Predator-prey models in heterogeneous environment: Emergence of functional response

In this work, we are interested in prey-predator models. More precisely, we study the spatial heterogeneity effects on the amount of prey eaten per predator per unit time, when different time scales occur. This amount and its relation with the amount of predators produced via the predation are interesting from an ecological point of view. Indeed, the knowledge of these quantities permits us to quantify the transfer of the biomass in the food chain. Our aim is to show how the spatial heterogeneity acts on these amounts. We consider prey-predator systems in a multi-patch environment. We show that density dependent migrations make emerge new models on the total population level and we exhibit some examples. Furthermore, we show that the aggregation method is a good tool for describing the mechanisms hidden behind complex models.