RUI: The Rate of Evolution in Structured Populations

进化通常被认为是一个缓慢、缓慢的过程。然而，它有时会出人意料地快，只需几代人就会发生明显的变化。进化的速度取决于自然选择的严重性、突变率和种群规模等因素。这个项目的重点是空间结构的影响：种群在其栖息地内扩散的方式。先前的研究表明，一些结构加快了进化，而另一些结构则减缓了进化。研究人员将使用数学模型来更深入地了解空间结构为什么以及在什么条件下可以改变进化的速度。本科生，包括那些来自STEM中代表性较低的群体的学生，将接受数学建模方面的培训，并参与研究过程的所有方面。这项研究的结果可能会为我们对人类进化历史上的重要事件的估计提供信息，例如人类何时从我们最接近的灵长类亲属中分离出来。这项工作还可能有助于我们对癌症的理解，癌症可以被视为发生在体内的不必要的进化。在数学上，空间结构种群的进化速度可以用进化图论来研究。空间结构被表示为一个图(或网络)，其中个人占据顶点，边表示空间关系。进化被建模为由出生和死亡事件驱动的随机过程，导致新的基因突变的固定或灭绝。十年的研究表明，图拓扑既可以影响突变的累积速度，也可以影响选择与漂移的平衡。然而，精确的结果只对非常简单的图是已知的，并且很少有一般的定理被证明。此外，进化图论到目前为止仅限于单倍体、无性种群。这个项目将把新的分析技术应用到进化图理论中，并将该理论扩展到包括有性繁殖的二倍体种群。

Evolution is generally thought to be a slow, plodding process. However, it can sometimes be surprisingly fast, with noticeable changes occurring in only a few generations. The speed of evolution depends on such factors as the severity of natural selection, the rate of mutation, and the size of the population. This project focuses on the effects of spatial structure: the way a population is spread out within its habitat. Previous research has shown that some structures speed up evolution while others slow it down. The investigators will use mathematical modeling to gain a deeper understanding of why, and under what conditions, spatial structure can change the rate of evolution. Undergraduate students, including those from groups typically underrepresented in STEM, will be trained in mathematical modeling and engaged in all aspects of the research process. Results of this investigation may inform the estimation of important events in our evolutionary past, such as when humans split from our closest primate relatives. This work may also aid our understanding of cancer, which can be seen as unwanted evolution occurring inside the body. Mathematically, the rate of evolution in spatially structured populations can be studied using evolutionary graph theory. Spatial structure is represented as a graph (or network), in which individuals occupy vertices and edges indicate spatial relationships. Evolution is modeled as a stochastic process driven by birth and death events, leading to the fixation or extinction of new genetic mutations. A decade of research has shown that graph topology can affect both the rate at which mutations accrue and the balance of selection versus drift. However, exact results are known only for very simple graphs, and few general theorems have been proven. Additionally, evolutionary graph theory is so far limited to haploid, asexual populations. This project will apply new analytical techniques to evolutionary graph theory, and extend the theory to include sexually reproducing diploid populations.