Living in a group has clear benefits, including expansion of sensory sensitivity (Miller and Bassler, 2001; Pratt et al., 2002; Berdahl et al., 2013; Ward et al., 2011), sharing of responsibilities and resources (Clutton-Brock et al., 1999; McGowan and Woolfenden, 1989; Chittka and Muller, 2009), collective computation (Miller and Bassler, 2001; Pratt et al., 2002; Berdahl et al., 2013; Ward et al., 2011; Karpas et al., 2017; Shklarsh et al., 2011; Ward et al., 2012), and the potential for symbiotic relations between members that would allow for specialization by individual members (Chittka and Muller, 2009; Gordon, 1996). Understanding the interactions among individuals that give rise to macroscopic behavior of groups is therefore central to the study and analysis of collective behavior in animal groups and other biological systems.

Group foraging is a prominent example of collective behavior, and social interactions among members have been suggested to increase foraging efficiency (Pitcher, 1986; Radakov, 1973; Giraldeau and Caraco, 2000; Zahavi, 1971; Brown, 1988; Pitcher et al., 1982) by allowing individuals to combine private and social information about the location of resources and their quality (see however (Laland and Williams, 1998; Giraldeau et al., 2002) for adverse effects of social information). Theoretical models have been used to study social foraging using various strategies, including producer-scrounger dynamics (Barnard and Sibly, 1981) and the use of 'public' information (Clark and Mangel, 1984; Bhattacharya and Vicsek, 2014; Valone, 1989). These models explored the efficiency of the underlying strategies and their evolutionary stability, as well as the effects of group composition and the distribution of resources (Barnard and Sibly, 1981; Bhattacharya and Vicsek, 2014; Tania et al., 2012; Torney et al., 2011; Clark and Mangel, 1986; Hein et al., 2016). Experimental work, in the field and in the lab, aimed to identify interactions between foraging individuals (Ward et al., 2012; Coolen et al., 2001; Harel et al., 2017; Krebs, 1974; Flemming et al., 1992; Miller et al., 2013) and their dependence on factors such as the distribution of resources, phenotypic diversity among foragers, animal personality, and foraging strategies of mixed species (Ryer and Olla, 1995; Farine et al., 2014; Michelena et al., 2009; Aplin et al., 2014; Jolles et al., 2017). The interaction rules studied with these theoretical models and the emerging group behavior had mostly qualitative correspondence to that of real groups, as the predictions of theoretical models were usually not tested against experimental data of groups at the individual level (Barnard and Sibly, 1981; Martínez-García et al., 2013; Hamilton and Dill, 2003; Mottley and Giraldeau, 2000; Giraldeau and Beauchamp, 1999).

Moreover, most models studying how schooling or flocking may improve foraging efficiency have explored the case of single sources, or clumped food patches (Karpas et al., 2017; Shklarsh et al., 2011; Ward et al., 2012; Hein et al., 2016; Miller et al., 2013; Aplin et al., 2014; Jolles et al., 2017). Yet, in many real-world situations, animals are likely to encounter distributed food sources, where maintaining a tight group may not be beneficial for all group members. Indeed, schooling and shoaling species have been shown to disperse when confronted with distributed resources (Ryer and Olla, 1995; Miller and Gerlai, 2007). A characterization of group foraging for multiple sources with complex spatial distribution is therefore needed.

The ability to track the behavior of groups of individuals with high temporal and spatial resolution under naturalistic conditions (Pérez-Escudero et al., 2014; Ballerini et al., 2008; Greenwald et al., 2015; Nagy et al., 2010; Dell et al., 2014) makes it possible to explore foraging models and behavior quantitatively in groups and individuals. Here, we studied food foraging by groups of adult zebrafish in a large arena, where multiple food items were scattered and individuals could seek them freely. We inferred social interaction rules between fish and compared the accuracy of several mathematical models of group foraging based on these rules and the swimming statistics of individual animals. We explored the performance of these models in terms of foraging dynamics and efficiency of food consumption by the group and of individuals for various resource distributions and group sizes. Our data-driven approach allowed us to analyze foraging strategies through the local dependencies between conspecifics and to show that social interactions increase foraging efficiency in real groups of fish. We further used these models to study the effect of social interactions on income equality between members of the group. Finally, we used our models to explore the implications of social interactions on the efficiency of collective foraging of larger groups under different distributions of resources, and asked how animals could choose an optimal foraging strategy under varying conditions.

