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The evolution of multilocus systems under weak selection

T Nagylaki1

  • 1Department of Ecology and Evolution, University of Chiacago, Illinois 60637.

Genetics
|June 1, 1993
PubMed
Summary

This study shows that multilocus systems under weak selection evolve towards linkage equilibrium rapidly. After a short time, genetic drift and epistasis become negligible, validating natural selection theorems with small errors.

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Area of Science:

  • Evolutionary genetics
  • Population genetics
  • Theoretical biology

Background:

  • Understanding multilocus genetic systems is crucial for evolutionary theory.
  • Weak selection presents unique challenges for modeling genetic evolution.
  • Linkage disequilibrium dynamics are complex and influenced by multiple factors.

Purpose of the Study:

  • To investigate the evolution of multilocus systems under weak selection.
  • To determine the conditions under which linkage equilibrium is approached.
  • To analyze the accuracy of natural selection theorems in such systems.

Main Methods:

  • Mathematical modeling of multilocus systems with discrete, non-overlapping generations.
  • Analysis of genotypic fitnesses, linkage maps, dominance, and epistasis.
  • Derivation of conditions for weak selection (s << cmin) and analysis of error terms.

Main Results:

  • Multilocus linkage disequilibria rapidly approach O(s) within approximately (ln s)/ln(1 - cmin) generations.
  • The system evolves as if in linkage equilibrium with an error of O(s) in gametic frequencies.
  • Linkage disequilibria become nearly constant after time t2 ≈ 2t1, proportional to epistatic deviations.
  • The change in mean fitness is approximately delta W = W⁻¹Vg + O(s³).
  • The mean of a character evolves at delta Z = W⁻¹Cg + O(s²).

Conclusions:

  • Under weak selection, multilocus genetic systems quickly approximate linkage equilibrium.
  • The fundamental and secondary theorems of natural selection hold with small absolute errors after a short evolutionary time.
  • These findings provide theoretical justification for simplified models in evolutionary genetics.

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