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Bistability in two-locus models with selection, mutation, and recombination.

Su-Chan Park1, Joachim Krug

  • 1Department of Physics, The Catholic University of Korea, Bucheon, 420-743 Korea. spark0@catholic.ac.kr

Journal of Mathematical Biology
|July 10, 2010
PubMed
Summary
This summary is machine-generated.

Recombination can be disadvantageous in evolution, especially with specific genetic interactions. This study provides analytic solutions for mutation-selection balance in a two-locus model, revealing critical recombination thresholds.

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Area of Science:

  • Evolutionary genetics
  • Population genetics
  • Theoretical biology

Background:

  • Recombination's evolutionary impact hinges on epistatic interactions between linked genetic loci.
  • Reciprocal sign epistasis in two-locus models presents a challenge, with recombination often being disadvantageous.
  • Previous analytic understanding of mutation-selection balance in such systems remained incomplete.

Purpose of the Study:

  • To analytically understand stationary states in a two-locus model with reciprocal sign epistasis and mutation-selection balance.
  • To investigate the bistability phenomenon induced by recombination.
  • To derive formulae for critical recombination probabilities and stationary genotype frequencies.

Main Methods:

  • Deterministic, haploid two-locus model analysis.
  • Incorporation of reversible mutations, selection, and recombination.
  • Derivation of analytic formulae for stationary states.

Main Results:

  • Analytic formulae for the critical recombination probability (r_c) were derived, determining the onset of bistability.
  • Two stable stationary solutions, localized on fitness peaks, emerge above r_c.
  • Stationary genotype frequencies were determined across various parameter regimes.
  • A cubic polynomial description, analogous to Landau theory, was obtained for specific parameter ranges.

Conclusions:

  • The study provides a comprehensive analytic understanding of mutation-selection-recombination balance in a challenging two-locus model.
  • The findings elucidate the conditions under which recombination leads to bistability and the emergence of distinct evolutionary outcomes.
  • The analogy to physical phase transitions offers a novel perspective on evolutionary dynamics.