2023/04/01 by Chakraborty, Suman, Chakraborty, Sagar
#FOS: Biological sciences #Populations and Evolution (q-bio.PE)
paper · doi:10.48550/arxiv.2304.00256
In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise non-overlapping unstructured population of individuals mating at random. Our main finding is that the dynamics is gradient-like when the point mutations at the two loci are independent. This is in stark contrast to the case of one-locus multi-allele where the existence gradient behaviour is contingent on a specific relationship between the mutation rates. When the mutations are not independent in the two-locus two-allele system, there is the possibility of non-convergent outcomes, like asymptotically stable oscillations, through either the Hopf bifurcation or the Neimark--Sacker bifurcation depending on the strength of the weak selection. The results can be straightforwardly extended for multi-locus two-allele systems.