We studied free foraging of single adult zebrafish and of groups of three or six fish in a large circular arena with shallow water, where small food flakes were scattered on the surface (Figure 1, Figure 1—figure supplement 1A, and Materials and methods; All data used in this study is avilabale online). The trajectories and heading of individual fish, the position of flakes, and food consumption events were extracted from video recordings of these experiments using a tracking software that was written in house (Harpaz et al., 2017). Tracking of fish identities in the videos were verified and corrected using IdTracker (Pérez-Escudero et al., 2014). Fish were highly engaged in the foraging task and consumed all flakes in less than 2 min in most cases (Figure 1B, Figure 1—figure supplement 1C, Figure 1—video 1). The number of identified consumption events varied between groups, since in some cases fish ate only a part of a flake or flakes disintegrated into smaller parts (Figure 1—figure supplement 1B). The time differences between flake consumption events reflect the nature of foraging and its efficiency.We found that in our setup, the time it took a group of $k$ fish to consume $n$ flakes, $T_k\left(n\right)$, was accurately predicted using a simple exponential model,

where parameters $b_k$ (the 'consumption rate' of the fish) and $a_k$ (time to detection of the first flake) were found numerically to minimize the mean squared error between the model predictions and the data. The correlation between the observed $T_k\left(n\right)$ and model predictions ${\displaystyle {\hat{T}}_k\left(n\right)}$ was very high, with median $r^2$ values: 0.94 [0.09], 0.96 [0.04], 0.96 [0.05] for groups of one, three, and six fish, respectively (brackets show interquartile range). Larger groups consumed the flakes faster than smaller ones (Figure 1B-C), and the feeding rates were higher than those predicted just from having a larger number of foragers, which we tested using a model of independent foragers (Figure 1—figure supplement 1D, see models below). Fish in groups of different size differed also in their average swimming statistics, with groups of three fish exhibiting higher swimming speeds, higher polarization, and larger variation of group cohesion (nearest neighbor distances) (Figure 1D). We also found that group polarity was highly correlated with group cohesion for both groups of three and six fish, but was not correlated with swimming speed (Figure 1—figure supplement 1E). We therefore asked what social interactions between fish may underlie group foraging and swimming trajectories.

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Characterizing social interactions during foraging

To explore the nature of interactions between foraging fish, we analyzed individual swimming behavior before and after flake consumption events and found that fish performed salient and stereotypic maneuvers around the consumption of food items. They increased their speed when approaching food and then abruptly turned in the process of consuming it (Figure 2A–C and Figure 2—video 1). This maneuver was characterized by a decrease in speed and an increase in the curvature of the trajectory (Figure 2B–C, Figure 2—figure supplement 1A). We found that for most groups of 3 and 6 fish analyzed (75%), neighboring fish responded to these salient behaviors and were more likely to visit areas of recent flake consumption within 1–4 s (Figure 2D–E), much more than expected by chance (p<0.05 for 3 and 6 fish, Wilcoxon’s signed rank test). Fish were less attracted to the location of a neighbor’s consumption maneuver if flakes were more abundant in the arena (Figure 2—figure supplement 1B). To confirm that these salient behavioral changes attracted fish to previous consumption areas and not a physical trace of the flake, we also analyzed 'pseudo consumption events', where fish performed speed changes similar to those seen near flake consumption, but with no food present (see Materials and methods). Neighboring fish were attracted to such pseudo-consumption events, affirming that fish responded to the specific behavior of their neighbors (Figure 2—figure supplement 1C–D).

