Linking rates of diffusion and consumption in relation to resources

The functional response is a fundamental model of the relationship between consumer intake rate and resource abundance. The random walk is a fundamental model of animal movement and is well approximated by simple diffusion. Both models are central to our understanding of numerous ecological processes but are rarely linked in ecological theory. To derive a synthetic model, we draw on the common logical premise underlying these models and show how the diffusion and consumption rates of consumers depend on elementary attributes of naturally occurring consumer-resource interactions: the abundance, spatial aggregation, and traveling speed of resources as well as consumer handling time and directional persistence. We show that resource aggregation may lead to increased consumer diffusion and, in the case of mobile resources, reduced consumption rate. Resource-dependent movement patterns have traditionally been attributed to area-restricted search, reflecting adaptive decision making by the consumer. Our synthesis provides a simple alternative hypothesis that such patterns could also arise as a by-product of statistical movement mechanics.