospect theory in the wild: evidence from the field, Advances in Behavioral Economics, The Roundtable Series in Behavioral Economics, New York, Princeton University Press.

    • Google Scholar
12. Book

    1. Camerer CF
    2. Loewenstein G
    3. Rabin M

    (2011) Advances in Behavioral Economics

    Princeton University Press.

    https://doi.org/10.2307/j.ctvcm4j8j

    • Google Scholar
13. 1. Clement TS
    2. Feltus JR
    3. Kaiser DH
    4. Zentall TR

    (2000) “ work ethic ” in pigeons: reward value is directly related to the effort or time required to obtain the reward

    Psychonomic Bulletin & Review 7:100–106.

    https://doi.org/10.3758/bf03210727

    • PubMed
    • Google Scholar
14. 1. Couvillon PA
    2. Bitterman ME

    (1984)

    The overlearning-extinction effect and successive negative contrast in honeybees (apis mellifera)

    Journal of Comparative Psychology 98:100–109.

    • PubMed
    • Google Scholar
15. 1. Czaczkes TJ
    2. Brandstetter B
    3. di Stefano I
    4. Heinze J

    (2018a) Greater effort increases perceived value in an invertebrate

    Journal of Comparative Psychology 132:200–209.

    https://doi.org/10.1037/com0000109

    • PubMed
    • Google Scholar
16. 1. Czaczkes TJ
    2. Koch A
    3. Fröber K
    4. Dreisbach G

    (2018b) Voluntary switching in an invertebrate: the effect of cue and reward change

    Journal of Experimental Psychology. Animal Learning and Cognition 44:247–257.

    https://doi.org/10.1037/xan0000171

    • PubMed
    • Google Scholar
17. 1. Czaczkes TJ

    (2018c) Using T- and Y-mazes in myrmecology and elsewhere: a practical guide

    Insectes Sociaux 65:213–224.

    https://doi.org/10.1007/s00040-018-0621-z

    • Google Scholar
18. 1. Czaczkes TJ
    2. Beckwith JJ
    3. Horsch AL
    4. Hartig F

    (2019) The multi-dimensional nature of information drives prioritization of private over social information in ants

    Proceedings. Biological Sciences 286:20191136.

    https://doi.org/10.1098/rspb.2019.1136

    • PubMed
    • Google Scholar
19. 1. Czaczkes T.J
    2. Kumar P

    (2020) Very rapid multi-odour discrimination learning in the ant Lasius niger

    Insectes Sociaux 67:541–545.

    https://doi.org/10.1007/s00040-020-00787-0

    • Google Scholar
20. Book

    1. Davies NB

    (2012)

    An Introduction to Behavioural Ecology

    Oxford; Hoboken, NJ: Wiley-Blackwell.

    • Google Scholar
21. 1. De Agrò M
    2. Oberhauser FB
    3. Loconsole M
    4. Galli G
    5. Dal Cin F
    6. Moretto E
    7. Regolin L

    (2020) Multi-Modal cue integration in the black garden ant

    Animal Cognition 23:1119–1127.

    https://doi.org/10.1007/s10071-020-01360-9

    • PubMed
    • Google Scholar
22. 1. De Agrò M
    2. Grimwade D
    3. Bach R
    4. Czaczkes TJ

    (2021) Irrational risk aversion in an ant

    Animal Cognition 24:1237–1245.

    https://doi.org/10.1007/s10071-021-01516-1

    • PubMed
    • Google Scholar
23. 1. Devigne C
    2. Detrain C

    (2006) How does food distance influence foraging in the ant Lasius niger: the importance of home-range marking

    Insectes Sociaux 53:46–55.

    https://doi.org/10.1007/s00040-005-0834-9

    • Google Scholar
24. 1. Emlen JM

    (1966) The role of time and energy in food preference

    The American Naturalist 100:611–617.

    https://doi.org/10.1086/282455

    • Google Scholar
25. 1. Evison SEF
    2. Petchey OL
    3. Beckerman AP
    4. Ratnieks FLW

    (2008) Combined use of pheromone trails and visual landmarks by the common garden ant Lasius niger

    Behavioral Ecology and Sociobiology 63:261–267.

    https://doi.org/10.1007/s00265-008-0657-6

    • Google Scholar
26. Book

    1. Fechner GT.

    (1860)

    Elemente der psychophysik

    Leipzig: Breitkopf und Härtel.

