Social interactions drive efficient foraging and income equality in groups of fish

The social interactions underlying group foraging and their benefits have been mostly studied using mechanistic models replicating qualitative features of group behavior, and focused on a single resource or a few clustered ones. Here, we tracked groups of freely foraging adult zebrafish with spatially dispersed food items and found that fish perform stereotypical maneuvers when consuming food, which attract neighboring fish. We then present a mathematical model, based on inferred functional interactions between fish, which accurately describes individual and group foraging of real fish. We show that these interactions allow fish to combine individual and social information to achieve near-optimal foraging efficiency and promote income equality within groups. We further show that the interactions that would maximize efficiency in these social foraging models depend on group size, but not on food distribution, and hypothesize that fish may adaptively pick the subgroup of neighbors they ‘listen to’ to determine their own behavior.

The social interactions underlying group foraging and their benefits have been mostly studied 12 using mechanistic models replicating qualitative features of group behavior, and focused on 13 a single resource or a few clustered ones. Here, we tracked groups of freely foraging adult 14 zebrafish with spatially dispersed food items and found that fish perform stereotypical 15 maneuvers when consuming food, which attract neighboring fish. We then present a 16 mathematical model, based on inferred functional interactions between fish, which 17 accurately describes individual and group foraging of real fish. We show that these 18 interactions allow fish to combine individual and social information to achieve near-optimal 19 foraging efficiency and promote income equality within groups. We further show that the 20 interactions that would maximize efficiency in these social foraging models depend on group 21 size, but not on food distribution -suggesting that fish may adaptively pick the subgroup of 22 neighbors they "listen to" to determine their own behavior .  23  24  25  26  27  28  29  30  31  32  33  34  35  Introduction   41   42 Living in a group has clear benefits, including expansion of sensory sensitivity (1)(2)(3)(4), sharing 43 of responsibilities and resources (5-7), collective computation (1)(2)(3)(4)(8)(9)(10), and the potential 44 for symbiotic relations between members that would allow for specialization by individual 45 members (7, 11). Understanding the interactions among individuals that give rise to 46 macroscopic behavior of groups is therefore central to the study and analysis of collective 47 behavior in animal groups and other biological systems. 48 49 Group foraging is a prominent example of collective behavior, and social interactions among 50 members have been suggested to increase foraging efficiency (12-17) by allowing individuals 51 to combine private and social information about the location of resources and their quality 52 (see however (18,19) for adverse effects of social information). Theoretical models have been 53 used to study social foraging using various strategies, including producer-scrounger dynamics 54 (20) and the use of `public' information (21-23). These models explored the efficiency of the 55 underlying strategies, their evolutionary stability, as well as the effects of group composition, 56 and of the distribution of resources (20, 22, 24-27). Experimental work, in the field and in the 57 lab, aimed to identify interactions between foraging individuals (10, 28-32) and their 58 dependence on factors such as the distribution of resources, phenotypic diversity among 59 foragers, animal personality, and foraging strategies of mixed species (33-37). The interaction 60 rules studied with these theoretical models and the emerging group behavior had mostly 61 qualitative correspondence to that of real groups, as the predictions of theoretical models 62 were usually not tested against experimental data of groups at the individual level (20, 38-63 41). 64 65 Moreover, most models studying how schooling or flocking may improve foraging efficiency 66 have explored the case of single sources, or clumped food patches (8-10, 27, 32, 36, 37). Yet, 67 in many real-world situations, animals are likely to encounter distributed food sources, where 68 maintaining a tight group may not be beneficial for all group members. Indeed, schooling and 69 shoaling species have been shown to disperse when confronted with distributed resources 70 (33,42). A characterization of group foraging for multiple sources with complex spatial 71 distribution is therefore needed. 72 73 The ability to track the behavior of groups of individuals with high temporal and spatial 74 resolution under naturalistic conditions (43-47) makes it possible to explore foraging models 75 and behavior quantitatively in groups and individual fish. Here, we studied food foraging by 76 groups of adult zebrafish in a large arena, where multiple food items were scattered and 77 individuals could seek these items freely. We inferred social interaction rules between fish 78 and compared the accuracy of several mathematical models of group foraging based on these 79 rules and the swimming statistics of individual animals. We explored the performance of 80 these models in terms of foraging dynamics and efficiency of food consumption by the group 81 and of individuals for various resource distributions and group sizes. Our data driven approach 82 allowed us to analyze foraging strategies through the local dependencies between 83 conspecifics, and to show that social interactions increase foraging efficiency in real groups 84 of fish. We further used these models to study the effect of social interactions on income 85 equality between members of the group. Finally, we use our models to explore the 86 implications of social interactions on the efficiency of collective foraging of larger groups 87 under different distributions of resources, and ask how animals could choose an optimal 88 foraging strategy under varying conditions. 89 90 91

