Ratio-dependent functional response emerges from optimal foraging on a complex landscape

A spatially implicit consumer–resource model, having the form of the Rosenzweig–MacArthur equations except for density-dependent loss on the consumer, is analyzed. Both the rates of resource intake and of mortality of the consumer are assumed to be proportional to the amount of risk it takes during foraging, and the consumer is assumed to take an amount of risk that maximizes its fitness as a tradeoff between growth and predation. Given these conditions, it is shown that a ratio-dependent functional response for the consumer–resource interaction emerges and that the system is highly stable.