    • Google Scholar
27. 1. Fewell JH
    2. Harrison JF
    3. Stiller TM
    4. Breed MD

    (1992) Distance effects on resource profitability and recruitment in the giant tropical ant, paraponera clavata

    Oecologia 92:542–547.

    https://doi.org/10.1007/BF00317846

    • PubMed
    • Google Scholar
28. Book

    1. Fox J
    2. Weisberg S.

    (2011)

    An R Companion to Applied Regression (Second. ed)

    Thousand Oaks CA: Sage.

    • Google Scholar
29. 1. Frank ET
    2. Linsenmair KE

    (2017) Individual versus collective decision making: optimal foraging in the group-hunting termite specialist megaponera analis

    Animal Behaviour 130:27–35.

    https://doi.org/10.1016/j.anbehav.2017.06.010

    • Google Scholar
30. 1. Garcia JE
    2. Dyer AG

    (2022) Why do animals want what they like?

    Science 376:456–457.

    https://doi.org/10.1126/science.abp8609

    • PubMed
    • Google Scholar
31. Book

    1. Gescheider GA.

    (1997)

    Psychophysics: The Fundamentals, Auflage (Revised. ed)

    Mahwah, N.J: Lawrence Erlbaum Assoc Inc.

    • Google Scholar
32. Website

    1. Hartig F

    (2018) DHARMa: Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models

    Accessed September 8, 2022.

    https://cran.r-project.org/web/packages/DHARMa/vignettes/DHARMa.html
33. 1. Hemingway CT
    2. Muth F

    (2022) Label-Based expectations affect incentive contrast effects in bumblebees

    Biology Letters 18:20210549.

    https://doi.org/10.1098/rsbl.2021.0549

    • PubMed
    • Google Scholar
34. 1. Huang J
    2. Zhang Z
    3. Feng W
    4. Zhao Y
    5. Aldanondo A
    6. de Brito Sanchez MG
    7. Paoli M
    8. Rolland A
    9. Li Z
    10. Nie H
    11. Lin Y
    12. Zhang S
    13. Giurfa M
    14. Su S

    (2022) Food wanting is mediated by transient activation of dopaminergic signaling in the honey bee brain

    Science 376:508–512.

    https://doi.org/10.1126/science.abn9920

    • PubMed
    • Google Scholar
35. 1. Hunter JD

    (2007) Matplotlib: a 2D graphics environment

    Computing in Science & Engineering 9:90–95.

    https://doi.org/10.1109/MCSE.2007.55

    • Google Scholar
36. 1. Jackson DE
    2. Châline N

    (2007) Modulation of pheromone TRAIL strength with food quality in Pharaoh’s ant, monomorium pharaonis

    Animal Behaviour 74:463–470.

    https://doi.org/10.1016/j.anbehav.2006.11.027

    • Google Scholar
37. 1. Johnson MD
    2. Herrmann A
    3. Bauer HH

    (1999) The effects of price bundling on consumer evaluations of product offerings

    International Journal of Research in Marketing 16:129–142.

    https://doi.org/10.1016/S0167-8116(99)00004-X

    • Google Scholar
38. 1. Kacelnik A
    2. Brito e Abreu F

    (1998) Risky choice and Weber’s law

    Journal of Theoretical Biology 194:289–298.

    https://doi.org/10.1006/jtbi.1998.0763

    • PubMed
    • Google Scholar
39. 1. Kahneman D
    2. Tversky A

    (1979) Prospect theory: an analysis of decision under risk

    Econometrica 47:263.

