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Disequilibrium, selection, and recombination: limits in two-locus, two-allele models
Genetics
|July 1, 1981
Summary
This study explores genetic disequilibrium in two-locus models, finding that recombination (r) limits disequilibrium (D) such that |rD| < s/10. This explains why nonzero D is rarely observed in genetic selection studies.
Area of Science:
- Population Genetics
- Evolutionary Biology
- Quantitative Genetics
Background:
- Two-locus, two-allele models are fundamental for understanding genetic drift and selection.
- The relationship between linkage disequilibrium (D), recombination (r), and selection (s) is crucial for predicting evolutionary trajectories.
- Previous studies have explored these dynamics, but comprehensive enumeration of all possible scenarios was lacking.
Purpose of the Study:
- To enumerate all possible combinations of equilibria and fitnesses in deterministic, discrete-generation, two-locus selection models.
- To establish precise mathematical limits on the relationship between linkage disequilibrium, selection, and recombination for fixed allele frequencies.
- To investigate the implications of these limits for observed genetic data in the literature.
Main Methods:
- Exhaustive enumeration of all equilibrium and fitness combinations in two-locus models.
- Derivation of theoretical limits for the magnitude of linkage disequilibrium (|rD|) relative to selection coefficients (s).
- Application of linear programming techniques to analyze empirical data on nonzero D values.
Main Results:
- Established a universal inequality: the magnitude of linkage disequilibrium (D) is limited by recombination (r) such that |rD| < s/10, where s represents selection intensity.
- Demonstrated that selection coefficients significantly influence the potential for disequilibrium.
- Showed that observed nonzero D values in the literature are consistent with these derived theoretical limits.
Conclusions:
- The theoretical framework provides precise bounds for genetic disequilibrium under various selection and recombination scenarios.
- The derived inequality explains the rarity of observing significant nonzero linkage disequilibrium in empirical studies.
- Failure to observe nonzero D is not surprising given the strong constraints imposed by recombination and selection.