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Effect of epistasis and linkage on fixation probability in three-locus models: An ancestral recombination–selection graph approach

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  • Kermany, Amir R.
  • Lessard, Sabin

Abstract

We study the probability of ultimate fixation of a single new mutant arising in an individual chosen at random at a locus linked to two other loci carrying previously arisen mutations. This is done using the Ancestral Recombination–Selection Graph (ARSG) in a finite population in the limit of a large population size, which is also known as the Ancestral Influence Graph (AIG). An analytical expansion of the fixation probability with respect to population-scaled recombination rates and selection intensities is obtained. The coefficients of the expansion are expressed in terms of the initial state of the population and the epistatic interactions among the selected loci. Under the assumption of weak selection at tightly linked loci, the sign of the leading term, which depends on the signs of epistasis and initial linkage disequilibrium, determines whether an increase in recombination rates increases the chance of ultimate fixation of the new mutant. If mutants are advantageous, this is the case when epistasis is positive or null and the initial linkage disequilibrium is negative, which is an expected state in a finite population under directional selection. Moreover, this is also the case for a neutral mutant modifier coding for higher recombination rates if the same conditions hold at the selected loci. Under the same conditions, deleterious mutants are disfavored for ultimate fixation and neutral modifiers for higher recombination rates still favored. The recombination rates between the modifier locus and the selected loci do not come into play in the leading terms of the approximation for the fixation probability, but they do in higher-order terms.

Suggested Citation

  • Kermany, Amir R. & Lessard, Sabin, 2012. "Effect of epistasis and linkage on fixation probability in three-locus models: An ancestral recombination–selection graph approach," Theoretical Population Biology, Elsevier, vol. 82(2), pages 131-145.
  • Handle: RePEc:eee:thpobi:v:82:y:2012:i:2:p:131-145
    DOI: 10.1016/j.tpb.2012.05.002
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    References listed on IDEAS

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    1. Peter D. Keightley & Sarah P. Otto, 2006. "Interference among deleterious mutations favours sex and recombination in finite populations," Nature, Nature, vol. 443(7107), pages 89-92, September.
    2. Lehmann, Laurent & Rousset, François, 2009. "Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill–Robertson effect and to the joint evolution of helping and punishment," Theoretical Population Biology, Elsevier, vol. 76(1), pages 35-51.
    3. Lessard, Sabin & Lahaie, Philippe, 2009. "Fixation probability with multiple alleles and projected average allelic effect on selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 266-277.
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    1. Eldon, Bjarki & Stephan, Wolfgang, 2018. "Evolution of highly fecund haploid populations," Theoretical Population Biology, Elsevier, vol. 119(C), pages 48-56.
    2. Durand, Guillermo & Lessard, Sabin, 2016. "Fixation probability in a two-locus intersexual selection model," Theoretical Population Biology, Elsevier, vol. 109(C), pages 75-87.

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