RUI: The Rate of Evolution in Structured Populations

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.