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

Augusta van Haren, Hanna Hoogen, Luca Pattavina

arXiv:2609.37885v1q-bio.PEcs.AI

TL;DR

The paper examines how prey should balance flocking and escape behaviours under different predator hunting strategies. It combines six prey tendencies in an extended boids model and uses an evolutionary strategy to optimise their coefficients. Survival was highest against attack-centroid and lowest against attack-nearest, while evolved behaviours differed by strategy.

  • Problem

    The paper asks which combination of six prey movement tendencies maximises collective survival under different predator hunting strategies.

    Source: §1.1 · p. 1

  • Method

    The study combines six prey tendencies in a weighted acceleration update and uses an evolutionary strategy to optimise their coefficients across four predator attack strategies.

    Source: §1.1 · p. 1, §2.2 · p. 5

  • Results

    Prey survival was highest under attack-centroid and lowest under attack-nearest, while attack-centroid favoured individualistic escape and the other strategies favoured flocking more.

    Source: §4 · pp. 9–10

  • Takeaways & Limitations

    Flocking was usually beneficial, while optimal escape behaviour varied somewhat with the predator’s hunting strategy.

    Source: §5 · p. 11

    Computational cost restricted evolutionary-strategy runs to 30 generations, limiting assessment of convergence.

    Source: §4.1 · p. 11

Abstract

from arXiv · show

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.

1 Introduction

Flocking and schooling may reduce predation losses, but prey must balance social and escape tendencies as predator strategies vary. This work evolves six prey-behaviour coefficients under four hunting strategies, extending prior boids work by combining tendencies in a weighted acceleration vector and using continuous optimisation.

1 Introduction

  • Collective behaviours such as flocking may reduce predation losses through predator confusion or shared information, while survival depends on balancing behavioural tendencies.The paper situates this question in predator–prey interactions among locally interacting agents.Source: §1 · p. 1

1.2 Related Work

  • The model combines six prey movement tendencies into one weighted acceleration vector, allowing escape and flocking behaviours to operate together.It also refines wiggle behaviour and uses an evolutionary strategy to optimise the tendency coefficients across four predator attack strategies.Source: §1.1 · p. 1, §1.2 · p. 2

1.1 Research Question

  • The study asks which relative contributions of alignment, cohesion, separation, dodge, repel, and wiggle maximise collective prey survival under different predator hunting strategies.It hypothesises that optimal combinations and survival rates differ by strategy, with highest survival under attack-centroid and lowest under attack-nearest.Source: §1.1 · pp. 1–2

1.2 Related Work

  • The work uses an evolutionary strategy to continuously optimise coefficients for combined prey behaviours against different predator attack strategies.Prior studies evolved broader flocking behaviours or focused on isolated escape strategies, whereas this work targets specific prey escape strategies.Source: §1.2 · p. 2

2 Methods

The methods adapt a predator–prey boids simulation and combine prey flocking and escape tendencies in a weighted acceleration update. An evolutionary strategy then optimises their relative coefficients while simulations model four predator attack strategies and prey capture.

2.1 Boids Model

  • The simulation adapts a predator–prey extension of Reynolds’s boids model, whose movement rules include alignment, cohesion, and separation.Boids have positions and velocities; their acceleration and velocity are bounded, and their neighbours are filtered by distance, field of view, and occlusion.Source: §2.1 · pp. 2–3

2.1.1 Predator

  • Predators use attack-centroid, attack-nearest, attack-random, or attack-peripheral strategies to target neighbouring prey.The strategies target, respectively, the average position, nearest prey, a randomly selected prey, or the most peripheral prey.Source: §2.1.1 · p. 3

2.1.2 Prey

  • Prey acceleration combines alignment, cohesion, separation, dodge, repel, and wiggle as a weighted sum whose coefficients determine each tendency’s contribution.The first three tendencies produce flocking; dodge, repel, and wiggle are escape manoeuvres, and wiggle is reformulated as a sine wave with an angle and frequency.Source: §2.1.2 · p. 4

2.1.3 Simulation

  • Each simulation begins with predators and prey in a field, and a prey boid is removed when a predator catches it.The simulation uses a capture-distance condition for removal.Source: §2.1.3 · p. 4

2.2 Evolutionary Strategy (ES)

The evolutionary strategy treats each simulation’s six prey coefficients as an individual and evaluates it by surviving prey. Across generations, selection, crossover, mutation, and coefficient bounds produce new candidate coefficient sets; experiments compare their evolution across predator strategies.

