Modeling and analysis of competing dynamic ecological systems

Abstract

The dynamic relationship between competing ecological systems has long been and will continue to be one of vital topics in both ecology and mathematical ecology because of its importance and universal existence. Mathematical modeling has become an effective tool to model and simulate the dynamic system, providing decision makers with strategy recommendations. Although a great amount of previous work has attempted to model the biological mechanisms including dispersal, only rarely has there been a systematic investigation on different spatial effects. The author introduces spatial games as a modeling approach with different constructions towards different dynamic systems in order to benefit from the systematic research on spatial dynamics when studying the competing ecological systems. This research developed models of two systems: (1) two-spotted spider mite prey-predator system; (2) tomato spotted wilt virus (TSWV) and west flower thrips (WFT) vector-borne disease system. For two-spotted spider mite system, the author presented four spatial mathematical models as well as a novel spatial game model to describe the spatial movement of two competing species. For the TSWV-WFT system, a spatial game was introduced to describe the spatial dynamics of adult thrips and the novel model was validated with experimental data. The author also gave suggestions for efficiently controlling the vector-borne disease by performing sensitivity analysis towards parameters. The major contribution of this research is to introduce spatial games as a tool to describe the dynamic schemes in ecological systems. Compared to a traditional dynamic model, a spatial game model is more expressive and informative. This approach uses a payoff function and a movement probability function that can be adjusted based on habits, characteristics and mobility schemes of different competing entities, which has enriched its modeling power. The methodology and modeling approach used in this dissertation can be applied to other competing species dynamic systems, and have a broad impact on research areas related to mathematical ecology, biology modeling, epidemiology, pest control, vector-borne disease control, and ecological decision-making processes.