The Effect of Recombination on the Speed of Evolution

• Main Author: Nantawat Udomchatpitak
• Other Authors: Mahidol University
• Format: Article
• Published: 2022
• Subjects: Mathematics
• Online Access: https://repository.li.mahidol.ac.th/handle/123456789/77390

It has been a puzzling question of why sexual reproduction has been so successful. Fisher and Muller hypothesized that reproducing by sex can speed up evolution; recombination could combine beneficial alleles on different chromosomes and speeds up the time that the beneficial alleles become fixated population. We consider a population of 2N chromosomes and focus on two loci on these chromosomes. The allele at each locus can mutate to a beneficial allele at rate μN. Chromosomes with 0, 1, and 2 beneficial alleles die at rates 1; 1–sN, and 1–2sN, respectively, and they are replaced immediately after death events. With probability 1 – rN, the replacement inherits both alleles from one parent chosen at random from the population at the time of replacement. With probability rN, recombination occurs, and the replacement receives its two alleles from two randomly chosen parents. Under certain assumptions on the parameters N; μN; sN; and rN, we obtain an asymptotic approximation to the time that both beneficial alleles are fixated in the population. When the recombination probability is small, recombination does not speed up the time that the two beneficial alleles become fixated. In contrast, when the recombination probability is significant, recombination shorten this time. The result agrees with the Fisher-Muller hypothesis and confirms the advantage of reproducing by sex.