Accumulating waves of random mutations before fixation

Abstract

Mutations provide variation for evolution to emerge. A quantitative analysis of how mutations arising in single individuals expand and possibly fixate in a population is essential for studying evolutionary processes. While it is intuitive to expect that a continuous influx of mutations will lead to a continuous flow of mutations fixating in a stable constant population, joint fixation of multiple mutations occur frequently in stochastic simulations even under neutral selection. We quantitatively measure and analyse the distribution of joint fixation events of neutral mutations in constant populations. We propose a new concept, the mutation "waves", where multiple mutations reach given frequencies simultaneously. We show that all but the lowest frequencies of the variant allele frequency are dominated by single mutation "waves" that approximately follow an exponential distribution both in their size and the time between two "waves". Consequently, large swaths of empty frequencies are observed in the variant allele frequency distributions, with a few frequencies having numbers of mutations far in excess of the expected average values. We further show that the discrete mutation waves average out to a continuous distribution named as the Wave Frequency Distribution (WFD), the shape of which is predictable based on few model parameters.