Mutation Accumulation and Fitness Collapse at Population Frontiers

Rapid, deleterious mutations occurring in, e.g., viral populations and cancerous tissue, may accumulate and lead to fitness loss. Previous studies show that sufficiently rapid accumulation in one-dimensional populations leads to a fitness collapse, governed by the directed percolation (DP) universality class. We compare this situation to the collapse in effectively two-dimensional populations, such as the frontiers of three-dimensional range expansions. A phase diagram is computed as a function of the mutation rate $\mu$ and strength $s$. Relative to one-dimensional populations, we find that the collapse occurs in a smaller region of phase space. The scaling combination governing the phase diagram shape is $\mu |\ln s|/s$ ($\mu/s^2$ for one-dimensional populations). We argue that the evolutionary dynamics is described by a set of coupled DP Langevin equations near the transition, and that the coupling terms lead to deviations from expected DP scaling.