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We studied free foraging of single adult zebrafish and of groups of 3 or 6 fish in a large circular 94 arena with shallow water, where small food flakes were scattered on the surface ( flake consumptions reflects the nature of foraging and its efficiency, and so we found that the 104 time it took a group of fish to consume flakes, ! ( ), was accurately predicted using a 105 simple exponential model, 106 where parameters ! (the "consumption rate" of the fish) and ! (time to detection of the 109 first flake) were found numerically to minimize the mean squared error between the model 110 predictions and the data. The correlation between the observed ! ( ) and model predictions 111 the flakes faster than smaller ones ( Figure 1B-C), and the feeding rates were higher than those 114 predicted just from having a larger number of foragers, which we tested using a model of 115 independent foragers (Figure 1-figure supplement 1D, see models below). Fish in groups of 116 different size differed also in their average swimming statistics, with groups of 3 fish exhibiting 117 higher swimming speeds, higher polarization, and larger variation in group cohesion (nearest 118 neighbor distances) ( Figure 1D). We also found that group polarity was highly correlated with 119 group cohesion for both groups of 3 and 6 fish, but was not correlated with swimming speed 120 ( Figure 1-figure supplement 1E). We therefore asked what social interactions between fish 121 may underlie group foraging and swimming trajectories. 122 is shown for each of the groups tested (thin lines show N=14, 10, and 10 groups of 1, 3, and 6 fish) overlaid with the mean of all groups for every group size (thick line); light shadings represent SEM. (Because individual groups of the same size did not always consume the same total number of flakes, averages were calculated over the first 5, 9, and 21 flakes consumed by the groups of 1, 3, and 6 fish, respectively, and the number of consumed flakes is truncated at 30 for clarity; the full curves are shown in Figure 1-figure supplement 1C; We emphasize that all analyses were conducted on the full curves). C. Boxplots show the rate of flake consumption bk that was fitted for each of the groups shown in B. Middle horizontal lines represent median values and box edges are the 1 st and 3 rd quartiles; asterisks denote P<0.05 under Wilcoxon's rank-sum test, N = 14,10,10 fish). D. Average speed, polarity, and nearest neighbor distance for individual fish and groups of fish. Horizontal lines represent median values and box edges are the 1 st and 3 rd quartiles.

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Characterizing social interactions during foraging 126 127 To explore the nature of interactions between foraging fish, we analyzed individual swimming 128 behavior before and after flake consumption events, and found that fish performed salient 129 and stereotypic maneuvers around the consumption of food items: They increased their 130 speed when approaching food and then abruptly turned in the process of consuming it ( Figure  131 2A-C and Video 2). This maneuver was characterized by a decrease in speed and an increase 132 in the curvature of the trajectory ( Figure 2B-C, Figure 2-figure supplement 1A). We found that 133 for most groups of 3 and 6 fish analyzed (75%), neighboring fish responded to these salient 134 behaviors and were more likely to visit areas of recent flake consumption within 1-4s ( Figure  135 2D-E), much more than expected by chance (P<0.05 for 3 and 6 fish, Wilcoxon's signed rank 136 test). Fish were less attracted to the location of a neighbor's consumption maneuver if flakes 137 were more abundant in the arena (Figure 2-figure supplement 1B). To confirm that these 138 salient behavioral changes attracted fish to previous consumption areas, and not a physical 139 trace of the flake, we also analyzed ``pseudo consumption events", where fish performed 140 speed changes similar to those seen near flake consumption, but with no food present (see 141 Methods). Neighboring fish were indeed attracted to such pseudo-consumption events, 142 affirming that fish responded to the specific behavior of their neighbors (Figure 2-figure  143 supplement 1C-D). 144 145 Figure 2: Stereotypical maneuvers before and during flake consumption by one fish attracts its neighbors. A. An example of the stereotypical behavior of one fish (in a group of 3) showing flake detection and consumption. Flake position is shown by a red circle before consumption and by a black circle after it has been eaten. B-C. Stereotypical behaviors around flake consumption (which we set as time 0 and mark by a red dot) include a transient increase in speed (shown in body length (BL) per second), followed by a sharp decrease (B); this is accompanied by an increase in the curvature of the trajectory (C). Bold blue lines are mean speed and curvature profiles over all detection events of all groups of 3 fish, and dotted green lines show a reference value calculated from random points along the trajectories not related to consumption events (curvature values were normalized such that the average curvature is zero). Light blue and green shadings show SEM. D. Probability of neighbors to cross within 2 BLs from the location of a previous flake consumption, within 1-4 s following the consumption event, for one group of 3 fish (blue arrow), compared to the distribution of such neighbor crossing events, if flake consumption events are ignored (Methods). This reference distribution of crossings is well fitted by a Gaussian distribution (mean = 0.25, SD = 0.056), which is shown by a black overlaid line. E. Crossing probabilities for groups of 3 and 6 fish show significant increase from the baseline neighbor crossing distribution of each group, similar to C; 0 represent the mean of the baseline crossing distributions, error bars represent SEM.

