Mathematical Sciences: Reaction-Diffusion Equations and Evolutionary Ecology

1937年，费舍尔写了一篇关于 生活在同质群体中的群体中的有利基因- 立体栖息地 费雪的模型是高度理想化的。 为 例如，他认为，个人和 人口规模是恒定的。 这使得模型很难 apply. 主要研究者将研究该模型 没有这样的假设，从而使模型更加现实。 这提出了许多具有挑战性的数学问题， 首席研究员打算利用拓扑 方法，如程度理论，射击参数和康利的 指数理论 所取得的成果将清楚地说明 应用数学在生物科学，特别是 自然选择中的非线性效应。

In 1937, Fisher wrote a classic paper on the spread of an advantageous gene in a population living in a homogeneous one- dimensional habitat. Fisher's model is highly idealized. For example, he assumed that the fitnesses of the individuals and the population size are constant. This makes the model difficult to apply. The principal investigator will to study this model without such assumptions, thus making the model more realistic. This poses many challenging mathematical problems which the principal investigator intends to surmount using topological methods such as degree theory, shooting arguments and Conley's index theory. Results obtained will clearly illustrate the impact of applied mathematics on biological sciences, in particular the effects of nonlinearities in natural selection.