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A general asymptotic property of two-locus selection models
1Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts 02138.
Theoretical Population Biology
|October 1, 1988
Summary
Genetic models with constant fitnesses demonstrate a polymorphic equilibrium where linkage disequilibrium (D) approaches zero as recombination (R) increases. The product of recombination and linkage disequilibrium (RD) converges to a finite, non-zero constant.
Area of Science:
- Population genetics
- Evolutionary biology
- Quantitative genetics
Background:
- Understanding genetic variation and linkage disequilibrium is crucial in population genetics.
- Previous models often assumed specific recombination rates or fitness landscapes.
Purpose of the Study:
- To investigate the behavior of linkage disequilibrium in two-locus, two-allele models with constant fitnesses.
- To determine the conditions under which polymorphic equilibria exist and their properties.
Main Methods:
- Mathematical modeling of population genetics.
- Analysis of equilibrium conditions in a two-locus selection model.
- Asymptotic analysis as recombination rate approaches infinity.
Main Results:
- Any two-locus, two-allele model with constant fitnesses exhibits at least one polymorphic equilibrium.
- Linkage disequilibrium (D) approaches zero as recombination (R) increases.
- The product RD converges to a finite, non-zero constant (l).
- The number of distinct asymptotic equilibria can be 1, 3, or 5, contingent on fitness parameters.
Conclusions:
- Constant fitness models predict predictable behavior of linkage disequilibrium under high recombination.
- The convergence of RD to a constant suggests a fundamental relationship between selection, recombination, and linkage disequilibrium.
- The number of equilibria highlights the complexity of evolutionary trajectories based on fitness landscapes.