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Social interaction models of group foraging 148 149 To study the implications of attraction to locations of feeding by other fish, we simulated 150 foraging groups of fish with various social interactions and without them (see Methods). 151 Simulations were based on the swimming characteristics of real fish and the empirical spatial 152 distributions of flakes ( Figure 1A, Figure 3A-B). The swimming trajectory of each fish was 153 simulated by successive drawing from the distribution of step sizes (the length of the path 154 traveled on discrete `bouts' according to our segmentation of real fish trajectories; Figure  155 3A,B) and turning angles (change of heading angle between two discrete bouts) of a specific 156 fish in the real group ( Figure 3A within the `range of detection' by a fish ( # ), then that fish oriented itself directly towards 158 the flake with a probability that monotonically decreased with the distance to the flake (see 159 Figure 3C). The independent foraging model (IND) is based on a collection of such fish. In 160 addition, we considered 6 social interaction models that combine attraction to neighbors' 161 feeding events and attraction and alignment between fish regardless of feeding (Attraction 162 to feeding events-Attfeed; Attraction to neighbors-Att; Alignment with neighbors-Align; and 163 their combinations: Attfeed+Align, Att+Align, Attfeed+Att+Align). In all these models, the 164 direction of motion of each fish was modulated by the behavior of neighboring fish within the 165 `neighbor detection range' $ ( Figure 3D   Middle: Distributions of step size and angle change , between discrete steps over 3 fish in one of the groups (Methods). Right: sketch of a simulated fish trajectory composed of successive drawings of and from the empirical distributions. C. A sketch of the independent model of fish foraging: At each time step, if a flake was present within a fish's detection range ( " < " depicted by the blue circle), the fish oriented towards that flake with a probability p(go to flake). D. Sketches of the different social interactions between fish. Each fish may detect consumption of flakes by another fish (left), if that fish was within the neighbor detection range ( # < # red circle). The observing fish was then attracted to the consumption point with probability p(go to consumption). Additionally, fish may respond to the swimming behavior of neighbors within # , regardless of flake consumption, by swimming towards the average position of their neighbors (middle) with probability p(go to neighbors) or by aligning their swimming direction (right) with neighbors within # , p(align to neighbors). Different combinations of these possible social interactions comprise the 6 different social models tested here (  Methods). For each set of # , $ values, we estimated the accuracy of the models in 187 predicting the sequence of consumption events as well as two swimming statistics of the 188 groups: the average polarity of the group (or alignment between fish) and the average 189 cohesion of the group (average distance to the nearest neighbor -$$ ) ( Figure 4A-B, 190 Methods). We evaluated the performance of each model on each of these measures ( Figure  191 4C), and their combination ( Figure 4D). We found that the IND model did not describe well 192 the consumption times of the groups, or their swimming statistics ( Figure 4C). Simple 193 attraction to neighbors (Att model) also failed to accurately represent the consumption times 194 or the polarity of the group, yet it accurately described distances between fish and slightly 195 improved overall accuracy over the IND model ( Figure  Importantly, the observed improvement in accuracy was not a result of increased model 212 complexity. First, the number of model parameters is the same for all social models. Second, 213 models that include attraction to neighbors regardless of flake consumption (Att+Align, 214 Attfeed+Att+Align models) were less accurate than the Attfeed+Align model ( Figure 4- figure  215 supplement 1B, D). We conclude that fish continuously respond to the swimming direction of 216 their neighbors, but also exhibit a specific attraction to neighbors' previous flake 217 consumptions during foraging. 218 219 220 221 222 223 Figure 4: Social models incorporating attraction to neighbors' flake consumptions give the best fit to real foraging groups. A. Example trajectories from simulations of foraging of a group of 6 fish, for the IND, Att, Align, and the Attfeed+Align models that use the parameters that gave the best fit to real group foraging. Colored lines show different individual fish and black dots are flake positions. Next to the simulated trajectories we plot the average group polarity and nearest neighbor distance in the simulations (colored dots), and the experimental values of the real foraging group (black dots); Error bars represent SD in the simulation. B. Flake detection times (black dots) of two groups of 6 fish (Top row shows the group whose trajectories are shown in A) and the average and standard deviation of the best-fit models (bold colored lines represent averages; shaded areas represent SD). C. Errors of best fit models for groups of 6 fish are shown for three statistics of interest: the polarity of the group , and the consumption times 2%#345$*)%#3 =