    https://doi.org/10.2307/1914185

    • Google Scholar
40. 1. Lakens D

    (2022) Sample size justification

    Collabra 8:33267.

    https://doi.org/10.1525/collabra.33267

    • Google Scholar
41. 1. Lakshminarayanan VR
    2. Chen MK
    3. Santos LR

    (2011) The evolution of decision-making under risk: framing effects in monkey risk preferences

    Journal of Experimental Social Psychology 47:689–693.

    https://doi.org/10.1016/j.jesp.2010.12.011

    • Google Scholar
42. 1. Lenth C
    2. Ctistis G
    3. Plachetka U
    4. Möller M
    5. Wackerbarth H

    (2020) Emmeans: estimated marginal means, aka least-squares means

    Scientific Reports 10:8260.

    https://doi.org/10.1038/s41598-020-65181-z

    • PubMed
    • Google Scholar
43. 1. Leyton M
    2. Boileau I
    3. Benkelfat C
    4. Diksic M
    5. Baker G
    6. Dagher A

    (2002) Amphetamine-Induced increases in extracellular dopamine, drug wanting, and novelty seeking: a PET/ [ 11C ] raclopride study in healthy men

    Neuropsychopharmacology 27:1027–1035.

    https://doi.org/10.1016/S0893-133X(02)00366-4

    • PubMed
    • Google Scholar
44. 1. Lydall ES
    2. Gilmour G
    3. Dwyer DM

    (2010) Rats place greater value on rewards produced by high effort: an animal analogue of the “ effort Justification ” effect

    Journal of Experimental Social Psychology 46:1134–1137.

    https://doi.org/10.1016/j.jesp.2010.05.011

    • Google Scholar
45. 1. MacArthur RH
    2. Pianka ER

    (1966) On optimal use of a patchy environment

    The American Naturalist 100:603–609.

    https://doi.org/10.1086/282454

    • Google Scholar
46. Software

    1. Magnusson A
    2. Skaug H
    3. Nielsen A
    4. Berg C
    5. Kristensen K
    6. Maechler M
    7. van BK
    8. Bolker B
    9. Sadat N
    10. Lüdecke D
    11. Lenth R
    12. O’Brien J
    13. Brooks M

    (2020)

    Generalized linear mixed models using template model builder, version V 2.0.2

    GlmmTMB.
47. 1. Mailleux AC
    2. Deneubourg JL
    3. Detrain C

    (2000) How do ants assess food volume?

    Animal Behaviour 59:1061–1069.

    https://doi.org/10.1006/anbe.2000.1396

    • PubMed
    • Google Scholar
48. 1. Mailleux AC
    2. Detrain C
    3. Deneubourg JL

    (2005) Triggering and persistence of trail-laying in foragers of the ant Lasius niger

    Journal of Insect Physiology 51:297–304.

    https://doi.org/10.1016/j.jinsphys.2004.12.001

    • PubMed
    • Google Scholar
49. 1. Mailleux A-C
    2. Detrain C
    3. Deneubourg J-L

    (2006) Starvation drives a threshold triggering communication

    The Journal of Experimental Biology 209:4224–4229.

    https://doi.org/10.1242/jeb.02461

    • PubMed
    • Google Scholar
50. Book

    1. Mankiw NG.

    (2011)

    Principles of Economics (International ed of 6th revised ed edition. ed)

    Mason, OH: South-Western.

