Abstract
Many animals spend large parts of their lives in groups. Within such groups, they need to find efficient ways of dividing available resources between them. This is often achieved by means of a dominance hierarchy, which in its most extreme linear form allocates a strict priority order to the individuals. Once a hierarchy is formed, it is often stable over long periods, but the formation of hierarchies among individuals with little or no knowledge of each other can involve aggressive contests. The outcome of such contests can have significant effects on later contests, with previous winners more likely to win (winner effects) and previous losers more likely to lose (loser effects). This scenario has been modelled by a number of authors, in particular by Dugatkin. In his model, individuals engage in aggressive contests if the assessment of their fighting ability relative to their opponent is above a threshold theta . Here we present a model where each individual can choose its own value theta . This enables us to address questions such as how aggressive should individuals be in order to take up one of the first places in the hierarchy? We find that a unique strategy evolves, as opposed to a mixture of strategies. Thus, in any scenario there exists a unique best level of aggression, and individuals should not switch between strategies. We find that for optimal strategy choice, the hierarchy forms quickly, after which there are no mutually aggressive contests.
Highlights
Very often, animals that share the same territory engage in pairwise aggressive interactions leading to the formation of dominance hierarchies Hand (1986)
We have introduced game-theoretical elements to the winner–loser model developed in Dugatkin (Dugatkin 1997; Dugatkin and Dugatkin 2007)
We considered a group of individuals that are characterised by their fighting ability score and a strategy θ that indicates whether an individual would engage in an aggressive interaction or retreat
Summary
Animals that share the same territory engage in pairwise aggressive interactions leading to the formation of dominance hierarchies Hand (1986). In Kura et al (2015), we analysed the temporal dynamic and the average behaviour of dominance hierarchy formation for different combinations of winner and loser effects, using the model developed by Dugatkin (1997) We concluded that it is not necessary for a group of individuals to have perfect knowledge of each other’s RHP in order to establish a linear dominance hierarchy; only a little information about the current RHP estimation of an individual’s opponent is enough to establish a linear dominance hierarchy. We note that Andersen et al (2004) developed an alternative optimisation-based model to analyse the effect of group size on aggression level and showed that the theoretical results obtained are supported by experimental data observed in domesticated pigs; we discuss this in Sect. We compare our theoretical results with experimental evidence which is rather different for different groups of animals such as birds, farmed animals or fish (see e.g. Andersen et al 2004; Bilcık and Keeling 2000; Estévez et al 1997; Estevez et al 2007; Kotrschal et al 1993; Nicol et al 1999; Syarifuddin and Kramer 1996; Turner et al 2001)
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