Consumer-resource matching in a food chain when both predators and prey are free to move

The classical theory of the ideal free distribution (IFD) predicts that the spatial distribution of consumers should follow the distribution of the resources they depend on. Here, we study consumer-resource matching in a community context. Our model for the community is a food chain with three levels. We study whether the primary consumers are able to match resources both under predation risk and in its absence. Both prey and predators have varying degrees of knowledge of the global and local resource distribution. We present two versions of the model. In the "resource maximising" model, the consumers consider the availability of their resource only. In the "balancing" model, individual consumers minimise predation risk per unit of resource that they can gain access to. We show that both models can lead to perfect matching of consumers on resources and predators on consumers, assuming that individuals have full knowledge of the whole environment. However, when the consumers' information and freedom of movement are greater than those of the predators, then the predators generally undermatch the consumers. In the opposite case, we observe overmatching and high consumer movement rates. Furthermore, undermatching of predators on consumers tends to induce overmatching of consumers on resources.