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Increased foraging efficiency is predicted by attraction to neighbor's flake consumptions 226 227 To understand the impact of social interactions on foraging efficiency, we compared the 228 feeding rates of foraging fish in the best fit social model (Attfeed+Align model) and the 229 reference IND model (Figure 4), for a wide range of model parameter values # , $ ( Figure  230 5A). The feeding rates were accurately approximated by an exponential function (as in Eq. 1; 231 " > 0.98 for all simulations). As expected, the simulated groups consumed flakes faster as 232 # increased ( Figure 5B). For relatively short flake detection range ( # ≤ 6 BL), flake 233 consumption rates increased with $ , reflecting the effect of directly responding to 234 neighbors' foraging behavior. For # > 6 BL, increasing $ had very little effect on 235 consumption rates ( Figure 5B). 236 237 Social interactions in the Attfeed+Align model resulted in a significant increase in consumption 238 rates, compared to the IND model, only for simulations with low # and high $ values (red 239 areas in Figure 5C). Importantly, most groups of real fish were best matched by simulated 240 groups with parameter values that were well within the area of the parameter space were 241 social interactions improve foraging efficiency (low # and high $ ), approaching the peak of 242 the expected improvement in foraging performance ( Figure 5C). The observed improvement 243 due to social interactions was model specific -social interaction models that did not include 244 attraction to neighbors' previous flake consumptions (e.g. the Align, Att, or Att+Align models) 245 did not show a similar improvement over the independent model ( Figure 5D, Figure 5- figure  246 supplement 1A-B). In fact, social foraging strategies that included attraction to neighbors' 247 positions (not specifically related to flake consumptions) were less efficient than independent 248 foragers ( Figure 5D, Figure 5-figure supplement 1A-B). 249 Figure 5: Attraction to neighbors' feeding results in increased foraging efficiency. A. Left: Sketch of two groups of 3 fish foraging, with their different interaction ranges " , # overlaid. For # = 0, the group is composed of independent foragers (IND model). Right: foraging efficiency was estimated by comparing the slope (b; see eq. 1) of the exponential function fitted to the rate of flake consumption of socially interacting agents (Attfeed+Align model) and independent (IND) foragers. B. Average consumption rates, b, for different combinations of " and # , the first column on the left ( # = 0) represent independent foragers. Contours denote 10, 50, and 90% of the highest observed rate. C. Difference in foraging efficiency for groups that utilize social interactions (Attfeed+Align) compared to groups of independent foragers (IND) for all model parameters. Dots represent " and # values of simulated groups that best fitted real foraging groups. D. Average improvement in the rate of flake consumption by socially interacting individuals compared to independent foragers. Colors indicate different social foraging strategies; dotted line represent no change compared to independent foragers (IND); results were averaged over all simulations with " ≤ 5 which was the parameter range where real groups were matched by simulations. Dots represent statistically significant differences (P<0.05, Wilcoxon's signed rank test).

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Individual efficiency and income equality in socially interacting fish 252 253 We next explored how the Attfeed+Align foraging strategy might affect the foraging success of 254 individual members of the group. We simulated groups in which only a fraction of the foragers 255 used social interactions, while the others foraged independently ( Figure 6A illustrates these 256 mixed strategy groups). Comparing foraging success of the social and non-social individuals 257 within the same group, we found that individuals using social information consumed up to 258 20% more flakes than their non-social companions, and this advantage decreased as the 259 number of interacting agents in the group increased ( Figure 6B-C, Figure 6-figure supplement 260 1A). These effects were most pronounced in models that used the same parameter range that 261 matched real foraging groups, namely low # and high $ (Figure 6-figure supplement 1A). 262 263 We further assessed the equality of food distribution among individuals in real groups and 264 simulated groups using the Theil index of inequality (52): 265  (Figure 6-figure supplement 2B). Equality values were averaged over " ≤ 5; dots show a significant difference from independent foragers (0 social fish) (Wilcoxon's signed rank test; N=5 for each group size and dispersion level).

