Abstract
There is a strong body of evidence that patterns of collective behaviour in grouping animals are governed by interactions between small numbers of individuals within the group. These findings contrast with study of the ‘selfish herd’, where increasingly complex individual-level movement rules have been proposed to explain the rapid increase in aggregation observed when prey groups are startled by or detect a predator. While individuals using simple rules take into account the position of only a few neighbours, those using complex rules incorporate multiple neighbours, and their relative distance, to determine their movement direction. Here, we simulate the evolution of selfish herd behaviour to assess the conditions under which simple and complex movement rules might evolve, explicitly testing predictions arising from previous work. We find that complex rules outperform simple ones under a range of predator attack strategies, but that simple rules can fix in populations particularly when they are already in the majority, suggesting strong positive frequency dependence in rule success. In addition, we explore whether a movement rule derived from studies of collective behaviour (where individuals use the position of seven neighbours to determine movement direction) performs as successfully as more complex rules, finding again positive frequency dependence in rule success, and a particular role for predator attack strategy (from within or outside the group).
Highlights
Aggregation into groups is a widely observed natural-‐history trait, both taxonomically and across different biomes
While it is of course feasible that the different situations of movement synchronisation and increasing aggregation use different methods of processing information, the discrepancy in research activity is worthy of further investigation. 117 In our previous work, we found that simpler mutant aggregation strategies experienced a reduced share of the risk in populations of more complex rules, when predators attacked during the process of aggregation (Morrell et al 2011a), and in populations that are of lower density (Morrell et al 2011b) and larger size (Morrell & James 2008)
This leads to the prediction that: 5. A rule whereby individuals account for the position of 7 neighbours is as likely to evolve as a more complex rule whereby individuals account for the position of up to 20 individuals
Summary
Aggregation into groups is a widely observed natural-‐history trait, both taxonomically and across different biomes. Theoretical research on the selfish herd focuses primarily on the point at which stable aggregations have formed, but recent work suggests that timing of predator attacks in relation to the point at which prey first detect the predator and initiate anti-‐predator behaviour is crucial in determining the success of movement rules, and that simpler rules, accounting for fewer neighbours, might evolve under a range of biologically-‐ plausible conditions (Morrell and James 2008; Morrell et al 2011a). Our previous work (Morrell & James 2008, Morrell et al 2011a, b) provides a series of predictions, based on reduction of individual risk in a group, as to when mutant individuals using simpler rules should be able to invade a population of more complex rules. This leads to the prediction that: 5. A rule whereby individuals account for the position of 7 neighbours (i.e. a relatively small number) is as likely to evolve as a more complex rule whereby individuals account for the position of up to 20 individuals (the “Local Crowded Horizon” rule; Viscido et al 2002, table 1)
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