    • Google Scholar
51. 1. Merkle T
    2. Knaden M
    3. Wehner R

    (2006) Uncertainty about nest position influences systematic search strategies in desert ants

    The Journal of Experimental Biology 209:3545–3549.

    https://doi.org/10.1242/jeb.02395

    • PubMed
    • Google Scholar
52. 1. Merkle T
    2. Wehner R

    (2010) Desert ants use foraging distance to adapt the nest search to the uncertainty of the path integrator

    Behavioral Ecology 21:349–355.

    https://doi.org/10.1093/beheco/arp197

    • Google Scholar
53. 1. Müller M
    2. Wehner R

    (1988) Path integration in desert ants, cataglyphis fortis

    PNAS 85:5287–5290.

    https://doi.org/10.1073/pnas.85.14.5287

    • PubMed
    • Google Scholar
54. 1. Narendra A

    (2007) Homing strategies of the Australian desert ant melophorus bagoti. I. proportional path-integration takes the ant half-way home

    The Journal of Experimental Biology 210:1798–1803.

    https://doi.org/10.1242/jeb.02768

    • PubMed
    • Google Scholar
55. 1. Naylor G
    2. Frank KE

    (2001) The effect of price bundling on consumer perceptions of value

    Journal of Services Marketing 15:270–281.

    https://doi.org/10.1108/EUM0000000005506

    • Google Scholar
56. 1. Noone BM
    2. Mattila AS

    (2009) Hotel revenue management and the Internet: the effect of price presentation strategies on customers’ willingness to book

    International Journal of Hospitality Management 28:272–279.

    https://doi.org/10.1016/j.ijhm.2008.09.004

    • Google Scholar
57. 1. Norton MI
    2. Mochon D
    3. Ariely D

    (2012) The IKEA effect: when labor leads to love

    Journal of Consumer Psychology 22:453–460.

    https://doi.org/10.1016/j.jcps.2011.08.002

    • Google Scholar
58. 1. Nyamukondiwa C
    2. Addison P

    (2014) Food preference and foraging activity of ants: recommendations for field applications of low-toxicity baits

    Journal of Insect Science 14:48.

    https://doi.org/10.1093/jis/14.1.48

    • PubMed
    • Google Scholar
59. 1. Oberhauser FB
    2. Czaczkes TJ

    (2018) Tasting the unexpected: disconfirmation of expectations leads to lower perceived food value in an invertebrate

    Biology Letters 14:20180440.

    https://doi.org/10.1098/rsbl.2018.0440

    • PubMed
    • Google Scholar
60. 1. Oberhauser FB
    2. Koch A
    3. Czaczkes TJ

    (2018) Small differences in learning speed for different food qualities can drive efficient collective foraging in ant colonies

    Behavioral Ecology and Sociobiology 72:1096.

    https://doi.org/10.1007/s00265-018-2583-6

    • Google Scholar
61. Thesis

    1. Oberhauser FB

    (2019)

    Individual cognition and collective behaviour in ants

    Springer.

    • Google Scholar
62. Book

    1. Oliphant TE.

    (2006)

    A guide to NumPy

    Trelgol Publishing USA.

    • Google Scholar
63. 1. Parrish AE
    2. Evans TA
    3. Beran MJ

    (2015a) Defining value through quantity and quality-chimpanzees (pan troglodytes) undervalue food quantities when items are broken

    Behavioural Processes 111:118–126.

    https://doi.org/10.1016/j.beproc.2014.11.004

    • PubMed
    • Google Scholar
64. 1. Parrish AE
    2. Evans TA
    3. Beran MJ

    (2015b) Rhesus macaques (macaca mulatta) exhibit the decoy effect in a perceptual discrimination task

    Attention, Perception & Psychophysics 77:1715–1725.

    https://doi.org/10.3758/s13414-015-0885-6

    • PubMed
    • Google Scholar
65. 1. Pool E
    2. Brosch T
    3. Delplanque S
    4. Sander D

    (2015) Stress increases cue-triggered “ wanting ” for sweet reward in humans

    Journal of Experimental Psychology. Animal Learning and Cognition 41:128–136.

    https://doi.org/10.1037/xan0000052

    • PubMed
    • Google Scholar
66. 1. Pyke GH
    2. Pulliam HR
    3. Charnov EL

    (1977) Optimal foraging: a selective review of theory and tests

    The Quarterly Review of Biology 52:137–154.