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Simulating larger groups and different distributions of food 295 296 Finally, we investigated the predictions of the Attfeed+Align foraging model for larger groups 297 and additional spatial distributions of food. We simulated groups of up to 24 fish in 298 environments with spatial distributions of food ranging from a single cluster of food items to 299 a uniform distribution ( Figure 7A, Video 3-8). The increase in efficiency due to social 300 interactions was most pronounced when food items were highly clustered in space, whereas 301 for the extreme cases of random or uniform distributions, the models predict that social 302 interactions would hinder foraging performance ( Figure 7B, Figure 7-figure supplement 303 1A)(14, 33, 53, 54). Importantly, our simulations predict that groups of 12 and 24 fish that 304 follow the Attfeed+Align strategy would be less efficient than independent foragers for almost 305 all the food distributions we tested. This is mainly due to the fact that the larger groups are 306 more cohesive and disperse less in the environment, making the search less efficient (Video 307 8). A social foraging strategy that only includes attraction to neighbors' flake consumption 308 events (without a tendency to align with neighbors -Attfeed model) increased foraging 309 efficiency also for the large group sizes ( Interestingly, simulated groups of 3 and 6 fish in the cases of clustered and real flake 313 distributions, were most efficient for intermediate $ values (~10-12 BL, see Figure 7B). 314 Simulations of groups with longer social interaction ranges added only a small gain to foraging 315 efficiency. In contrast, for simulated groups foraging with non-clustered food distributions 316 (Random and Grid, Figure 7A), increasing $ values resulted in decreased efficiency for larger 317 groups, but had almost no effect for groups of 3 fish. These simulations suggest that 318 regardless of the flake distribution, optimal interaction ranges for groups of 3 fish could be 319 long, while groups of 6 fish should use intermediate interaction ranges to balance their gains 320 at high clustered environments with their losses at distributed environments. The parameter 321 values of the best fit models to real groups conform with these predictions with median $ 322 values of 21.5 and 11.5 for groups of 3 and 6 fish respectively. 323  We studied free foraging behavior in groups of adult zebrafish and found that fish responded 339 to the salient swimming maneuvers of shoal mates that indicated the presence of food, by 340 swimming to these locations. Mathematical models of group behavior that combined the 341 tendency of fish to align with one another and to attract to the locations of previous flake 342 consumptions by other fish, accurately described fish foraging behavior and their success 343 rates, and were superior to several other (commonly used) social interaction models. This 344 foraging strategy increased efficiency of groups specifically in models that best matched real 345 foraging groups, improved income equality within the groups, and was efficient under 346 different resource distribution settings. Simulations of the models also show that socially 347 interacting individuals that would rely on attraction to feeding events by other fish would 348 consume more food than shoal mates that forage independently. Our results thus present a 349 detailed social foraging heuristic that matches fish behavior in a naturalistic context, and 350 constitutes a highly efficient and robust foraging strategy. 351 352 Our modeling predicts that the inferred interaction ranges that best fit real foraging groups 353 would result in a robust foraging strategy for groups of 3 and 6 fish for various spatial 354 distributions of food. This implies that to forage efficiently fish could adjust their interaction 355 range according to the perceived group size, regardless of the (usually unknown) distribution 356 of food. Additionally, the reduction in foraging efficiency predicted by our models for larger 357 simulated groups (12 and 24 fish) predicts that these groups are more likely to break down 358 into smaller groups that will exhibit increased efficiency. This finding is consistent with the 359 observation that zebrafish both in the wild and in the laboratory are rarely found in cohesive 360 groups of 12 fish or more (48, 55). Interestingly, when simulating groups that only utilize 361 attraction to neighbors' consumption events (without the general schooling tendency 362 observed in real fish) the models predicted increased efficiency for all group sizes. We 363 therefore hypothesize that this interaction type represents a general behavioral strategy for 364 individuals foraging in a social context, also for non-schooling species (16, 21, 31, 32). 365 366 Since zebrafish rely heavily on their visual system (52, 53), our modeling focused on vision as 367 the main source of social information between individuals. It is likely that other sensory 368 modalities, namely tactile or odor pathways, also play a role in information transfer during 369 foraging. However, the inferred parameters of the best fit models in our data indicated that 370 neighbor detection ranges were ~4-8 times larger than flake detection ranges -reaching up 371 to 21 body lengths, on average. It is unclear whether odors or tactile information may be 372 detected from such large distances on such short time scales (54 Observations of groups in nature, and related theoretical models, suggest that groups may 386 contain a fraction of individuals whose search is based on their personal information 387 (``producers") as well as individuals that rely mostly on social information (``scroungers") (20, 388 58, 59). Our results suggest that when individuals in the group have similar foraging 389 capabilities and a limited social interaction range (22, 60), using both individual and social 390 information is the most efficient strategy for the individual. An interesting extension of our 391 models would be to explore individual differences between members of the group and their 392 effect on individual social foraging strategies (36, 37, 61, 62), or the existence of stable sub-393 groups of individuals with higher tendencies to interact with one another in larger groups of 394 foragers. 