Evolution of condition-dependent dispersal under kin competition

Dispersers often differ in body condition from non-dispersers. The social dominance hypothesis explains dispersal of weak individuals, but it is not yet well understood why strong individuals, which could easily retain their natal site, are sometimes exposed to risky dispersal. Based on the model for dispersal under kin competition by Hamilton and May, we construct a model where dispersal propensity depends on body condition. We consider an annual species that inhabits a patchy environment with varying patch qualities. Offspring body condition corresponds to the quality of the natal patch and competitive ability increases with body condition. Our main general result balances the fitness benefit from not dispersing and retaining the natal patch and the benefit from dispersing and establishing somewhere else. We present four different examples for competition, which all hint that dispersal of strong individuals may be a common outcome under the assumptions of the present model. In three of the examples, the evolutionarily stable dispersal probability is an increasing function of body condition. However, we found an example where, counterintuitively, the evolutionarily stable dispersal probability is a non-monotone function of body condition such that both very weak and very strong individuals disperse with high probability but individuals of intermediate body condition do not disperse at all.