Many-Eyes and Sentinels in Selfish and Cooperative Groups

TL;DR

The paper develops a general, minimal-assumption model of collective vigilance where an individual’s net fitness is $f_i = b(S) - c(v_i)$ with $S = \sum_i v_i$. It shows that many-eyes and sentinel strategies are alternative solutions determined by the curvature of the vigilance cost $c(v)$ relative to the benefit $b(S)$, yielding many-eyes under convex costs and sentinels under concave costs in both selfish and cooperative settings. The authors provide analytical results, dynamical-systems stability analysis, and extensive simulations, and they extend the framework to explain behavioral switching (e.g., sigmoidal costs) and edge effects arising from heterogeneity. The work synthesizes disparate literature into a unified explanation for when distributed vigilance or concentrated sentinel roles emerge, with broad ecological and theoretical implications for understanding collective sensing across species and domains. Overall, the study provides a versatile framework linking environmental structure, cost curvature, and vigilance strategies to predict and interpret observed vigilance patterns in diverse social groups.

Abstract

Collective vigilance describes how animals in groups benefit from the predator detection efforts of others. Empirical observations typically find either a many-eyes strategy with all (or many) group members maintaining a low level of individual vigilance, or a sentinel strategy with one (or a few) individuals maintaining a high level of individual vigilance while others do not. With a general analytical treatment that makes minimal assumptions, we show that these two strategies are alternate solutions to the same adaptive problem of balancing the costs of predation and vigilance. Which strategy is preferred depends on how costs scale with the level of individual vigilance: many-eyes strategies are preferred where costs of vigilance rise gently at low levels but become steeper at higher levels (convex; e.g. an open field); sentinel strategies are preferred where costs of vigilance rise steeply at low levels and then flatten out (concave; e.g. environments with vantage points). This same dichotomy emerges whether individuals act selfishly to optimise their own fitness or cooperatively to optimise group fitness. The model is extended to explain discrete behavioural switching between strategies and differential levels of vigilance such as edge effects.

Figures (4)

• Figure 1: Phase portraits of fitness gradients with a selfish group of size $N=2$, with individual vigilances of $v_1$ (x-axis) and $v_2$ (y-axis). Flow lines show how the group strategy changes. a) With flattening (concave) costs there is d) a single dynamically unstable interior equilibrium and $N$ symmetric stable equilibria on the edges of the strategy space. b) With linear vigilance costs there is e) a $N-1$ dimensional ridge of neutrally stable equilibria with a fixed optimal collective vigilance. c) With steepening (convex) costs there is f) a single interior many-eyes stable point with all $N$ watchers having the same individual vigilance.
• Figure 2: Cooperative groups with $N=16$ individuals. The vigilance cost functions (a-c) determine the fitness landscapes panels d-f) over the number of watchers, n, with non-zero vigilance, and the vigilance of these watchers, v. Optimal strategies are denoted with black dots. a) Flattening (concave) vigilance costs favour d) a sentinel strategy with a single watcher, $n=1$, with high vigilance. b) Linear vigilance cost functions lead to e) indifference between strategies along an optimal ridge. c) Steepening (convex) vigilance costs favour f) a many-eyes strategy with the entire group, $n=16$, maintaining a low individual vigilance. Heatmaps only show positive average fitness, otherwise white.
• Figure 3: Simulated vigilance behaviour in a) selfish and b) cooperative groups with varying scaling in vigilance costs (x-axis) and predation threat levels (y-axis log scale). In both selfish and cooperative groups, there is a clear dichotomy where we see many-eyes behaviour (green) with steepening (convex) costs and sentinel behaviour (blue) with flattening (concave) costs.
• Figure 4: Model extensions. a,b) Example of behavioural switching with S-shaped cost curves. a) At low predation threat, the many-eyes strategy (green circles) has a lower average vigilance cost (gradient of green dashed line) than a sentinel strategy (gradient of dashed grey line). b) At high predation threat levels, a sentinel strategy (blue square) has a lower average vigilance cost (gradient of dashed blue line) than a many-eyes strategy (gradient of dashed grey line). c) Example of edge effects with heterogenous cost curves. Lower costs at the edge of the group leads to higher vigilance at the edge (dark green pentagons) than the interior (green circles), with all individuals having the same marginal costs (dotted tangents).