395 396 Finally, we note that our work reflects the power of detailed behavioral analysis of individuals 397 in real groups for building accurate mathematical models of social interactions. Learning the 398 models from the data and testing them on real groups allowed us to explore the efficiency 399 and robustness of the interactions among group members in a quantitative manner. This To facilitate food searching behavior we conducted a 5-day gradual acclimation procedure: After being introduced to the experimental arena with no food present (day 1), on each of the following days (2-5), fish were placed in a box in the middle of the arena, and then released to an experimental tank (which was larger on each day) where small flakes of food were scattered on the water surface (orange dots). Fish were given 5 minutes to explore the tank and consume the flakes. Next, fish were deprived of food for 2 days (days 6-7) in their home tanks, and on day 8 we tested foraging behavior of the fish in the large experimental tank; fish images in this panel are not to scale. B. Number of consumption events recorded for each of the groups tested. Horizontal lines show the median values of consumption events, and the rectangles show the 1 st and 3 rd quartiles. Figure 1B, showing all consumption events for all group sizes (soft lines) and the averages for the first 5, 9, and 21 flakes as depicted in Figure 1B (dotted lines). D. Same as in Figure  1B, but showing in addition the expected average rate of simulated independent groups (dotted black lines) (see Figure 3 and Methods), indicating that social interactions increase foraging rates in real groups. E. Average group polarity is strongly correlated with average nearest neighbor distance in groups of 3 and 6 fish (Pearson's correlation coefficient, for 10 groups in each case). Dark lines represent the best fit linear model and shaded area is the 95% confidence interval of the model.  Increase of probability to attract to the location of neighbors' previous flake consumption decreased as flakes were more abundant in the arena. Pearson's correlation coefficient, N=20 (since no significant difference in this relationship was found between groups of 3 and 6 fish, both group sizes are included in the same analysis); The shaded area shows the 95% confidence interval of the linear regression model in black. C. Fish showed a significant increase in tendency to swim towards neighbors when the latter changed their speed in a way that resembled flake consumption events ('pseudo consumptions')(P<0.005 for both group sizes, N=10,10 for groups of 3 and 6 fish; Wilcoxon's signed rank test ). D. The tendency to swim towards flake consumption events and pseudo consumptions was significantly correlated over groups, N=20 groups (10 groups of 3 fish and 10 groups of 6 fish, no differences between group sizes); the shaded area shows the 95% confidence interval of the linear regression model in black.  Figure  3B); error bars represent SEM. B. Same as in A but for the distributions of turns. C. Sketches of all models used in the study: In the IND model fish swims towards flakes that were closer than the flake detection range " < " . In all social models, if flakes were not detected within " , fish responded to the behavior of conspecifics that were within the neighbor detection range # < # . In the Attfeed model, fish oriented towards neighbors' flake consumptions. In the Att model, fish oriented towards the center of mass of neighbors. In the Align model, fish oriented towards the average swimming direction of their neighbors. In the Attfeed+Align model, fish responded first to neighbors' previous consumptions. If no consumption events were detected, fish responded as in the Align model. In the Att+Align model, fish responded as in the Align model to neighbors within # /2, and as in the Att model to neighbors within # /2 < # < # . If there were other fish in both zones, the focal fish responded according to the average of the two response vectors. In the Figure 4-figure supplement 1: Social models incorporating attraction to flake consumption by neighbors show the best fit to real foraging groups. A. Calculated error for the best fit models for groups of 3 fish, for three statistics of interest -nearest neighbor distance, group polarity and consumption times (See Figure 4C-D) and the combined error based on these three measures (right). Dots represent different experimental groups; horizontal lines are median values and boxes represent the 1 st and 3 rd quartiles. Dotted lines represent 0 error in prediction or a perfect fit to the data (Methods). B. Combined error values for all 7 models tested for groups of 3 and 6 fish ( Figure  4D, Methods). The Attfeed+Align model is significantly more accurate than all other models for both group sizes (P < 0.005, Wilcoxson's signed rank test, N=10 groups) except for the Att+Align model for groups of 6 fish (P=0.21). Dots represent different groups; horizontal lines are median values and boxes represent the 1 st and 3 rd quartiles. C. The inferred detection ranges for both the flake detection range ( " ) and the neighbor detection range ( # ) for the Attfeed+Align model. Horizontal lines are median values and boxes represent the 1 st and 3 rd quartiles. D. Calculated error for all models for groups of 3 (top row) and 6 (bottom row) fish, for three statistics of interest -nearest neighbor distance, group polarity and consumption times (See Figure 4A-    (see eq. 2) is shown for real foraging groups (black) and simulated groups using the Attfeed+Align strategy (orange). Horizontal lines show median values, boxes represent the 1 st and 3 rd quartiles; no statistical differences were found between equality values in simulations and those of real groups of 3 fish (P=0.23, N=10) and 6 fish (P = 0.77, N = 10); Wilcoxon's signed rank test. B. Average Increase in equality for simulated groups of foragers using the Attfeed+Align strategy, compared to independent foragers for the maximal social interaction range tested ( " ≤ 5, # = 25) plotted against the estimated dispersion of flakes in the arena (Methods). Horizontal dotted line represents 0 increase in equality and the vertical dotted line is the median dispersion value. Note that for groups of 6 fish, foraging for flakes with lower dispersion values (or high clustering) resulted in an increase in equality while foraging for flakes with higher dispersion showed a decrease in equality. C. Average difference in equality values between different social foraging strategies and independent foragers (IND model). Equality values were averaged over " ≤ 5 and over simulations corresponding to different groups (N = 10 groups for 3 fish and N=5,5 for low and high flake dispersion in groups of 6 fish). Note that the largest increase in equality was for models that incorporate specific attraction to neighbor's flake consumptions. D. Equality of food distribution among foragers for all " , # values for all mixed strategy groups of 3 and 6 fish. Different panels show different fractions of individuals using the Attfeed+Align strategy out of the total group; results are shown for groups of 3 fish (top row) and for groups of 6 fish (bottom row).