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Social interaction models of group foraging

To study the implications of attraction to locations of feeding by other fish, we simulated foraging groups of fish with various social interactions and without them (see Materials and methods). Simulations were based on the swimming characteristics of real fish and the empirical spatial distributions of flakes (Figure 1A, Figure 3A-B). The swimming trajectory of each fish was simulated by successive drawing from the distribution of step sizes (the length of the path traveled on discrete 'bouts' according to our segmentation of real fish trajectories; Figure 3A, B) and turning angles (change of heading angle between two discrete bouts) of a specific fish in the real group (Figure 3A-B, Figure 3—figure supplement 1A-B). However, if a flake was within the 'range of detection' by a fish ($D_f$), then that fish oriented itself directly towards the flake with a probability that monotonically decreased with the distance to the flake (see Figure 3C). The independent foraging model (IND) is based on a collection of such fish. In addition, we considered six social interaction models that combine attraction to neighbors’ feeding events and attraction and alignment between fish regardless of feeding (Attraction to feeding events- Att_feed; Attraction to neighbors- Att; Alignment with neighbors- Align; and their combinations: Att_feed+Align, Att+Align, Att_feed+Att+Align). In all these models, the direction of motion of each fish was modulated by the behavior of neighboring fish within the 'neighbor detection range' $D_n$ (Figure 3D and Materials and methods) (Bhattacharya and Vicsek, 2014; Torney et al., 2011; Couzin et al., 2002; Huth and Wissel, 1992; Vicsek et al., 1995). These different models allowed us to tease apart the specific contribution of attraction to neighbor’s previous flake consumptions and of the general schooling or shoaling tendencies of the fish (see Figure 3—figure supplement 1C and Materials and methods for a description of all models ; all simulation codes are avilabale online).

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For each of the real groups in our data, we simulated each of the models using a range of possible values of the model’s parameters $D_f$ and $D_n$ (Figure 3—figure supplement 1C, Materials and methods). For each set of $D_f,D_n$ values, we estimated the accuracy of the models in predicting the sequence of consumption events as well as two swimming statistics of the group: the average polarity of the group (or alignment between fish) and the average cohesion of the group (average distance to the nearest neighbor -$D_{nn}$) (Figure 4A-B, Materials and methods). We evaluated the performance of each model on each of these measures (Figure 4C), and their combination (Figure 4D). We found that the IND model did not describe well the consumption times of the groups or their swimming statistics (Figure 4C). Simple attraction to neighbors (Att model) also failed to accurately represent the consumption times or the polarity of the group, yet it accurately described distances between fish and slightly improved overall accuracy over the IND model (Figure 4C-D). Alignment interactions among fish (Align model) was significantly better than the Att model, specifically in describing the polarity of the groups and the sequence of consumptions, indicating that fish respond to their neighbors' direction while foraging (P<0.005, for groups of three fish with N=10, and P<0.01 for groups of six fish with N=10; Wilcoxon’s signed rank test)(Figure 4C-D, Figure 4—figure supplement 1A). The most accurate model of fish swimming and foraging behavior was the one that included both alignment and attraction to neighbors’ previous consumption events (Att_feed+Align), showing high accuracy in describing both the swimming statistics of the groups and the sequence of consumptions, which was significantly better than the competing models (P<0.005 when comparing the Att_feed+Align to all other models shown, N=10,10 for groups of three and six fish, Wilcoxon's signed rank test)(Figure 4C-D, Figure 4—figure supplement 1A). The inferred range of social interactions of the best fitted model (Att_feed+Align) were ~4 and 8 times larger than the range of flake detection (median $D_n$ values: 21.5 [11], 11.5 [6] and median $D_f$ values: 2.5[2], 3[3] for groups of three and six fish, interquartile range in parenthesis; see Figure 4—figure supplement 1C).

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Importantly, the observed improvement in accuracy was not a result of increased model complexity: First, the number of model parameters was the same for all social models. Second, models that include attraction to neighbors regardless of flake consumption (Att+Align, Att_feed+Att+Align models) were less accurate than the Att_feed+Align model (Figure 4—figure supplement 1B,D). We conclude that while fish continuously respond to the swimming direction of their neighbors, they also exhibit a specific attraction to neighbors’ previous flake consumptions during foraging.

