A General Class of Growth Models in a Patchy Environment Exhibiting Enhanced Production

It has been shown in several works that a population dispersing in a heterogeneous habitat can reach a higher density than it would get if dispersal was not allowed or if space was homogeneous. Those previous works have extended and completed the study of this phenomenon and the conditions under which it occurs, but mainly using very specific models. In the present paper, we propose a more general extension based on a very large class of models, among which the previous ones belong. Furthermore, we propose a framework based on a time scale separation method to illustrate that the previous class of models may also include more complex ones. We illustrate this framework on two examples based on mass balanced equations, a resource–consumer system in a two patch habitat and a resource–consumer–predator system in a two patch habitat. In each case, we show how our general approach allows us to determine explicit conditions under which the above mentioned phenomenon is occurring. It is note worthy that our conditions extend the well-known conditions discovered in the previous works. We think that this robust result may be of strong interest for environmental management for fragmented habitats.