Towards a mechanistic framework that explains correlated random walk behaviour: Correlated random walkers can optimize their fitness when foraging under the risk of predation

Correlated random walk models are the dominant and most successful framework for describing non-orientated animal movement patterns. These models can be adjusted to provide very good fits to movement pattern data. Nonetheless, it seems that these models typically cannot explain how the observed movement patterns come about. This is because of a widely held but unverified theoretical principle; namely that correlated random walks cannot be optimized for typical foraging scenarios and so cannot represent archetypal, innate, evolved optimal behaviours. As a consequence a mechanistic framework to explain correlated random walk behaviour and to generate novel hypotheses about its evolution has not been formulated. This is a significant shortcoming because the key to prediction and understanding lies in the elucidation of mechanisms underlying the observed patterns. Here with the aid of a simple analytically tractable model it is shown how particular correlated random walk behaviours can, in fact, confer benefits to foragers that are acting under predation. Predation risks are ubiquitous. The mathematical analysis and the accompanying numerical simulations are the first to show that by varying their correlated random walks behaviour animals can control both their rate of energetic gain and the probability of encountering a predator, and can thereby optimize their expected total energy intake. This mechanism can provide selection pressures for particular habitat-specific correlated random walk behaviours and thereby shows that correlated random walks can have explanatory as well as descriptive capability.