Optimum search speed and activity: a dynamic game in a three-link trophic system

We analysed how a consumer should simultaneously trade-off search speed and time active in a game with predators that optimise their search speed. Both the consumers and the predators are continuously reproducing and maximise fitness by maximising the per capita growth rate. The impact of the predator's presence on consumer behaviour, and the effects of type I and II functional responses on the behaviour of both species are considered. In the analyses, consumers were allowed to co-ordinate activity or behave independently in relation to other consumers. The ESS-analysis of the game ensures that no mutant can invade the system. The independent activity was found to be optimal in all analyses, while the co-ordinated activity was only optimal at full activity where the two activity strategies coincided. The model showed that consumers should change activity to account for predation risk. Activity generally decreased with predation risk. Concerning the energetic aspects, both activity and search speed were important to account for the reproductive output. The functional responses influenced the optimum activity and search speed of consumers and predators. In general, the optimum behaviours showed complex non-linear responses in relation to the resource and the consumer density. A predator type II functional response had profound impacts on the properties of the optima, the stability and presence of alternative strategies. As a result of the optimum behaviours, the realised functional responses of both species became sigmoidal.