Linkage Disequilibrium Under Skewed Offspring Distribution Among Individuals in a Population

Abstract

Correlations in coalescence times between two loci are derived under selectively neutral population models in which the offspring of an individual can number on the order of the population size. The correlations depend on the rates of recombination and random drift and are shown to be functions of the parameters controlling the size and frequency of these large reproduction events. Since a prediction of linkage disequilibrium can be written in terms of correlations in coalescence times, it follows that the prediction of linkage disequilibrium is a function not only of the rate of recombination but also of the reproduction parameters. Low linkage disequilibrium is predicted if the offspring of a single individual frequently replace almost the entire population. However, high linkage disequilibrium can be predicted if the offspring of a single individual replace an intermediate fraction of the population. In some cases the model reproduces the standard Wright-Fisher predictions. Contrary to common intuition, high linkage disequilibrium can be predicted despite frequent recombination, and low linkage disequilibrium under infrequent recombination. Simulations support the analytical results but show that the variance of linkage disequilibrium is very large. L INKAGE disequilibrium (LD) refers to the nonrandom association of alleles at different loci (Lewontin and Kojima 1960). Changes in population size, natural selection, population structure, and random drift can all lead to LD. Recombination, or the reciprocal exchange of material between homologous chromosomes, breaks down associations between alleles at different loci. Estimating LD can thus give insight into the forces that have shaped extant genetic diversity. The potential utility of LD for fine-scale mapping of human disease loci has also raised interest in estimating levels of linkage disequilibrium in human populations ( Jorde 1995;Lander 1996;Risch and Merikangas 1996). The evolutionary history of many organisms is marked by growth and decline of populations as well as various kinds of subdivision (with or without migration and admixture). As an example, the Icelandic human population has undergone severebottlenecks, accompanied byrecent population growth, in its $1100-year history Linkage disequilibrium is a function of the frequencies of alleles in the population and LD can be quantified as a function of allele frequencies in a number of ways (cf. Hedrick 2000). One commonly used measure of LD is the coefficient D of linkage disequilibrium and is defined as the difference between the observed frequency of a gametic type (haplotype) and the frequency expected on the basis of random association of alleles in gametes (Lewontin and Kojima 1960). The coefficient D can be written as D ¼ P AB P ab -P aB P Ab in which P xy is the frequency of haplotype xy. High absolute values of D correspond to high linkage disequilibrium in the population.Following Slatkin (1994) we can understand the effects of population history on LD between two diallelic loci by c...

Patterns of Neutral Diversity Under General Models of Selective Sweeps

“…In that limit, the coalescent is equivalent to the standard neutral model and as such the decay of linkage disequilibrium will be the same as in the standard neutral model with an N e given by Equation 24. A natural way to extend this exploration would be the genealogical framework developed by McVean (2007) that has recently been extended to a multiple-mergers coalescent by Eldon and Wakeley (2008).…”

The Equilibrium Allele Frequency Distribution for a Population with Reproductive Skew

“…have already been described, the specific populationgenetic consequences of reproductive skew have only recently begun to be worked out. In many cases, the classical picture of population genetics must be considerably enlarged to accommodate new phenomena-see, for example, Möhle (2006) on generalizations of the Ewens sampling formula, Eldon and Wakeley (2006b) on linkage disequilibrium in processes with skewed offspring distributions, Birkner and Blath (2008) and Birkner et al (2011) on inference and sampling in the L-coalescent, and Der et al (2012) on the fixation probability of an adaptive allele in the L-process.…”

Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

“…This has for consequences that events affecting the genealogy, such as intra-locus recombination, can affect a smaller or larger number of branches compared to that expected under the Kingman's coalescent (Eldon & Wakeley 2008;Birkner et al 2012). In biological terms, this means that if sweepstake reproduction events are frequent, the efficiency of recombination and meisosis in reshuffling genotypes is very limited as present genotypes descent from a very recent ancestor (Eldon & Wakeley 2008). As a result under MMC models, the amount of linkage disequilibrium (LD) can be uncorrelated .…”

“…21, 2014; to the genomic recombination rate (the Ancestral Recombination Graph for MMC model; Birkner et al 2012). For example, high LD can be observed despite high genomic rates of recombination and vice and versa, depending on where multiple merging events occur in the coalescent tree (Eldon & Wakeley 2008). Moreover, genealogies for loci far apart on the same chromosome may remain correlated, and LD is a function of the rate of recombination and of the reproduction parameter (of the skew in offspring distribution; Birkner et al 2012).…”

“…The proportion of the genome which is affected by genetic draft due to selection (Neher & Hallatschek 2013;, and thus the extent of linkage disequilibrium (Eldon & Wakeley 2008;Birkner et al 2012), will depend on the frequency of recombination in a given parasite species .…”