Trimming to coexistence: how dispersal strategies should be accounted for in resource management

For two resource-sharing species we explore the interplay of harvesting and dispersal strategies, as well as their influence on competition outcomes. Although the extinction of either species can be achieved by excessive culling, choosing a harvesting strategy such that the biodiversity of the populations is preserved is much more complicated. We propose a type of heterogeneous harvesting policy, dependent on dispersal strategy, where the two managed populations become an ideal free pair, and show that this strategy guarantees the coexistence of the species. We also show that if the harvesting of one of the populations is perturbed in some way, then it is possible for the coexistence to be preserved. Further, we show that if the dispersal of two species formed an ideal free pair, then a slight change in the dispersal strategy for one of them does not affect their ability to coexist. Finally, in the model, directed movement is represented by the term $\Delta (u/P)$ , where P is the dispersal strategy and target distribution. We justify that once an invading species, which has an advantage in carrying capacity, chooses a dispersal strategy that mimics the resident species distribution, then successful invasion is guaranteed. However, numerical simulations show that invasion may be successful even without an advantage in carrying capacity. More work is needed to understand the conditions, in addition to targeted culling, under which the host species would be able to persist through an invasion.