Critical Fitness Collapse in Three-Dimensional Spatial Population Genetics

TL;DR

This paper investigates how deleterious mutations cause fitness collapse in three-dimensional spatial populations, revealing different critical behaviors in expanding versus fixed-size habitats and the impact of interspecies competition.

Contribution

It extends the understanding of fitness collapse from 1D and 2D to 3D populations, analyzing the effects of habitat inflation and species competition on critical dynamics.

Findings

Different scaling laws for inflating and fixed-size frontiers.

Competition causes deviation from directed percolation behavior.

Inflating fronts disrupt population connectivity, affecting critical behavior.

Abstract

If deleterious mutations near a fitness maximum in a spatially distributed population are sufficiently frequent or detrimental, the population can undergo a fitness collapse, similarly to the Muller's ratchet effect in well-mixed populations. Recent studies of one-dimensional habitats (e.g., the frontier of a two-dimensional range expansion) have shown that the onset of the fitness collapse is described by a directed percolation phase transition with its associated critical exponents. We consider population fitness collapse in three-dimensional range expansions with both inflating and fixed-size frontiers (applicable to, e.g., expanding and treadmilling spherical tumors, respectively). We find that the onset of fitness collapse in these two cases obeys different scaling laws, and that competition between species at the frontier leads to a deviation from directed percolation scaling. As in two-dimensional range expansions, inflating frontiers modify the critical behavior by causally disconnecting well-separated portions of the population.