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Note that the effects observed when only attraction to neighbors' previous consumptions is included 514 in the model are very similar to those in the Attfeed+Align model (see Figure 7), but also span the larger 515 group sizes (12 and 24 fish). 517  518  519  520  521  522  523  524  525  526  527  528  529  530  531  532  533  534  535  536  537  538  539  540  541  542  543  544  545  546  547  548  purchased from a local supplier (Aquazone LTD, Israel) and housed separately in their 577 designated groups for more than a month prior to behavioral experiments. Fish were housed 578 in a standard fish holding system consisting of a recirculating multistage filtration system 579 where temperature, conductivity, PH, and light-dark cycle were monitored. 580

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Imaging of fish foraging behavior was done using an industrial recording system composed of 581 a Vieworks VC-2MC-M340 camera with an 8 mm lens, a Karbon-CL frame grabber, and a 582 recording server. Camera was suspended 150 cm above the experimental tank. During 583 experiments we changed the effective experimental tank size by using different size arenas 584 (Figure 1-figure supplement 1A and see below). All water conditions were similar between 585 the holding tanks and the experimental tank. 586 587 Fish acclimation and behavioral experiments. To facilitate food searching behavior and to 588 lower fish anxiety, the following acclimation procedure was followed: On day 1, all fish were 589 transferred to the designated experimental tank (D = 95cm; water depth of 5 cm) and were 590 allowed to explore the tank for 5 minutes. On days 2-5, all groups and individual fish were 591 transferred from their home tanks to test tanks of increasing size (start box -25x25cm, 592 D=47.5,cm D=67.2cm, D=95cm, Figure 1-figure supplement 1A) where 6, 12, or 18 flakes were 593 randomly scattered over the water in the area outside the start box (for groups of sizes 1, 3, 594 and 6 respectively, Figure 1-figure supplement 1A). The number of flakes used in the 595 experiments for individual fish and for groups were chosen based on preliminary 596 experiments, as the amount of food that would entice single fish to engage in the task yet not 597 to overcrowd the arena with flakes (especially for the larger groups). Fish were first placed in 598 a small starting box (25x25 cm) that was inside a larger arena. The small box was raised after 599 5 minutes and the fish were allowed to forage and consume the flakes in the larger arena for 600 an additional 5 minutes. After the allotted time ended the fish were netted and returned back 601 to their home tanks, keeping their original groups. Over the 4 days of training, we increased 602 the size of the test tank from the small start box itself (day 2) to the largest arena with D = 603 47.5, 67.2, 95cm on days 3-5 ( Figure 1-figure supplement 1A). On days 6-7 fish were deprived 604 of food and kept in their home tanks. Foraging was then tested on day 8. During training, no 605 food was administered to the fish outside of the experimental arena. In total, n = 106 adult 606 fish (3 months old or older) were used at approximately 1:1 male to female ratio. 16 single 607 individuals were tested, 10 groups of 3 fish (30 fish in total), and 10 groups of 6 fish (60 fish 608 in total). Two single individual fish were excluded from analysis as they did not swim when 609 transferred to the experimental tank. where R is the radius of the circle that gave the best Euclidean fit to a trajectory segment of 622 length 600 ms, centered on time . 623 624 Tracking flakes. Flakes' locations were tracked with the same software that we have 625 developed and used for tracking the fish (48). Flakes that were larger than 4 pixels (which 626 correspond to a radius of about 1.15 mm) were reliably detected. Flakes typically disappeared 627 when eaten, but when consumed flakes broke into smaller pieces, new (sub)flakes appeared. 628 Consumption events were defined at times when a fish made contact with a flake and the 629 flake disappeared from the camera's field of view. The resolution of our camera did not allow 630 us to confirm whether the fish digested the flake entirely. 631 632 Flake consumption events and pseudo consumption events. We estimated the probability 633 of fish to cross near locations of consumption events by another fish, ( ), by 634 counting all events where at least one fish passed within 2 BL of that location within 1-4 s 635 after a neighbor's flake consumption, and dividing it by the total number of consumption 636 events. Since zebrafish tend to swim in groups, regardless of the presence of food, we 637 compared this number to the probability of one fish to cross near a neighbor's position within 638 1-4 s when no food was recently consumed by that neighbor (within the last 4 s) or will be 639 consumed in the near future (within the next 4s). We therefore estimated $9** ( ) 640 by drawing random fish positions (mimicking k flake detection events) 10000 times, from 641 times when no flake was detected for at least 8 s ( Figure 2D). The tendency to attract to flake 642 position was then given by: ( ) − 〈 $9** ( )〉, where angle brackets 643 represent the average over random drawings for a given group. 