Diffusion, Directed Movement, Spatial and Temporal Heterogeneity in Population Dynamics

点击翻译按钮获取中文摘要

"Competition-exclusion" principle in evolution and ecology was first proposed by Darwin. In modern era, understanding "biodiversity" has become a central theme in plant ecology, and it has been observed that "spatial heterogeneity" plays an important role in biodiversity. On the other hand, diffusion has been used extensively and successfully in modeling various phenomena in nature and science. In this project, the Principal Investigator and his collaborators in ecology and biology, will continue to explore the effect of dispersal in heterogeneous environment which has led to a re-examination of the fundamental concept of "carrying capacity" and its relation to "intrinsic growth rates" in population dynamics. Both mathematical theories and rigorous biological experiments involving yeast will be used. Other related issues, such as temporal variations, will also be investigated.In this project, the main theme is to understand the consequences of interactions between diffusion (dispersal of species) and spatial, as well as temporal, variations in environment. An important element in this understanding is the intricate relation between the fundamental concepts of "carrying capacity" and "intrinsic growth rates". Those will be studied - first by biological experiments (which have been inspired by mathematical theories) and then by new mathematical models created to describe those experiments. The concavity or convexity of the relation between the two quantities would play an important role in population dynamics. Mathematically, what biological experiments suggest is to replace the classical (single) logistic equation for a single species population by a system containing an extra equation governing the "renewable" resources. This seems to be much closer to reality, and will change the well-known Lotka-Volterra system for two competing species to a much more challenging one, a new system of 3 equations with renewable resources. In this project, we will study these new systems thoroughly.