Prey-predator "host-parasite" models with adaptive dispersal: application to social animals

Foraging strategies in social animals are often shaped by change in an organism's natural surrounding. Foraging behavior can hence be highly plastic, time, and condition dependent. The motivation of my research is to explore the effects of dispersal behavior in predators or parasites on population dynamics in heterogeneous environments by developing varied models in different contexts through closely working with ecologists. My models include Ordinary Differential Equation (ODE)-type meta population models and Delay Differential Equation (DDE) models with validation through data. I applied dynamical theory and bifurcation theory with carefully designed numerical simulations to have a better understanding on the profitability and cost of an adaptive dispersal in organisms. My work on the prey-predator models provide important insights on how different dispersal strategies may have different impacts on the spatial patterns and also shows that the change of dispersal strategy in organisms may have stabilizing or destabilizing effects leading to extinction or coexistence of species. I also develop models for honeybee population dynamics and its interaction with the parasitic Varroa mite. At first, I investigate the effect of dispersal on honeybee colonies under infestation by the Varroa mites. I then provide another single patch model by considering a stage structure time delay system from brood to adult honeybee. Through a close collaboration with a biologist, a honeybee and mite population data was first used to validate my model and I estimated certain unknown parameters by utilizing least square Monte Carlo method. My analytical, bifurcations, sensitivity analysis, and numerical studies first reveal the dynamical outcomes of migration. In addition, the results point us in the direction of the most sensitive life history parameters affecting the population size of a colony. These results provide novel insights on the effects of foraging and Varroa mites on colony survival.