Negotiation may lead selfish individuals to cooperate: the example of the collective vigilance game

Etienne Sirot () 0 0 Laboratoire Ecobio, UMR CNRS 6553, Universite de Rennes 1, Campus de Beaulieu , 35042 Rennes , France Game-theoretical models have been highly influential in behavioural ecology. However, these models generally assume that animals choose their action before observing the behaviour of their opponents while, in many natural situations, individuals in fact continuously react to the actions of others. A negotiation process then takes place and this may fundamentally influence the individual attitudes and the tendency to cooperate. Here, I use the classical model system of vigilance behaviour to demonstrate the consequences of such behavioural negotiation among selfish individuals, by predicting patterns of vigilance in a pair of animals foraging under threat of predation. I show that the game played by the animals and the resulting vigilance strategies take radically different forms, according to the way predation risk is shared in the pair. In particular, if predators choose their target at random, the prey respond by displaying moderate vigilance and taking turns scanning. By contrast, if the individual that takes flight later in an attack endures a higher risk of being targeted, vigilance increases and there is always at least one sentinel in the pair. Finally, when lagging behind its companion in fleeing from an attacker becomes extremely risky, vigilance decreases again and the animals scan simultaneously. 1. INTRODUCTION Evolutionary game theory is a dedicated approach of studying strategies involved in interactions among organisms and their shaping by natural selection. It has been highly influential in evolutionary biology, particularly in the field of animal behaviour [1]. The main concept of evolutionary game theory is the evolutionarily stable strategy (ESS); that is, a strategy which, once implanted in a population, may not be supplanted by any mutant strategy [2]. ESSs are used as theoretical landmarks to better understand real strategies. In general, game-theoretical models of animal behaviour consider that each individual decides what action to take before noting its opponents behaviour. For example, in models of conflicts, each protagonist chooses its level of aggressiveness [2] and in models of parental care, each parent decides how much to invest in feeding young ones [3]. However, interactions between individuals often spread over long periods, allowing each individual to continuously adapt its behaviour to the attitude of others. Natural selection should then favour efficient ways to respond to the attitude of others and, thereby, efficient ways to manipulate others behaviour through ones own attitude. To take this negotiation process into account, it is thus necessary to focus on evolutionarily stable responding rules, instead of considering that attitudes are fixed [4,5]. Negotiation affects the outcome of evolutionary games in a complex way. In particular, the resulting level of cooperation between individuals is rather unpredictable. Through negotiation, each individual may indeed try to exploit its partners by reducing its own effort [4], which corresponds to a defecting attitude. However, the tendency to cooperate with other cooperative individuals may also prove to be evolutionarily stable, so negotiation may promote cooperation through the process of reciprocity [5]. In groups of prey, the survival probability of each individual depends on its own vigilance towards predators and on the vigilance of its companions [6,7], which makes collective vigilance a dedicated subject of study for evolutionary game theory [8 10]. In general, scanning for predators is perceived as a cooperative attitude, as the information gleaned by scanning individuals may benefit other group members. Such collective vigilance does indeed allow members of large groups to detect predators more easily than members of small groups or isolated individuals [7,11]. However, individuals that do not detect a predator by themselves may also fail to detect the flight of a companion [12], or flee with a significant delay [13,14]. Indirect detection is thus less valuable than direct detection. Furthermore, individuals that only benefit from indirect detection may, because of an inappropriate reaction, become preferential targets for the predator [13]. Scanning for predators then becomes a defecting attitude that exposes non-vigilant companions to a higher risk of being targeted [15,16]. Collective vigilance is thus a complex and polymorphous game. Several elements suggest that it could be the object of a negotiation process within groups of prey. Bouts of antipredator vigilance do indeed spread over long periods dedicated to their activities, such as feeding or resting, propitious for reciprocal influences between group members. In addition, individuals in groups do often observe the attitude of their neighbours ([17 20] but see [21,22]) and the information thus gleaned influences their own vigilance behaviour [20,23,24]. Downloaded from http://rspb.royalsocietypublishing.org/ on November 16, 2014 Negotiation over antipredator vigilance E. Sirot 2863 In the present study, I derive evolutionarily stable responding rules for antipredator vigilance within a pair of foraging animals. In other words, I consider that natural selection acts on individual responsiveness to the attitudes of other prey, instead of acting on vigilance levels only. I analyse the resulting patterns of vigilance and study to what extent selfish responding rules may lead flock companions to cooperate. 2. MODEL DESCRIPTION I consider a pair of animals foraging under predation threat. At any moment in time, each member of the pair may either be feeding or vigilant. The reward for feeding is a gain in energy and the reward for vigilance is an increased probability of escaping, should an attack occur. A vigilance strategy is described by two probabilities, Pv/f and Pv/v, corresponding to the probabilities of choosing to be vigilant when ones companion is feeding and when it is vigilant, respectively. Individuals make their decisions in turn, so that each one responds to the decision immediately taken by its partner and, reciprocally, influences its next decision. The objective is to derive the evolutionarily stable values of Pv/f and Pv/v, which govern the proportions of time spent in vigilance by both individuals and the level of overlap between their respective scanning bouts. When individual A plays strategy fPv/f ; Pv/vg and individual B strategy fPv0=f ; Pv0=vg, the resulting proportions of time during which A is vigilant and B feeding, B is vigilant and A feeding, A and B are vigilant, and A and B are feeding, determine the levels of risk endured by each individual. They are denoted by Wvf, Wfv, Wvv and Wff, respectively. To make the responding process possible, we consider time as a series of infinitely small moments when A can switch its activity which alternate with moments wh (...truncated)