    https://doi.org/10.1086/409852

    • Google Scholar
67. Software

    1. R Development Core Team

    (2020) R: A language and environment for statistical computing, version 1.1.1

    R Foundation for Statistical Computing, Vienna, Austria.

    http://www.r-project.org
68. Software

    1. Reback J
    2. McKinney W
    3. jbrockmendel JDB
    4. Augspurger T
    5. Cloud P
    6. gfyoung S
    7. Klein A
    8. Roeschke M
    9. Hawkins S
    10. Tratner J
    11. She C
    12. Ayd W
    13. Petersen T
    14. Garcia M
    15. Schendel J
    16. Hayden A
    17. MomIsBestFriend VJ

    (2020) Pandas-dev/pandas, version 1.5.1

    Github.

    https://github.com/pandas-dev/pandas
69. 1. Rosenström T
    2. Wiesner K
    3. Houston AI

    (2016) Scalar utility theory and proportional processing: what does it actually imply?

    Journal of Theoretical Biology 404:222–235.

    https://doi.org/10.1016/j.jtbi.2016.06.003

    • PubMed
    • Google Scholar
70. 1. Sasaki T
    2. Pratt SC

    (2011) Emergence of group rationality from irrational individuals

    Behavioral Ecology 22:276–281.

    https://doi.org/10.1093/beheco/arq198

    • Google Scholar
71. 1. Scarpi D

    (2011) The impact of phantom decoys on choices in cats

    Animal Cognition 14:127–136.

    https://doi.org/10.1007/s10071-010-0350-9

    • PubMed
    • Google Scholar
72. 1. Schuck-Paim C
    2. Pompilio L
    3. Kacelnik A

    (2004) State-dependent decisions cause apparent violations of rationality in animal choice

    PLOS Biology 2:e402.

    https://doi.org/10.1371/journal.pbio.0020402

    • PubMed
    • Google Scholar
73. Software

    1. Schutten GJ
    2. Chan C
    3. Leeper TJ
    4. Foster J

    (2020)

    Read and write ODS files., contributors and other, version 1.1.1

    ReadODS.
74. 1. Schwarz S
    2. Wystrach A
    3. Cheng K

    (2011) A new navigational mechanism mediated by ant ocelli

    Biology Letters 7:856–858.

    https://doi.org/10.1098/rsbl.2011.0489

    • PubMed
    • Google Scholar
75. 1. Shafir S
    2. Waite TA
    3. Smith BH

    (2002) Context-Dependent violations of rational choice in honeybees (Apis mellifera) and gray jays (perisoreus canadensis)

    Behavioral Ecology and Sociobiology 51:180–187.

    https://doi.org/10.1007/s00265-001-0420-8

    • Google Scholar
76. 1. Tan K
    2. Dong S
    3. Liu X
    4. Chen W
    5. Wang Y
    6. Oldroyd BP
    7. Latty T

    (2015) Phantom alternatives influence food preferences in the eastern honeybee Apis cerana

    The Journal of Animal Ecology 84:509–517.

    https://doi.org/10.1111/1365-2656.12288

    • PubMed
    • Google Scholar
77. 1. Treit D
    2. Berridge KC

    (1990) A comparison of benzodiazepine, serotonin, and dopamine agents in the taste-reactivity paradigm

    Pharmacology, Biochemistry, and Behavior 37:451–456.

    https://doi.org/10.1016/0091-3057(90)90011-6

    • PubMed
    • Google Scholar
78. 1. Tversky A
    2. Kahneman D

    (1974) Judgment under uncertainty: heuristics and biases

    Science 185:1124–1131.

    https://doi.org/10.1126/science.185.4157.1124

    • PubMed
    • Google Scholar
79. 1. Tversky A
    2. Kahneman D

    (1981) The framing of decisions and the psychology of choice

    Science 211:453–458.

