Special Seminar by Dr. Nantawat Udomchatpitak, Department of Mathematics, Faculty of Science, Mahidol University

Title: The Effect of Recombination on the Speed of Evolution

Date: 30 October 2019 13:30 – 14:30

Venue: B201 Faculty of Science, Mahidol University

Abstract:

We explore how recombination affect the speed of Evolution. Here, we study a population model of fixed size N, consisting of N chromosomes. The first locus on the chromosomes can be either a or A allele, and the second locus can be b or B allele, which make 4 possible types of chromosome. All the chromosomes in the population starts as type ab. At any time, each a and each b allele waits for an exponentially distributed time with rate \mu_N and mutates to A and B alleles respectively. Each chromosome of types ab, Ab, aB, and AB waits to be removed (considerably dies from the population) for an exponentially distributed time with rate 1, 1-s_N, 1-s_N, and 1-2s_N, respectively, which means that both A and B alleles are beneficial. A new chromosome is created to replace the removed chromosome. With probability 1-r_N, recombination does not occur and the new chromosome’s type is randomly chosen from existing chromosomes in the population at that time. With probability r_N, recombination occurs and the a/A and b/B loci of the new chromosome are randomly and independently chosen from two existing chromosomes in the population at that time. All the exponentially distributed times are assumed to be independent. With some assumptions on N,\mu_N,s_N, and r_N, we obtain an asymptotic approximation as N\rightarrow\infty for the fixation time of type AB. We also obtain a threshold for r_N such that when r_N is below this threshold, the fixation time is asymptotically the same as the fixation time without recombination. When r_N is above this threshold, the approximated fixation time is decreasing as the function of r_N.