# Benjamin Allen

Neutral drift and weak selection on graphs

Evolutionary graph theory is a mathematical framework for studying evolution in spatially structured populations. Despite a decade of active research, some fundamental questions remain open. I will discuss recent results regarding neutral drift and weak selection on graphs. Under neutral drift, mutations have no phenotypic effect and accrue at a rate known as the ``molecular clock”. I will show that, surprisingly, spatial structure can either accelerate or slow a population’s molecular clock. Weak constant selection refers to the case that a mutation confers a small fitness advantage relative to the wild-type population. Spatial structure can either amplify or suppress the mutation’s fixation probability. I will discuss a conjecture, motivated by recent numerical results, that amplification is impossible under the process known as death-Birth updating.