Lévy Walks Suboptimal under Predation Risk

A key challenge in movement ecology is to understand how animals move in nature. Previous studies have predicted that animals should perform a special class of random walks, called Lévy walk, to obtain more targets. However, some empirical studies did not support this hypothesis, and the relationship between search strategy and ecological factors is still unclear. We focused on ecological factors, such as predation risk, and analyzed whether Lévy walk may not be favored. It was remarkable that the ecological factors often altered an optimal search strategy from Lévy walk to Brownian walk, depending on the speed of the predator’s movement, density of predators, etc. This occurred because higher target encounter rates simultaneously led searchers to higher predation risks. Our findings indicate that animals may not perform Lévy walks often, and we suggest that it is crucial to consider the ecological context for evaluating the search strategy performed by animals in the field.Author Summary: Moving agents should efficiently search for targets (e.g., food, prey, or specific locations) when lacking information about the location of the targets. For this random search problem, the Lévy walk hypothesis claims that Lévy walk movement patterns (i.e., each step length follows a distribution that is heavy-tailed) enable the searcher to capture more targets. However, most searchers may have antagonistic agents (e.g., predators) that can lead to death. Thus, the searcher needs to seek targets while avoiding encounters with antagonistic agents. Here, we show that the Lévy search strategy is less efficient in terms of total lifetime fitness when the predators are abundant, and especially when predators adopt a sit-and-wait strategy. Moreover, the results indicate that the life-cycle type of the searcher is an important fitness factor. These ecological aspects significantly influence the consequences of the random search. Therefore, it is critical to consider the ecological properties of searchers and other interacting agents when examining and estimating animal movements.