2.2 Evolutionary Strategy (ES)

  • Each simulation’s six prey coefficients form its gene, and its fitness is evaluated within an evolutionary strategy of generations and simulation populations.The strategy carries the two fittest simulations forward, then creates the remaining population through parent selection, crossover, and mutation; coefficients are clipped to [0, 1].Source: §2.2 · p. 5, §2.2.2 · p. 5

2.2.1 Fitness

  • Fitness is the number of prey surviving at the end of a simulation after T time-steps.The measure is defined from the prey’s perspective, with NT ≤ N.Source: §2.2.1 · p. 5

2.3 Experimental Design

  • The study treats predator hunting strategy as the independent variable and prey-coefficient distributions over generations as the outcomes of interest.Most other parameters are fixed, and their potential influence is examined through sensitivity analyses.Source: §2.3 · pp. 5–6
  • The experiments run 30 generations of 30 simulations from random coefficient initialisations and repeat each predator-strategy trial five times.The researchers track coefficient distributions and fitness over generations, expecting convergence and increasing mean fitness.Source: §2.3 · p. 5

3 Results

Across five ES trials per strategy, mean fitness stayed stable or rose while coefficients converged within trials, sometimes to different local optima. Prey survival and evolved movement patterns varied with the predator’s hunting strategy.

3 Results

  • Across trials, mean fitness stayed stable or rose consistently within each strategy; coefficients converged within runs but sometimes bifurcated into distinct local optima.Convergence patterns across trials did not always agree, with some coefficients reaching different local optima.Source: §3 · pp. 6–7
  • Centroid attacks left prey near maximal fitness, whereas nearest-attack survival plateaued at 60% after about 10 generations.Under attack-nearest, initial survival was below 50%.Source: §3.1 · p. 7, §3.2 · p. 8

3.1 Attack-Centroid Hunting Strategy (ˆa(B) = ˆaattc(B))

  • Under centroid attacks, escape coefficients generally converged high, while flocking coefficients varied; prey avoided predators but usually retained some formation.Repel showed the strongest agreement among escape tendencies across trials; flocking tendencies showed little agreement.Source: §3.1 · pp. 7–8

3.2 Attack-Nearest Hunting Strategy (ˆa(B) = ˆaattn(B))

  • Under nearest attacks, repel converged to [0.0, 0.2]; three of five trials kept the starting formation, with prey eaten one by one.The passage describes repel’s low value as a crucial requirement for survival under this strategy.Source: §3.2 · p. 8

3.3 Attack-Random Hunting Strategy (ˆa(B) = ˆaattr(B))

  • Attack-random produced near-negligible fitness improvement; escape coefficients aligned across trials while flocking coefficients varied, and prey mostly retained formation.Repel favored [0.0, 0.4], while dodge and wiggle tended toward medium-to-high values.Source: §3.3 · pp. 8–9

3.4 Attack-Peripheral Hunting Strategy (ˆa(B) = ˆaattp(B))

  • Under peripheral attacks, fitness ranged from 52 to 91 with slight improvement; trials favored low repel and high wiggle, and prey generally kept formation.The fittest simulations also showed wiggling behavior, which was not observed under the other strategies.Source: §3.4 · p. 9

4 Discussion

Prey survival was highest against attack-centroid and lowest against attack-nearest; evolved behavior also differed, with more individualistic escape against attack-centroid and more flocking against the other strategies. The study’s conclusions are bounded by fixed simulation conditions, short ES runs, and a limited parameter exploration.

4 Discussion

  • Attack-centroid favored individualistic predator avoidance with high escape coefficients, whereas attack-nearest, attack-random, and attack-peripheral favored flock formation.For random and peripheral attacks, prey turned away when they spotted the predator but avoided sharp maneuvers that broke formation.Source: §4 · pp. 9–10
  • Prey survival was highest under attack-centroid and lowest under attack-nearest, while attack-random and attack-peripheral fell between these extremes.Attack-nearest reliably favored staying in the initial formation; centroid attacks often targeted empty space.Source: §4 · p. 10
  • Across strategies, evolution favored relatively low repel and relatively high dodge and wiggle coefficients, but no clear pattern emerged for flocking coefficients.The authors suggest coefficient interactions may explain the contrast with Ojo et al. (2023), who found position-based repel performed better than direction-based dodge in isolation.Source: §4 · pp. 10–11

4.1 Limitations & Future Work

  • Simulations used a limited-size 2D toroidal environment, so the reported behaviors do not establish what occurs in open or higher-dimensional spaces.The authors also propose adding obstacles or other environmental features for future study.Source: §4.1 · p. 11
  • Every simulation began with the same boid positions and directions, limiting assessment of how evolved behaviors vary across initial setups.The authors suggest exploring different initial setups to introduce stochasticity and enhance realism.Source: §4.1 · p. 11
  • Computational cost limited ES runs to Ng = 30 generations, and the broad parameter space leaves other strategies and settings unexplored.The authors recommend more extensive ES runs to assess convergence and further exploration of parameter settings, combined hunting strategies, and multiple predators.Source: §4.1 · p. 11

5 Conclusion

The conclusion is that prey behavior optimizing collective survival varies somewhat with predator strategy: flocking is usually beneficial, while the optimal escape contribution varies. The authors also conclude that attacking the nearest prey is reliably most successful among the strategies considered.

5 Conclusion

  • Attacking the nearest prey was reliably most successful for predators, while attacking the centroid or a randomly selected prey was not effective.Source: §5 · p. 11
  • Flocking was usually beneficial for prey, while the optimal contribution of escape tendencies varied somewhat with the predator’s hunting strategy.Source: §5 · p. 11
  • The study examined how prey evolve relative contributions of alignment, cohesion, separation, dodge, repel, and wiggle to maximize collective survival across predator strategies.Source: §5 · p. 11

A Fixed Parameter Settings

The main experiments held Boids and evolutionary-strategy settings fixed, choosing them to support naturalistic motion and convergence. The fixed setup used one predator and 100 prey, with deterministic initial placement but stochastic simulation outcomes.

