Fitness-dependent mutation rates in finite populations

Mutation rate may be condition dependent, whereby individuals in poor condition, perhaps from high mutation load, have higher mutation rates than individuals in good condition. Agrawal (J. Evol. Biol.15, 2002, 1004) explored the basic properties of fitness-dependent mutation rate (FDMR) in infinite populations and reported some heuristic results for finite populations. The key parameter governing how infinite populations evolve under FDMR is the curvature (k) of the relationship between fitness and mutation rate. We extend Agrawal's analysis to finite populations and consider dominance and epistasis. In finite populations, the probability of long-term existence depends on k. In sexual populations, positive curvature leads to low equilibrium mutation rate, whereas negative curvature results in high mutation rate. In asexual populations, negative curvature results in rapid extinction via 'mutational meltdown', whereas positive curvature sometimes allows persistence. We speculate that fitness-dependent mutation rate may provide the conditions for genetic architecture to diverge between sexual and asexual taxa.