Dispersal in multi-patch metapopulations: The impact of patch number and network topology

Habitat fragmentation is a leading cause of biodiversity loss, and efforts to enhance connectivity through, for example, biological corridors are a common conservation strategy to mitigate it. However, understanding the effects of dispersal variation on the total biomass of spatially structured populations is still far from being well understood. For the simplest situation, i.e., a population occupying a habitat divided into two patches, recent studies have shown that there are only four possible response scenarios to increased connectivity in discrete- and continuous-time models under Beverton-Holt and logistic local dynamics, respectively. This paper explores whether the number of patches in a metapopulation influences the number of response scenarios to increased dispersal. We will show that for given local dynamics the number of possible response scenarios significantly increases when the number of patches increases from two to three. Moreover, the paper revisits the problem of how network topology affects total biomass dynamics for low dispersal rates. We will show that the previous claim that bidirectional connectivity always increases biomass at low dispersal rates when connecting sources is false. Indeed, we will prove that transiting from a chain topology to a ring topology can either increase or decrease the total biomass for low dispersal rates if one considers more realistic production functions or if the probability of using a concrete path is not the same in the whole metapopulation.