    https://doi.org/10.1126/science.7455683

    • PubMed
    • Google Scholar
80. Software

    1. Ushey K
    2. Allaire JJ
    3. Tang Y

    (2021) Reticulate: interface to “Python, version 2.0

    Github.

    https://rstudio.github.io/reticulate/
81. 1. van der Walt S
    2. Colbert SC
    3. Varoquaux G

    (2011) The numpy array: a structure for efficient numerical computation

    Computing in Science & Engineering 13:22–30.

    https://doi.org/10.1109/MCSE.2011.37

    • Google Scholar
82. Book

    1. Van Rossum G
    2. Drake FL.

    (2009)

    Python 3 Reference Manual

    Scotts Valley, CA: CreateSpace.

    • Google Scholar
83. Software

    1. Waskom M
    2. Botvinnik O
    3. O’Kane D
    4. Hobson P
    5. Lukauskas S
    6. Gemperline DC
    7. Augspurger T
    8. Halchenko Y
    9. Cole JB
    10. Warmenhoven J
    11. Pye C
    12. Hoyer S
    13. Vanderplas J
    14. Villalba S
    15. Kunter G
    16. Quintero E
    17. Bachant P
    18. Martin M
    19. Meyer K
    20. Miles A
    21. Ram Y
    22. Yarkoni T
    23. Williams ML
    24. Evans C
    25. Fitzgerald C
    26. Brian FC
    27. Lee A
    28. Qalieh A

    (2017) Mwaskom/seaborn, version v0.8.1

    Zenodo.

    https://doi.org/10.5281/zenodo.883859
84. Book

    1. Weber

    (1834)

    De Pulsu Resorptione Auditu et Tactu. Annotationes Anatomicae et Physiologicae

    C.F. Koehler, Lipsiae.

    • Google Scholar
85. 1. Wendt S
    2. Strunk KS
    3. Heinze J
    4. Roider A
    5. Czaczkes TJ

    (2019) Positive and negative incentive contrasts lead to relative value perception in ants

    eLife 8:e45450.

    https://doi.org/10.7554/eLife.45450

    • PubMed
    • Google Scholar
86. 1. Wendt S
    2. Czaczkes TJ

    (2020) Labeling effect in insects: cue associations influence perceived food value in ants (lasius niger)

    Journal of Comparative Psychology 134:280–292.

    https://doi.org/10.1037/com0000212

    • PubMed
    • Google Scholar
87. 1. Wickham H

    (2007) Reshaping data with the reshape package

    Journal of Statistical Software 21:1–20.

    https://doi.org/10.18637/jss.v021.i12

    • Google Scholar
88. 1. Wittlinger M
    2. Wehner R
    3. Wolf H

    (2006) The ant odometer: stepping on stilts and stumps

    Science 312:1965–1967.

    https://doi.org/10.1126/science.1126912

    • PubMed
    • Google Scholar
89. 1. Zentall TR

    (2015) When animals misbehave: analogs of human biases and suboptimal choice

    Behavioural Processes 112:3–13.

    https://doi.org/10.1016/j.beproc.2014.08.001

    • PubMed
    • Google Scholar

Author details

1. Massimo De Agrò

   1. Animal Comparative Economics laboratory, Department of Zoology, University of Regensburg, Regensburg, Germany
   2. Department of Biology, University of Florence, Florence, Italy

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Supervision, Visualization, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   massimo.deagro@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9284-5964

2. Chiara Matschunas

   Animal Comparative Economics laboratory, Department of Zoology, University of Regensburg, Regensburg, Germany

   Contribution

   Investigation, Methodology, Writing – review and editing

   Competing interests

   No competing interests declared

3. Tomer J Czaczkes

   Animal Comparative Economics laboratory, Department of Zoology, University of Regensburg, Regensburg, Germany

   Contribution

   Conceptualization, Supervision, Funding acquisition, Investigation, Writing – original draft, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

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