Bistability in two-locus models with selection, mutation, and recombination
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In this paper, the authors considered a deterministic, haploid two-locus model with reversible mutations, selection, and recombination, and derived the stationary genotype frequencies in various parameter regimes.Abstract:
The evolutionary effect of recombination depends crucially on the epistatic interactions between linked loci. A paradigmatic case where recombination is known to be strongly disadvantageous is a two-locus fitness landscape displaying reciprocal sign epistasis with two fitness peaks of unequal height. Although this type of model has been studied since the 1960s, a full analytic understanding of the stationary states of mutation-selection balance was not achieved so far. Focusing on the bistability arising due to the recombination, we consider here the deterministic, haploid two-locus model with reversible mutations, selection and recombination. We find analytic formulae for the critical recombination probability r ( c ) above which two stable stationary solutions appear which are localized on each of the two fitness peaks. We also derive the stationary genotype frequencies in various parameter regimes. In particular, when the recombination rate is close to r ( c ) and the fitness difference between the two peaks is small, we obtain a compact description in terms of a cubic polynomial which is analogous to the Landau theory of physical phase transitions.read more
Citations
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Journal ArticleDOI
The evolutionary epidemiology of multilocus drug resistance.
Troy Day,Sylvain Gandon +1 more
TL;DR: It is shown how interventions such as social distancing and isolation can influence rates of recombination, and how this then can slow the spread of multilocus resistance and increase the likelihood of reversion to drug sensitivity once drug therapy has ceased.
Journal ArticleDOI
The effect of bacterial recombination on adaptation on fitness landscapes with limited peak accessibility.
TL;DR: It is concluded that recombination has complex effects on adaptation that are highly dependent on the particular fitness landscape, population size and recombination rate.
Journal ArticleDOI
Multidimensional epistasis and the transitory advantage of sex.
TL;DR: It is shown that the adaptive advantage of recombination on static rugged landscapes is strictly transitory and can be prolonged indefinitely in fluctuating environments, and it is maximal when the environment fluctuates on the same time scale on which trapping at local optima typically occurs.
Journal ArticleDOI
Time to fixation in the presence of recombination.
TL;DR: An analytical method is developed to calculate the fixation time T to the fittest locus for various choices of epistasis and it is found that for negative epistasis, T decreases slowly for small r but decays fast at larger r; and for compensatory mutation, T diverges as a power law with logarithmic corrections as the recombination fraction approaches a critical value.
Journal ArticleDOI
Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher-Muller Effect
Su-Chan Park,Joachim Krug +1 more
TL;DR: In this article, a detailed analysis of the Fisher-Muller mechanism for a model consisting of two loci with an infinite number of beneficial alleles each and multiplicative (nonepistatic) fitness effects is presented.
References
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Journal ArticleDOI
Evolution in Mendelian Populations.
TL;DR: Page 108, last line of text, for "P/P″" read "P′/ P″."
Journal ArticleDOI
Deleterious mutations and the evolution of sexual reproduction
TL;DR: If the deleterious mutation rate per genome per generation is greater than 1, then the greater efficiency of selection against these mutations in sexual populations may be responsible for the evolution of sex and related phenomena.
Book
The Mathematical Theory of Selection, Recombination, and Mutation
TL;DR: The emphasis here is on models that have a direct bearing on evolutionary quantitative genetics and applications concerning the maintenance of genetic variation in quantitative traits and their dynamics under selection are treated in detail.