How is the time for evolution affected by effective population size?

We examine how the effective size of the population affects the time for evolution. The analysis is based on an established evolutionary model that accounts for natural selection, and it shows that the mean number of rounds of guessing letters needed to change the complete genome to its desirable form is asymptotically a function of L and K. Here, L is the number of letters of the genomic “word,” where each letter has been chosen from an alphabet of K letters. We extend this model so that the mean number of rounds is also a function of the effective population size. Using the same numerical values of L and K as in the original formulation, we find that there has been sufficient time for evolution, which is in line with previous analyses. The exception in our model is for cases with very small effective population sizes.