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 six fish, for the IND, Att, Align, and the Att_feed+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 standard deviation (SD) in the simulation. (B) Flake consumption times (black dots) of two groups of six 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 six fish are shown for three statistics of interest: the polarity of the group $E^{polarity}=\frac{P^{data}-P^{model}}{S{D(P}^{data})}$, the nearest neighbor distance $E^{D_{nn}}=\frac{{D_{nn}}^{data}-{D_{nn}}^{model}}{S{D(D_{nn}}^{data})}$, and the consumption times $E^{consumptions}=\frac{1}{N}\sum _n\left[log\right(t^{data}\left(n\right))-log(t^{model}\left(n\right)){]}^2,$ where N is the number of flakes consumed. Dots represent different experimental groups; horizontal lines are median values and boxes represent the 1^st and 3^rd quartiles. Dotted line represents 0 error in prediction or a perfect fit to the data. (D) Combined error of each of the models presented in C. $E^{combined}={(E}^{polarity}+E^{D_{nn}}+E^{consumptions})/3$, where all error measures were scaled to be between 0 and 1, by dividing by the largest observed error for that measure. The Att_feed+Align model is significantly more accurate than the IND, Att, and Align models (p<0.005 for all, Wilcoxson’s signed rank test, N = 10 groups, Materials and methods). Each dot represents one group; horizontal lines are median values and boxes represent the 1^st and 3^rd quartiles.

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 (Materials and methods). (B) Combined error values for all models tested for groups of three and six fish (Figure 4D, Materials and methods). The Att_feed+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 six 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 ($D_f$) and the neighbor detection range ($D_n$) for the Att_feed+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 three fish (top row) and six fish (bottom row), for three statistics of interest - nearest neighbor distance, group polarity and consumption times (See Figure 4A-B). 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 (Materials and methods).