Boids of a Feather Flock Together - Evolving Prey Behaviours Under Different Predator Attack Strategies

Augusta van Haren; Hanna Hoogen; Luca Pattavina

q-bio.PESep 29, 2026

Boids of a Feather Flock Together - Evolving Prey Behaviours Under Different Predator Attack Strategies

Authors: Augusta van Haren, Hanna Hoogen, Luca Pattavina

Organizations: Radboud University

Abstract

Flocking and schooling are thought to have evolved partly as defences against predation, but how prey should balance social and escape tendencies may depend on the predator's hunting strategy. We extend the predator-prey boids model of Ojo et al. (2023), itself based on Reynolds' boids, by combining six prey movement tendencies (alignment, cohesion, separation, dodge, repel and wiggle) into a single weighted acceleration update, and by reformulating wiggle as a sinusoidal manoeuvre. We then use an evolutionary strategy to optimise the six behaviour coefficients for collective prey survival against four predator hunting strategies: attack-centroid, attack-nearest, attack-random and attack-peripheral. Across five independent trials per strategy, coefficients converged within trials and mean fitness remained stable or increased, although trials often settled in different local optima. Prey survival was highest under attack-centroid and lowest under attack-nearest, in line with our hypotheses. Against attack-centroid, prey evolved individualistic predator avoidance with high escape coefficients, whereas against the other three strategies they largely kept their flock formation. Across all strategies, evolution favoured a low repel coefficient and relatively high dodge and wiggle coefficients. Our results suggest that optimal anti-predator behaviour depends on the interplay between escape tendencies and the predator's hunting strategy.

Figures & tables

Panel of Figure 1 — Figure 1 : Evolution of the distribution of fitnesses $f(s)$ over generations, for five different ES trials (corresponding to five different colours), per predator hunting strategy. Each dot corresponds to an individual simulation, where overlapping simulations result in darker-shaded dots. The line represents the population’s mean fitness. Note that for every ES trial, the mean fitness remains stable or rises over generations.

Figure 2 : From left to right, top to bottom: evolution of prey coefficients $gene(s):=\langle c_{ali},c_{coh},c_{sep},c_{dod},c_{rep},c_{wig}\rangle$ under the attack-centroid hunting strategy, $\mathbf{\hat{a}}(B)=\mathbf{\hat{a}_{attc}}(B)$ , for five different ES trials – corresponding to five different colours. Each dot (●) corresponds to an individual simulation, where overlapping simulations result in darker-shaded dots. The vertical bars indicate the population’s error margin (mean $\pm$ std) at the last generation of each ES, whereas the stars ( $\bigstar$ ) indicate the coefficient’s value of the fittest individual of the last generation.

Figure 3 : From left to right, top to bottom: evolution of prey coefficients $gene(s):=\langle c_{ali},c_{coh},c_{sep},c_{dod},c_{rep},c_{wig}\rangle$ under the attack-nearest hunting strategy, $\mathbf{\hat{a}}(B)=\mathbf{\hat{a}_{attn}}(B)$ , for five different ES trials – corresponding to five different colours. Each dot (●) corresponds to an individual simulation, where overlapping simulations result in darker-shaded dots. The vertical bars indicate the population’s error margin (mean $\pm$ std) at the last generation of each ES, whereas the stars ( $\bigstar$ ) indicate the coefficient’s value of the fittest individual of the last generation.

Figure 4 : From left to right, top to bottom: evolution of prey coefficients $gene(s):=\langle c_{ali},c_{coh},c_{sep},c_{dod},c_{rep},c_{wig}\rangle$ under the attack-random hunting strategy, $\mathbf{\hat{a}}(B)=\mathbf{\hat{a}_{attr}}(B)$ , for five different ES trials – corresponding to five different colours. Each dot (●) corresponds to an individual simulation, where overlapping simulations result in darker-shaded dots. The vertical bars indicate the population’s error margin (mean $\pm$ std) at the last generation of each ES, whereas the stars ( $\bigstar$ ) indicate the coefficient’s value of the fittest individual of the last generation.

Figure 5 : From left to right, top to bottom: evolution of prey coefficients $gene(s):=\langle c_{ali},c_{coh},c_{sep},c_{dod},c_{rep},c_{wig}\rangle$ under the attack-peripheral hunting strategy, $\mathbf{\hat{a}}(B)=\mathbf{\hat{a}_{attp}}(B)$ , for five different ES trials – corresponding to five different colours. Each dot (●) corresponds to an individual simulation, where overlapping simulations result in darker-shaded dots. The vertical bars indicate the population’s error margin (mean $\pm$ std) at the last generation of each ES, whereas the stars ( $\bigstar$ ) indicate the coefficient’s value of the fittest individual of the last generation.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Boids Model
Parameter	Explanation	Value
$S_{x}\times S_{y}$	field size (px)	$1920\times 1080$
		Predator	Prey
$M,N$	number of boids	1	100
$r_{P}^{pred,prey}$	perception radius (px)	3000	{300, 750 , 1500, 3000}
$r_{S}^{pred,prey}$	separation radius (px)	100	50

Appendix

Table 1 : Fixed parameter settings relating to the Boids Model and the evolutionary strategy (ES) that were used for running the main experiments. The settings were tweaked such, that they produced naturalistic predator and prey motion dynamics, and furthermore allowed ES convergence over generations. The parameter values in light grey correspond to the settings examined in the sensitivity analyses (see Appendix B ), but not selected for running the main experiments.

Figure 6 : Initial layout of the predator (red) and prey (white) that was fixed for every simulation.

Panel of Figure 7 — Figure 7 : Comparison of ES convergence in terms of the simulations’ prey coefficients and fitnesses, when varying the prey’s perception radius $r_{P}^{prey}\in\{300,750,1500,3000\}$ . The sensitivity analyses were run for $\mathcal{N}_{g}=20$ generations. Other parameter settings were fixed to the settings in Table 1 .

Panel of Figure 8 — Figure 8 : Comparison of ES convergence in terms of the simulations’ prey coefficients and fitnesses, when varying the prey’s field of view (per eye) $fov^{prey}\in\{\frac{60}{2},\frac{120}{2},\frac{240}{2},\frac{360}{2}\}$ . The sensitivity analyses were run for $\mathcal{N}_{g}=20$ generations. Other parameter settings were fixed to the settings in Table 1 .

Panel of Figure 9 — Figure 9 : Comparison of ES convergence in terms of the simulations’ prey coefficients and fitnesses, when varying the number of simulations per generation (population size) $\mathcal{N}_{s}\in\{30,50\}$ . The sensitivity analyses were run for $\mathcal{N}_{g}=20$ generations. Other parameter settings were fixed to the settings in Table 1 .

Panel of Figure 10 — Figure 10 : Comparison of ES convergence in terms of the simulations’ prey coefficients and fitnesses, when varying the mutation rate $\mu\in\{0.05,0.3,0.7\}$ . The sensitivity analyses were run for $\mathcal{N}_{g}=20$ generations. Other parameter settings were fixed to the settings in Table 1 .

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