Rare beneficial mutations cannot halt Muller's ratchet in spatial populations

TL;DR

This paper investigates how spatial structure in populations affects Muller's ratchet, showing that beneficial mutations cannot stop the irreversible accumulation of deleterious mutations in spatial populations, unlike in well-mixed ones.

Contribution

The study develops a scaling theory linking spatial Muller's ratchet to directed percolation, revealing the limitations of beneficial mutations in halting mutation accumulation in spatial populations.

Findings

Beneficial mutations cannot halt Muller's ratchet in spatial populations.

The speed of the ratchet remains nonzero in the infinite size limit when deleterious mutation rate exceeds a critical value.

Theoretical predictions are confirmed by extensive simulations in one and two dimensions.

Abstract

Muller's ratchet describes the irreversible accumulation of deleterious mutations in asexual populations. In well-mixed populations the speed of fitness decline is exponentially small in the population size, and any positive rate of beneficial mutations is sufficient to reverse the ratchet in large populations. The behavior is fundamentally different in populations with spatial structure, because the speed of the ratchet remains nonzero in the infinite size limit when the deleterious mutation rate exceeds a critical value. Based on the relation between the spatial ratchet and directed percolation, we develop a scaling theory incorporating both deleterious and beneficial mutations. The theory is verified by extensive simulations in one and two dimensions.