Increased foraging efficiency is predicted by attraction to neighbor’s flake consumptions

To understand the impact of social interactions on foraging efficiency, we compared the feeding rates of foraging fish in the best fit social model (Att_feed+Align model) and the reference IND model (Figure 4), for a wide range of model parameter values $D_f,D_n$ (Figure 5A). The feeding rates were accurately approximated by an exponential function (as in Eq. 1; ${\displaystyle R^2>0.98}$ for all simulations). As expected, the simulated groups consumed flakes faster as $D_f$ increased (Figure 5B). For relatively short flake detection range (${\displaystyle D_f\le 6}$ BL), flake consumption rates increased with $D_n$, reflecting the effect of directly responding to neighbors’ foraging behavior. For ${\displaystyle D_f>6}$ BL, increasing $D_n$ had a very little effect on consumption rates (Figure 5B).

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Social interactions in the Att_feed+Align model resulted in a significant increase in consumption rates, compared to the IND model, only for simulations with low $D_f$ and high $D_n$ values (red areas in Figure 5C). Importantly, most groups of real fish were best matched by simulated groups with parameter values that were well within the area of the parameter space were social interactions improve foraging efficiency (low $D_f$ and high $D_n$), approaching the peak of the expected improvement in foraging performance (Figure 5C). The observed improvement due to social interactions was model specific - social interaction models that did not include attraction to neighbors’ previous flake consumptions (e.g. the Align, Att, or Att+Align models) did not show a similar improvement over the independent model (Figure 5D, Figure 5—figure supplement 1A-B). Moreover, social foraging strategies that included attraction to neighbors’ positions (not specifically related to flake consumptions) were less efficient than independent foragers (Figure 5D, Figure 5—figure supplement 1A-B).

Individual efficiency and income equality in socially interacting fish

We next explored how the Att_feed+Align foraging strategy might affect the foraging success of individual members of the group. We simulated groups in which only a fraction of the foragers used social interactions, while the others foraged independently (Figure 6A illustrates these mixed strategy groups). Comparing foraging success of the social and non-social individuals within the same group, we found that individuals using social information consumed up to 20% more flakes than their non-social companions, and this advantage decreased as the number of interacting agents in the group increased (Figure 6B-C, Figure 6—figure supplement 1A). These effects were most pronounced in models that used the same parameter range that matched real foraging groups, namely low $D_f$ and high $D_n$ (Figure 6—figure supplement 1A).

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We further assessed the equality of food distribution among individuals in real groups and simulated groups using the Theil index of inequality (Theil, 1967):

(2) $I_{Theil}\left(k,n\right)=\frac{1}{k}{\sum }_{i=1}^k\frac{n_i}{\mu }log\left(\frac{n_i}{\mu }\right),$

where $k$ is the number of fish in the group, $n_i$ is the number of flakes consumed by the $i^{th}$ fish, and $\mu =\frac{n}{k}$ is the average number of flakes consumed by a fish in the group. We normalized $I_{Theil}$ by its maximal possible value, $logk$ (the case where one fish consumes all flakes), and measured equality using $1-\frac{I_{Theil}}{logk}$, which ranges between 0 (a single fish who consumed all flakes) and 1 (full equality). Real groups showed high equality values, with median values of 0.89 [0.21] for groups of three fish and 0.92 [0.16] for groups of six fish (values in brackets show the interquartile range). The corresponding simulated groups using the Att_feed+Align strategy exhibited similar high equality values (Median = 0.92 [0.05], 0.90 [0.1] for simulated groups of three and six fish), indicating that resources were distributed relatively equally among real and simulated fish (Figure 6—figure supplement 2A). We then compared income equality for the different social foraging models and found that only models that include specific attraction to neighbors’ previous flake consumptions exhibited increased equality compared to independent foraging (Figure 6—figure supplement 2C). In simulated groups using the Att_feed+Align strategy, equality was a function of both the number of socially interacting individuals within the group and the spatial dispersion of the flakes (Figure 6—figure supplement 2B). For low spatial dispersion of flakes, simulated groups composed of just independent foragers showed the highest inequality of all groups with mixed strategies, and equality increased with the number of foragers in the group that used the Att_feed+Align strategy (Figure 6D-E, Figure 6—figure supplement 2DA). When all individuals in the group used the Att_feed+Align strategy, equality was higher than in groups of independent foragers for groups of three and six fish, for most parameter values that match real foraging groups (Figure 6D-E). In contrast, in environments with high dispersion of flakes these effects disappeared or even reversed, with groups of three fish showing only a moderate non-significant increase in equality and groups of six fish showing a significant decrease in equality (Figure 6D-E). Thus, attraction to neighbors’ consumption events increases income equality among group members only when resources are hard to come by.

