Can deleterious mutations surf deterministic population waves?
arXiv:2607.12864
The paper analyzes a deterministic reaction‑diffusion model of an asexual population expanding into new territory and shows that deleterious mutations cannot surf the expansion front, despite being present there as recent descendants of the wild type.
Abstract
In spatially structured populations, rare neutral mutations can spread through large regions during a range expansion, a phenomenon known as gene surfing. Whether deleterious mutations can also surf remains poorly understood. To address this question, we study a deterministic version of the spatial Muller's ratchet, given by an infinite system of reaction-diffusion equations describing an asexual population subject to mutation, migration, and density-dependent reproduction and death. After establishing that the system of PDEs is well-posed, we analyse the distribution of deleterious mutations within the population. In the monostable regime, we derive quantitative bounds on the ratio between the density of individuals carrying a given number of mutations and the density of mutation-free individuals. Under a Fisher-KPP condition, we further determine the spreading speed of the population into an empty habitat, confirming non-rigorous computations of Foutel-Rodier and Etheridge. Finally, using a tracer dynamics approach, we show that deleterious mutations cannot surf deterministic waves: although they are present at the expansion front, they only arise as recent descendants of the wild type.
55 pages, 1 figure. This work was originally part of arXiv:2603.06478 and has been separated into a standalone manuscript