Managing Interacting Populations under Time Scale Separation

Renewable resource modelling is usually characterized by different time scales where some state variables such as biomass may evolve relatively faster than other state variables such as carrying capacity. Ignoring this time scale separation means that a slowly changing variable is treated as constant over time. Management rules that ignore time scale separation do not account for a time scale externality and this may induce inefficiencies in resource management. In the current work, we study multispecies resource management under time scale separation by adopting the framework of singular perturbation reduction methods. By extending recent work by Vardas and Xepapadeas (2015) to interacting populations, we study regulation with full internalization of the time scale externality. We further study regulation and noncooperative outcomes when the time scale separation is ignored, and identify deviations in harvesting and biomass paths among these cases. Deviations indicate the inefficiencies associated with ignoring time scale separation.