How Landscape Heterogeneity Frames Optimal Diffusivity in Searching Processes

Theoretical and empirical investigations of search strategies typically have failed to distinguish the distinct roles played by density versus patchiness of resources. It is well known that motility and diffusivity of organisms often increase in environments with low density of resources, but thus far there has been little progress in understanding the specific role of landscape heterogeneity and disorder on random, non-oriented motility. Here we address the general question of how the landscape heterogeneity affects the efficiency of encounter interactions under global constant density of scarce resources. We unveil the key mechanism coupling the landscape structure with optimal search diffusivity. In particular, our main result leads to an empirically testable prediction: enhanced diffusivity (including superdiffusive searches), with shift in the diffusion exponent, favors the success of target encounters in heterogeneous landscapes. Author Summary: Understanding how animals search for food is crucial for animal ecology. Although much has been learned about the main aspects of the so-called foraging problem, some important questions still remain unanswered. In this work we address the issue of the relevance of heterogeneity in the resources distribution to efficient animal foraging behavior. Our results unveil the key mechanism coupling landscape heterogeneity dynamics with optimal search diffusivity. Indeed, although the effect of (global) resource density on animal foraging behavior is well documented, much less has been known about how spatiotemporal landscape heterogeneity affects the efficiency of encounter interactions by foraging organisms. In this sense, we propose a new empirically testable theoretical prediction on the dynamics (e.g. diffusion exponent) of foraging organisms in heterogeneous environments. We also show that the conditions in which Lévy strategies are optimal are much broader than previously considered.