RUI: The Rate of Evolution in Structured Populations

进化通常被认为是一个缓慢而艰难的过程。然而，它有时会出奇地快，仅仅几代人就发生了明显的变化。进化的速度取决于自然选择的严酷程度、变异的速度和种群的规模等因素。这个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，一些结构加速了进化，而另一些则减慢了进化。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会改变进化速度。本科生，包括那些来自STEM中代表性不足的群体的学生，将接受数学建模方面的培训，并参与研究过程的各个方面。这项调查的结果可能为我们进化史上重要事件的估计提供信息，比如人类何时从我们最近的灵长类亲戚中分离出来。这项工作也可能有助于我们对癌症的理解，癌症可以被视为身体内部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。空间结构以图（或网络）的形式表示，其中个体占据顶点，边缘表示空间关系。进化被建模为一个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。十年来的研究表明，图拓扑既可以影响突变产生的速率，也可以影响选择与漂移的平衡。然而，只有非常简单的图才知道确切的结果，而且很少有一般定理被证明。此外，进化图论目前仅限于单倍体、无性种群。本项目将应用新的分析技术到进化图论，并将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.