Managing Interacting Populations Under Time Scale Separation

Abstract

Renewable resource modeling 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. A strong form of time scale separation (STSS) means that a slowly changing variable is treated as constant over time. Management rules that assume STSS 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 under STSS and identify deviations in harvesting and biomass paths among these cases. Deviations indicate the inefficiencies associated with adopting STSS.