Simulating larger groups and different distributions of food

Finally, we investigated the predictions of the Att_feed+Align foraging model for larger groups and additional spatial distributions of food. We simulated groups of up to 24 fish in environments with spatial distributions of food ranging from a single cluster of food items to a uniform distribution (Figure 7A, Figure 7—videos 1–6). The increase in efficiency due to social interactions was most pronounced when food items were highly clustered in space, whereas for the extreme cases of random or uniform distributions, the models predict that social interactions would hinder foraging performance (Figure 7B, Figure 7—figure supplement 1A; Giraldeau and Caraco, 2000; Ryer and Olla, 1995; Ryer and Olla, 1998; Ranta et al., 1993). Importantly, our simulations predict that groups of 12 and 24 fish that follow the Att_feed+Align strategy would be less efficient than independent foragers for almost all the food distributions we tested. This is mainly due to the fact that the larger groups are more cohesive and disperse less in the environment, making the search less efficient (Figure 7—video 6). A social foraging strategy that only includes attraction to neighbors’ flake consumption events (without a tendency to align with neighbors - Att_feed model) increased foraging efficiency also for the large group sizes (Figure 7—figure supplement 2A). Income equality in the group also increased in clustered food distributions and decreased in non-clustered ones, for all group sizes (Figure 7C, Figure 7—figure supplement 1B, Figure 7—figure supplement 2B).

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Interestingly, simulated groups of three and six fish were most efficient for intermediate $D_n$ values in the cases of clustered and real flake distributions (~10-12 BL, see Figure 7B). Simulations of groups with longer social interaction ranges added only a small gain to foraging efficiency. In contrast, for simulated groups foraging with non-clustered food distributions (Random and Grid, Figure 7A), increasing $D_n$ values resulted in decreased efficiency for larger groups, but had almost no effect for groups of three fish. These simulations suggest that regardless of the flake distribution, optimal interaction ranges for groups of three fish could be long, while groups of six fish should use intermediate interaction ranges to balance their gains at high clustered environments with their losses at distributed environments. The parameter values of the best fit models to real groups conform with these predictions with median $D_n$ values of 21.5 and 11.5 for groups of three and six fish, respectively.

We studied free foraging behavior in groups of adult zebrafish and found that fish responded to the salient swimming maneuvers of shoal mates that indicated the consumption of food, by swimming to these locations. Mathematical models of group behavior that combined the tendency of fish to align with one another and to attract to the locations of previous flake consumptions by other fish, accurately described fish foraging behavior and their success rates, and were superior to several other (commonly used) social interaction models. This foraging strategy increased efficiency of groups specifically in models that best matched real foraging groups, improved income equality within the groups, and was efficient under different resource distribution settings. Simulations of the models also show that socially interacting individuals that would rely on attraction to feeding events by other fish would consume more food than shoal mates that forage independently. Our results thus present a detailed social foraging heuristic that matches fish behavior in a naturalistic context, and constitutes a highly efficient and robust foraging strategy.

