Cyclical dynamics under constant selection against mutations in haploid and diploid populations with facultative selfing

Abstract

We have found that constant selection against mutations can cause cyclical dynamics in a population with facultative selfing. When this happens, the distribution of the number of deleterious mutations per genotype fluctuates with the period approximately 1/sHe generations, where sHe is the coefficient of selection against a heterozygous mutation. The amplitude of oscillations of the mean population fitness often exceeds an order of magnitude. Cyclical dynamics can occur under intermediate selfing rates if selection against heterozygous mutations is weak and selection against homozygous mutations is much stronger. Cycling is possible without epistasis or with diminishing-returns epistasis, but not with synergistic epistasis. Under multiplicative selection, cycling might happen if the haploid mutation rate exceeds 1.9 in the case of selfing of haploids, and if this diploid mutation rate exceeds 4.5 in the case of selfing of diploids. We propose a heuristic explanation for cycling under facultative selfing and discuss its possible relevance.

Population Models of Genomic Imprinting. II. Maternal and Fertility Selection

“…Moreover, these cycles disappear at a second Hopf bifurcation, as the fitness parameter is further changed. We know of no other single-locus population-genetic models exhibiting such behavior, although single Hopf bifurcations do arise in models of (i) constant viability selection and recombination for two loci each with two alleles (Hastings 1981;Akin 1982Akin , 1983 and (ii) constant selection and multilocus mutation with selfing (Yang and Kondrashov 2003).…”

Two linked loci under mutation-selection balance and Muller’s ratchet

“…Negative selection against deleterious mutations occurs in all populations. As long as random drift can be ignored, such selection leads, with rare exceptions (Yang and Kondrashov, 2003), to deterministic mutation-selection equilibrium. Analysis of this equilibrium at a single locus represents one of the foundational results of population genetics (Haldane, 1937;Muller, 1950).…”

Two linked loci under mutation-selection balance and Muller’s ratchet

“…Negative selection against deleterious mutations occurs in all populations. As long as random drift can be ignored, such selection leads, with rare exceptions (Yang and Kondrashov, 2003), to deterministic mutation-selection equilibrium. Analysis of this equilibrium at a single locus represents one of the foundational results of population genetics (Haldane, 1937;Muller, 1950).…”