THE CONSTRAINTS OF FINITE-SIZE IN ASEXUAL POPULATIONS AND THE RATE OFTHE RATCHET

An analysis of mutation accumulation in finite, asexual populations sh ows that by modeling discrete individuals, a necessary condition for m utation-selection balance is often not met. It is found that over a wi de parameter range (whenever N e(-mu/s) < 1, where N is the population size, mu is the genome-wide mutation rate, and s is the realized stre ngth of selection), asexual populations will fail to achieve mutation- selection balance. This is specifically because the steady-state stren gth of selection on the best individuals is too weak to counter mutati on pressure. The discrete nature of individuals means that if the equi librium level of mutation and selection is such that less than one ind ividual is expected in a class, then equilibration towards this level acts to remove the class. When applied to the classes with the fewest mutations, this drives mutation accumulation. This drive is in additio n to the well-known identification of the stochastic loss of the best class as a mechanism for Muller's ratchet. Quantification of this proc ess explains why the distribution of the number of mutations per indiv idual can be markedly hypodispersed compared to the Poisson expectatio n. The actual distribution, when corrected for stochasticity between t he best class and the mean, is akin to a shifted negative binomial. Th e parameterization of the distribution allows for an approximation for the rate of Muller's ratchet when N e(-mu/s) < 1. The analysis is ext ended to the case of variable selection coefficients where incoming mu tations assume a distribution of deleterious effects. Under this condi tion, asexual populations accumulate mutations faster, yet may be able to survive longer, than previously estimated.