Mathematical Treatment of Evolutionary Ecology

这个项目是关于研究 自然选择和扩散的人口组成的一个 一个进化的物种，一个基因座的遗传系统， 两个等位基因 该模型是进化生态学的一个例子， 它是种群生态学和种群遗传学的融合。 该模型比在 种群遗传学的经典理论，因为它允许 密度依赖选择 据估计， 种群规模降低了个体的适应性， 人口 未来的目标将是研究几个案例， 相互作用的物种，或扩散的共同进化理论。 从数学上讲，这是一个反应扩散方程组。 有必要证明行波的存在 连接位于不同不变量上的两个静止点 流形 这些流形中的每一个都对应着 一个等位基因。 这些波的稳定性将被检查。 的 结果将给出一个更完整的图片， 由首席研究员对渐近行为的 反应扩散方程组的解 它会让我们 如何处理最大值原则 很难应用。

This project is concerned with the study of the effects of natural selection and diffusion on a population consisting of a single evolving species with a genetic system of one locus with two alleles. The model is an example from evolutionary ecology, which is a fusion of population ecology with population genetics. The model is more realistic than those encountered in the classical theory of population genetics because it allows density dependent selection. It is assumed that increase in population size decreases the fitness of the individuals in the population. A future goal will be to study the case of several interacting species, or coevolutionary theory with diffusion. Mathematically, this is a system of reaction-diffusion equations. It is necessary to prove the existence of travelling waves connecting two rest points lying on different invariant manifolds. Each of these manifolds corresponds to the absence of one allele. The stability of these waves will be examined. The results will give a more complete picture of what has been shown by the principal investigator on the asymptotic behavior of solutions to the reaction-diffusion system. It will give insight into the ways to handle systems where the maximum principle is hard to apply.