Effects of Fitness Gradient

Speaker: Jakub Svoboda (Dartmouth)

Date: 4/7/26

Abstract: In this talk, we will explore evolutionary dynamics in populations that experience gradients of chemicals or nutrients that cause mutations to be beneficial in some spatial regions and harmful in others. We will determine the fixation probability of a single advantageous mutant that attempts to invade a homogeneous population of \(N\) residents. One initial mutant is placed on a simple one-dimensional spatial structure that experiences a gradient that varies linearly from \(1-s\) to \(1+s\), whereas the resident fitness is constant and equal to 1. The average change in fitness is neutral, but for some slopes parametrized by \(s\), the mutant’s fixation probability increases, and for some slopes it decreases. This behavior is counterintuitive. In the talk, I will give precise bounds for the fixation probability as a function of \(s\). Moreover, at the end of the talk, I will briefly introduce other models and problems I am interested in.