RUI: The Rate of Evolution in Structured Populations

进化通常被认为是一个缓慢而缓慢的过程。然而，它有时会令人惊讶地快，仅在几代人中就发生了明显的变化。进化的速度取决于自然选择的强度、突变的速度和种群的规模等因素。该项目的重点是空间结构的影响：人口在其栖息地内分布的方式。 先前的研究表明，一些结构加快了进化，而另一些结构则减慢了进化。研究人员将使用数学模型来更深入地了解为什么以及在什么条件下，空间结构可以改变进化的速度。本科生，包括那些来自通常在STEM中代表性不足的群体的学生，将接受数学建模培训，并参与研究过程的各个方面。这项研究的结果可能会为我们进化史上的重要事件提供信息，例如人类何时与我们最亲近的灵长类亲属分离。这项工作也可能有助于我们理解癌症，癌症可以被视为体内发生的不必要的进化。在数学上，空间结构种群的进化速率可以用进化图论来研究。空间结构被表示为图（或网络），其中个体占据顶点，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，导致新基因突变的固定或灭绝。十年的研究表明，图的拓扑结构可以影响突变的发生率以及选择与漂移的平衡。然而，确切的结果只知道非常简单的图，很少有一般定理已被证明。 此外，进化图论到目前为止仅限于单倍体，无性种群。 本计画将应用新的分析技术于演化图论，并将理论延伸至有性繁殖的二倍体族群。

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.