A Fixed Parameter Settings

  • Table 1 lists the fixed Boids and ES settings, with light-grey values marking sensitivity-analysis settings not used in the main experiments.Settings were tuned for naturalistic predator and prey motion and ES convergence over generations.Source: Table 1 · p. 13, A Fixed Parameter Settings · p. 13
  • One predator and 100 prey were used to isolate hunting-strategy effects while keeping fitness quantification practical.The fixed initial layout placed prey evenly, with sufficient candidates in the predator’s field of view; outcomes remained stochastic despite deterministic initial conditions.Source: A Fixed Parameter Settings · p. 13
  • The simulation duration, population size, and generation count were chosen to allow coefficient changes to affect fitness while balancing convergence and computational time.The generational update parameters were set to balance exploration and exploitation.Source: A Fixed Parameter Settings · pp. 13–14

B Sensitivity Analyses

Sensitivity analyses tested whether selected simulation and ES parameters affected convergence stability under attack-nearest. The best-performing setting for each parameter was fixed in the main experiments.

B Sensitivity Analyses

  • Under attack-nearest, sensitivity analyses varied prey perception radius, prey field of view, simulations per generation, and mutation rate across 20 generations.All other parameters remained fixed to Table 1 settings; the best-performing setting for each tested parameter was chosen for the main experiments.Source: B Sensitivity Analyses · p. 14
  • Favourable settings were assessed by rising mean fitness across generations alongside stable convergence of prey coefficients toward the fittest simulation’s values.This was treated as the population’s ability to “learn” how to survive.Source: B Sensitivity Analyses · p. 14

B.1 Perception Radius (rprey

Perception radius affected convergence stability only partly: 300 produced unstable coefficient distributions, while 750, 1500, and 3000 showed slight learning and more stable convergence. The main experiments used 750 to reduce computational load.

B.1 Perception Radius (rprey

  • At rprey_P = 300, coefficient distributions stayed broad or bifurcated, with jumpy fittest coefficients and no steady convergence toward higher collective fitness.The authors interpreted this as reflecting multiple local optima in the coefficient landscape.Source: §B.1 · p. 14
  • For rprey_P values of 750, 1500, and 3000, mean fitness rose slightly and prey-coefficient convergence appeared more stable.The comparison showed no clear preference among these three radii.Source: §B.1 · p. 14
  • The main experiments used rprey_P = 750 because larger perception radii imply more neighbours per prey and greater computational load..Source: §B.1 · p. 14

B.2 Field of View (fovprey)

Prey field of view had a minor effect on coefficient-convergence stability, which appeared similar across tested settings. The main experiments used 240 degrees, a setting associated with rising mean fitness across generations.

B.2 Field of View (fovprey)

  • Across the tested prey fields of view, coefficient convergence appeared similarly stable, though 360 degrees showed little-to-no rise in mean fitness.The overall impact on convergence stability was described as minor.Source: §B.2 · p. 14
  • The main experiments used fovprey = 240 degrees, which produced a clear rise in mean fitness across generations.This setting was chosen to mimic prey having a larger field of view than the predator’s 120 degrees.Source: §B.2 · p. 14

B.3 Number of simulations per generation (Ns)

With 30 simulations per generation, prey coefficients converged more stably than with 50. The authors selected 30 generations for the main experiments.

B.3 Number of simulations per generation (Ns)

  • Ns = 30 produced more stable convergence of prey coefficients toward the fittest simulation than Ns = 50.At Ns = 50, coefficient distributions remained broad or strongly bifurcated across generations.Source: §B.3 · p. 14
  • With Ns = 50, more simulations with suboptimal fitness remained in the population; with Ns = 30, almost all reached the fitness ceiling.Source: §B.3 · p. 14
  • The authors selected Ng = 30 for the main experiments based on these sensitivity-analysis dynamics.Source: §B.3 · p. 14

B.4 Mutation rate (µ)

Mutation rate shaped the balance between exploration and exploitation in the evolutionary strategy. The authors found the best convergence and population fitness at µ = 0.3 and selected it for the main experiments.

B.4 Mutation rate (µ)

  • µ = 0.3 yielded the best prey-coefficient convergence and population fitness by balancing exploration and exploitation.The authors selected this mutation rate for the main experiments.Source: §B.4 · pp. 14, 18, Figure 10 · p. 18
  • At µ = 0.05, limited mutation left prey-coefficient distributions with little-to-no change, impeding exploration toward higher-fitness configurations.Source: §B.4 · p. 14, Figure 10 · p. 18
  • At µ = 0.7, prey coefficients struggled to converge and remained broadly distributed, while mean fitness did not steadily rise.The passage attributes this to the 70% chance of gene mutation and overemphasis on exploration.Source: §B.4 · pp. 14, 18, Figure 10 · p. 18
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