Two Applications of a Spatial, Hybrid, Consumer-Resource Model

Abstract

Semi-discrete models provide unique insights into the dynamics of some biological populations that purely continuous or purely discrete models cannot. In this thesis, we formulate and analyze a semi-discrete consumer-resource model on two patches. We extend the model by Pachepsky et al. to account for a spatial dimension and analyze equilibria and their stability. We perform an asymptotic analysis to determine the benefit of small dispersal on total asymptotic density and find that dispersal benefits one population while harming the other. We extend our results numerically to find novel responses to dispersal. We then use the Spruce Budworm and Fir Tree systems as inspiration to study the optimal control of the Budworm population. We determine that spatial heterogeneity and dispersal heterogeneity both lead to higher control intensity. We find interesting cyclic control dynamics in the case that the control is applied long-term.