Kleptoparasitic melees--modelling food stealing featuring contests with multiple individuals.

Kleptoparasitism is the stealing of food by one animal from another. This has been modelled in various ways before, but all previous models have only allowed contests between two individuals. We investigate a model of kleptoparasitism where individuals are allowed to fight in groups of more than two, as often occurs in real populations. We find the equilibrium distribution of the population amongst various behavioural states, conditional upon the strategies played and environmental parameters, and then find evolutionarily stable challenging strategies. We find that there is always at least one ESS, but sometimes there are two or more, and discuss the circumstances when particular ESSs occur, and when there are likely to be multiple ESSs.

A game theoretical analysis of the mating sign behavior in the honey bee.

Queens of the honey bee, Apis mellifera (L.), exhibit extreme polyandry, mating with up to 45 different males (drones). This increases the genetic diversity of their colonies, and consequently their fitness. After copulation, drones leave a mating sign in the genital opening of the queen which has been shown to promote additional mating of the queen. On one hand, this signing behavior is beneficial for the drone because it increases the genetic diversity of the resulting colony that is to perpetuate his genes. On the other hand, it decreases the proportion of the drone's personal offspring among colony members which is reducing drone fitness. We analyze the adaptiveness and evolutionary stability of this drone's behavior with a game-theoretical model. We find that theoretically both the strategy of leaving a mating sign and the strategy of not leaving a mating sign can be evolutionary stable, depending on natural parameters. However, the signing strategy is not favored for most scenarios, including the cases that are biologically plausible in reference to empirical data. We conclude that leaving a sign is not in the interest of the drone unless it serves biological functions other than increasing subsequent queen mating chances. Nevertheless, our analysis can also explain the prevalence of such a behavior of honey bee drones by a very low evolutionary pressure for an invasion of the nonsigning strategy.

The evolution of a kleptoparasitic system under adaptive dynamics.

Kleptoparasitism, the stealing of food items, is a common biological phenomenon which has been modelled mathematically in a series of recent papers. A common assumption, following early work, was that mixed strategy solutions were not possible. In this paper we consider the evolution of mixed strategies under adaptive dynamics and show that such mixed strategies can be stable solutions under certain assumptions. In particular we revisit the recent paper of Broom et al. (Bull math Biol 66, 1645-1658, 2004) which assumed pure solutions only, and reanalyze the model under this new formulation.