'Selfish herders' finish last in mobile animal groups

Abstract

Predation is a powerful selective pressure and probably a driver of why many animal species live in groups. One key explanation for the evolution of sociality is the 'selfish herd' model, which describes how individuals who stay close to others effectively put neighbours between themselves and a predator to survive incoming attacks. This model is often illustrated with reference to herds of ungulates, schools of fish or flocks of birds. Yet in nature, when a predator strikes, herds are often found fleeing cohesively in the same direction, not jostling for position in the centre of the group. This paper highlights a critical assumption of the original model, namely that prey do not move in response to position of their predator. In this model, I relax this assumption and find that individuals who adopt 'selfish herd' behaviour are often more likely to be captured, because they end up at the back of a fleeing herd. By contrast, individuals that adopt a rule of 'neighbour to neighbour alignment' are able to avoid rearmost positions in a moving herd. Alignment is more successful than selfish herding across much of the parameter space, which may explain why highly aligned fleeing behaviour is commonly observed in nature.

Keywords: alignment; cooperation; coordination; predator–prey dynamics; selfish.

Figure 1.

(a) At prey capture, density of individuals in front-back and left-right distance to centroid (density scale defined in [21]). The group which consists of 50–50% centroid-focused to alignment-focused individuals is headed from left to right. Top (centroid-focused individuals), middle (alignment-focused individuals), bottom (predator). Coloured lines below are median x-axis values. (b) Alignment benefit represents how much alignment-focused individuals are safer than centroid-focused individuals; dotted line p = 0.05. Negative values represent centroid-focused being safer. Each data point (N = 81) represents N = 10 000 simulations for each set of parameters (see results split by parameter in figure 2). For visual communication, χ² results are transformed, where ‘alignment benefit' = sgn(x)·log(|x| + 1) (see Methods: Statistics). (c) Distribution of N = 10 000 group speeds (median centroid speed) for each composition at default parameters (see Methods). (Online version in colour.)

Figure 2.

Alignment benefit for compositions with different (a) predator speeds, (b) border avoidance conditions and (c) all other parameters not directly referenced in main text. All parameters set at default except the parameter explored on the x-axis of each panel (table 1 and Methods). For visual communication, χ² results are transformed, where ‘alignment benefit' = sgn(x) · log(|x| + 1) (see Methods: Statistics). (Online version in colour.)