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Multilocus Behavior in Random Environments. II. Linkage Disequilibrium in an Additive Model.
1Department of Biology, G7, University of Pennsylvania, Philadelphia, Pennsylvania, 19174.
Genetics
|November 1, 1977
Summary
Stochastic environments impact diploid populations. Mean linkage disequilibrium becomes non-zero when alleles at different loci are correlated, with its sign determined by the correlation sign.
Area of Science:
- Population genetics
- Mathematical biology
- Stochastic processes
Background:
- Understanding the influence of environmental stochasticity on genetic diversity is crucial in population genetics.
- Additive genetic models are fundamental for studying the inheritance of traits in diploid organisms.
- Linkage disequilibrium quantifies non-random association of alleles at different loci.
Purpose of the Study:
- To investigate the effects of a stochastic environment on a two-locus additive genetic model in a diploid population.
- To derive and analyze the diffusion equation governing this model under environmental fluctuations.
- To approximate the asymptotic properties of the system using an Ornstein-Uhlenbeck process.
Main Methods:
- Derivation of a diffusion equation for the two-locus additive model.
- Approximation of the diffusion equation's asymptotic behavior using an Ornstein-Uhlenbeck process.
- Calculation of the first and second-order moments of the approximating process.
Main Results:
- The derived diffusion equation accurately models the population dynamics under stochastic conditions.
- The Ornstein-Uhlenbeck process provides a valid approximation for the system's long-term behavior.
- Mean linkage disequilibrium is non-zero when alleles at different loci exhibit correlation.
- The sign of the mean linkage disequilibrium directly corresponds to the sign of the allelic correlation.
Conclusions:
- Environmental stochasticity can induce significant linkage disequilibrium in diploid populations.
- Allelic correlation is a key determinant of the magnitude and direction of linkage disequilibrium.
- The Ornstein-Uhlenbeck process serves as a valuable tool for analyzing genetic models in fluctuating environments.
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