644 We defined ``pseudo flake consumptions" at times when fish exhibited a similar speed profile 645 to that of a fish during real consumption events, namely gradual increase in speed followed 646 by a sudden sharp decrease back to baseline ( Figure 2B). To detect such events, we convolved 647 the speed profile of individual fish in the group at all times when no flakes were present near 648 the fish (for at least 8 s) with the calculated average speed profile near all real flake 649 consumption events of that group ( Figure 2B) and obtained a correlation measure for each 650 point in time. We then treated the top 2.5 percent of this distribution as pseudo consumption 651 events. The average number of events was 12.6 ± 4 and 21.8 ± 6.6 for groups of 3 and 6 fish, 652 respectively. We compared the probability of neighbors to cross near the locations of such 653 events, ( ) to $9** ( ). The tendency of neighboring fish to cross 654 near pseudo consumption events was high, and was correlated with their tendency to cross 655 near real flake consumption events over groups ( were negligible compared to the motion of the fish. Since real flakes sometimes disintegrated 684 into smaller bits after a consumption event, we copied that in the simulations. I.e. if flake i at 685 position ⃗ % has appeared after flake j was (partially) consumed, so did the corresponding 686 flakes in the simulation. 687 688 c. Sensory range of flake detection. Each simulated fish had a circular range # , within which, 689 it could detect a flake, and orient towards it with probability p(go to flake) = 53 & /; & , where 690 # is the distance to the flake ( Figure 3C). If the fish oriented itself towards the flake, its next 691 step size was drawn from the empirical distribution. If the fish reached the flake (or passed 692 it) during this movement, that flake was considered as consumed. If the simulated fish did not 693 reach the flake, the procedure was repeated. In the IND foraging model, k such fish were 694 simultaneously simulated, independent of one another. 695 696 d. Sensory range of neighbor detection. Since foraging fish in real groups were found to be 697 attracted to areas of previous flake consumptions, and since zebrafish are known to exhibit 698 schooling and shoaling tendencies, we allowed agents in our simulated social models to 699 detect and respond to neighbors' swimming and foraging behavior within the sensory range 700 of neighbor detection, $ . Specifically, agents in the social foraging models could combine 701 various types of social interactions ( Figure 3D, Figure  neighbor detection, $ in the previous times step, fish adopted the average direction 717 of these neighbors with probability P(align) = 5⟨ ⟩/ where ⟨ # ⟩ is the distance to 718 the center of mass of the neighbors, such that the new direction of fish i is ⃗ % ( + 1) = 719 where J is the number of neighbors within $ . 720 721 722 e. Hierarchical nature of the social models. In the simulations, fish actions were given by the 723 following hierarchy: If a flake was within the # range of a fish, that fish would turn towards 724 it with p(go to flake). If a flake was not detected (i.e. no flake was within # ), and a neighbor 725 consumed a flake at a distance smaller than $ , then the fish would move towards that 726 location with the appropriate probability (for the cases where the model included response 727 to food consumption by neighbors). If neither a flake nor a neighbor consumption event was 728 detected, but neighbors were within a distance shorter than $ , the fish responded to the 729 position/orientation of these neighbors (given that the model includes response to neighbors' 730 swimming). If no flakes or neighbors were detected, or if motion towards these areas was not 731 successfully drawn, then the next direction of motion of the fish was randomly chosen from 732 the empirical turning angle distribution. 733 Sample sizes and power estimation. As the current research tests novel effects of social 833 behavior on group foraging, precise estimation of sample sizes and statistical power could not 834 be conducted a-priori. Instead, we have based our choice of sample sizes on previously 835 published studies of collective behavior and social foraging behavior of zebrafish (42, 48). In 836 addition, we chose to include more than one group size in the study design (groups of 3 and 837 6 fish) to support the generality of our findings. Finally