Abstract
The multilocus analysis of polymorphisms has emerged as a vital ingredient of population genetics and evolutionary biology. A fundamental assumption used for existing multilocus analysis approaches is Hardy–Weinberg equilibrium at which maternally- and paternally-derived gametes unite randomly during fertilization. Given the fact that natural populations are rarely panmictic, these approaches will have a significant limitation for practical use. We present a robust model for multilocus linkage disequilibrium analysis which does not rely on the assumption of random mating. This new disequilibrium model capitalizes on Weir’s definition of zygotic disequilibria and is based on an open-pollinated design in which multiple maternal individuals and their half-sib families are sampled from a natural population. This design captures two levels of associations: one is at the upper level that describes the pattern of cosegregation between different loci in the parental population and the other is at the lower level that specifies the extent of co-transmission of non-alleles at different loci from parents to their offspring. An MCMC method was implemented to estimate genetic parameters that define these associations. Simulation studies were used to validate the statistical behavior of the new model.
Highlights
Linkage disequilibria have been used as a fundamental concept for studying the pattern of genetic diversity in a natural population (Lewontin, 1964, 1988; Hedrick, 1987; Weir, 1996; Lou et al, 2003; Li et al, 2007; Slatkin, 2008) as well as for fine-mapping the genetic architecture of complex traits (Kruglyak, 1999)
The theoretical basis of estimating gametic linkage disequilibria is founded on the assumption that the population under study is at Hardy–Weinberg equilibrium (HWE), in which individuals are randomly mating to produce generations
While most of the previous work was implemented with the EM algorithm, we develop a Markov chain Monte Carlo (MCMC) procedure to estimate the parameters that define zygotic disequilibria
Summary
Linkage disequilibria have been used as a fundamental concept for studying the pattern of genetic diversity in a natural population (Lewontin, 1964, 1988; Hedrick, 1987; Weir, 1996; Lou et al, 2003; Li et al, 2007; Slatkin, 2008) as well as for fine-mapping the genetic architecture of complex traits (Kruglyak, 1999). The traditional definition of linkage disequilibrium is the non-random association of alleles at different loci within the same gametes. The theoretical basis of estimating gametic linkage disequilibria is founded on the assumption that the population under study is at Hardy–Weinberg equilibrium (HWE), in which individuals are randomly mating to produce generations. For a traditional population genetic strategy that samples unrelated individuals at random from a natural population, Weir’s approach cannot separate the gametic and non-gametic disequilibria. This is because it provides insufficient information to distinguish two diplotypes of a double heterozygote which have the same genotype. Linkage disequilibrium analysis in a non-equilibrium population to simultaneously estimate the linkage and (gametic) linkage disequilibrium between different markers.
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