Our modeling predicts that the inferred interaction ranges that best fit real foraging groups would result in a robust foraging strategy for groups of three and six fish for various spatial distributions of food. This implies that to forage efficiently fish could adjust their interaction range according to the perceived group size, regardless of the (usually unknown) distribution of food. Additionally, the reduction in foraging efficiency predicted by our models for larger simulated groups (12 and 24 fish) predicts that these groups are more likely to break down into smaller groups that will exhibit increased efficiency. This finding is consistent with the observation that zebrafish both in the wild and in the laboratory are rarely found in cohesive groups of 12 fish or more (Harpaz et al., 2017; Suriyampola et al., 2016). Interestingly, when simulating groups that only utilize attraction to neighbors’ consumption events (without the general schooling tendency observed in real fish) the models predicted increased efficiency for all group sizes. We therefore hypothesize that this interaction type represents a general behavioral strategy for individuals foraging in a social context, also for non-schooling species (Brown, 1988; Clark and Mangel, 1984; Flemming et al., 1992; Miller et al., 2013).

Since zebrafish rely heavily on their visual system (Saverino and Gerlai, 2008; Pita et al., 2015), our modeling focused on vision as the main source of social information between individuals. It is likely that other sensory modalities, namely tactile or odor pathways, also play a role in information transfer during foraging. However, the inferred parameters of the best fit models in our data indicated that neighbor detection ranges were ~4–8 times larger than flake detection ranges - reaching up to 21 body lengths, on average. It is unclear whether odors or tactile information may be detected from such large distances on such short time scales (Moore and Crimaldi, 2004). Thus, while various modalities may modulate fish behavior, we suggest that vision plays the prominent role in processing social information during foraging.

We focused here on attraction-based strategies for the fish, since in our experiments fish were attracted to areas where neighbors detected food. However, previous studies have suggested other search strategies that were based on repulsion between individuals (Tani et al., 2014) or on maximizing information about the location of food (Karpas et al., 2017). Although our modeling framework gave an excellent fit to the data, it is possible that foraging fish combine or alternate between strategies in different environmental conditions, based on group composition or their internal state (Farine et al., 2014; Michelena et al., 2009; Harpaz et al., 2017; Kurvers et al., 2011). Thus, models that incorporate additional strategies according to an explicit policy, might prove to be even more accurate in explaining fish behavior.

Observations of groups in nature, and related theoretical models, suggest that groups may contain a fraction of individuals whose search is based on their personal information ('producers') as well as individuals that rely mostly on social information ('scroungers') (Barnard and Sibly, 1981; Mottley and Giraldeau, 2000; Harten et al., 2018). Our results suggest that when individuals in the group have similar foraging capabilities and a limited social interaction range (Bhattacharya and Vicsek, 2014; Bhattacharya and Vicsek, 2015), using both individual and social information is the most efficient strategy for the individual. An interesting extension of our models would be to explore individual differences between members of the group and their effect on individual social foraging strategies (Aplin et al., 2014; Jolles et al., 2017; Michelena et al., 2010; Brown and Irving, 2014), or the existence of stable sub-groups of individuals with higher tendencies to interact with one another in larger groups of foragers.

Finally, we note that our work reflects the power of detailed behavioral analysis of individuals in real groups for building accurate mathematical models of social interactions. Learning the models from the data and testing them on real groups allowed us to explore the efficiency and robustness of the interactions among group members in a quantitative manner. This data-driven approach would be applicable and potentially imperative in the analysis of social behavior of large groups of individuals - where macroscopic or mean field like models would not suffice to characterize the interplay between complex and possibly idiosyncratic traits of individuals and emerging group behavior.

All data used in this work have been made available via the main author's public GitHub account: https://github.com/schneidmanlab/zebrafishForaging (copy archived at https://github.com/elifesciences-publications/zebrafishForaging).

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Author details

1. Roy Harpaz

   1. Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel
   2. Department of Molecular and Cellular Biology, Harvard University, Cambridge MA, United States

   Contribution

   Conceptualization, Software, Formal analysis, Validation, Visualization, Methodology, Writing - original draft, Writing - review and editing

   For correspondence

   roy_harpaz@fas.harvard.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9587-3389

2. Elad Schneidman

   Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel

   Contribution

   Conceptualization, Software, Formal analysis, Supervision, Funding acquisition, Validation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   elad.schneidman@weizmann.ac.il

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-8653-9848

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