Coalescent patterns in diploid exchangeable population models

A large offspring-number diploid biparental multilocus population model of Moran type is our object of study. At each time step, a pair of diploid individuals drawn uniformly at random contributes offspring to the population. The number of offspring can be large relative to the total population size. Similar "heavily skewed" reproduction mechanisms have been recently considered by various authors (cf. e.g., Eldon and Wakeley 2006, 2008) and reviewed by Hedgecock and Pudovkin (2011). Each diploid parental individual contributes exactly one chromosome to each diploid offspring, and hence ancestral lineages can coalesce only when in distinct individuals. A separation-of-timescales phenomenon is thus observed. A result of Möhle (1998) is extended to obtain convergence of the ancestral process to an ancestral recombination graph necessarily admitting simultaneous multiple mergers of ancestral lineages. The usual ancestral recombination graph is obtained as a special case of our model when the parents contribute only one offspring to the population each time. Due to diploidy and large offspring numbers, novel effects appear. For example, the marginal genealogy at each locus admits simultaneous multiple mergers in up to four groups, and different loci remain substantially correlated even as the recombination rate grows large. Thus, genealogies for loci far apart on the same chromosome remain correlated. Correlation in coalescence times for two loci is derived and shown to be a function of the coalescence parameters of our model. Extending the observations by Eldon and Wakeley (2008), predictions of linkage disequilibrium are shown to be functions of the reproduction parameters of our model, in addition to the recombination rate. Correlations in ratios of coalescence times between loci can be high, even when the recombination rate is high and sample size is large, in large offspring-number populations, as suggested by simulations, hinting at how to distinguish between different population models. D IPLOIDY, in which each offspring receives two sets of chromosomes, one from each of two distinct diploid parents, is fairly common among natural populations. Mathematical models in population genetics tend to assume, however, that all individuals in a population are haploid, simplifying the mathematics. Mendel's laws describe the mechanism of inheritance as composed of two main steps, equal segregation (first law) and independent assortment (second law). The first law proclaims gametes are haploid, i.e., carry only one of each pair of homologous chromosomes. Most models in population genetics are thus models of chromosomes or gene copies. Mendel's second law proclaims independent assortment of alleles at different genes, or loci, into gametes. Linkage of alleles on chromosomes, resulting in nonrandom association of alleles at different loci into gametes, is of course an important exception to the second law.Coalescent processes (Kingman 1982a,b;Hudson 1983b;Tajima 1983) describe the ancestral relations of chromosome...

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“…Analogous to the notation and convention of Möhle and Sagitov (2003), we assume that in every configuration j n,N (m) from (2) …”

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confidence: 99%

An Ancestral Recombination Graph for Diploid Populations with Skewed Offspring Distribution

2013

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“…In terms of genetics, our model is novel because we include the possibility of recombination. Sagitov (1999) and Pitman (1999) did not consider recombination, but proved convergence to an ancestral process that allows for many ancestral lines to reach a common ancestor, or coalesce, at exactly the same instant (or same generation) and that occurs on a shorter timescale than in the standard coalescent (Pitman 1999;Sagitov 1999;Schweinsberg 2000;Mö hle and Sagitov 2001). Predictions of patterns of genetic diversity also differ from those under Kingman's coalescent (Eldon and Wakeley 2006;Mö hle 2006).…”

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Linkage Disequilibrium Under Skewed Offspring Distribution Among Individuals in a Population

Eldon

Wakeley

2008

Genetics

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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...

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“…While Kingman's coalescent is robust to many deviations from its assumptions (Mö hle 1998, 1999), a major shift in the behavior of the ancestral process occurs when the variance of offspring number is large. The general ancestral process allows for multiple mergers of ancestral lines and happens on a timescale that is faster than that of Kingman's coalescent (Pitman 1999;Sagitov 1999;Schweinsberg 2000;Mö hle and Sagitov 2001).…”

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Coalescent Processes When the Distribution of Offspring Number Among Individuals Is Highly Skewed

2006

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We report a complex set of scaling relationships between mutation and reproduction in a simple model of a population. These follow from a consideration of patterns of genetic diversity in a sample of DNA sequences. Five different possible limit processes, each with a different scaled mutation parameter, can be used to describe genetic diversity in a large population. Only one of these corresponds to the usual population genetic model, and the others make drastically different predictions about genetic diversity. The complexity arises because individuals can potentially have very many offspring. To the extent that this occurs in a given species, our results imply that inferences from genetic data made under the usual assumptions are likely to be wrong. Our results also uncover a fundamental difference between populations in which generations are overlapping and those in which generations are discrete. We choose one of the five limit processes that appears to be appropriate for some marine organisms and use a sample of genetic data from a population of Pacific oysters to infer the parameters of the model. The data suggest the presence of rare reproduction events in which $8% of the population is replaced by the offspring of a single individual.

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Coalescent patterns in diploid exchangeable population models

Cited by 80 publications

References 3 publications

An Ancestral Recombination Graph for Diploid Populations with Skewed Offspring Distribution

An Ancestral Recombination Graph for Diploid Populations with Skewed Offspring Distribution

Linkage Disequilibrium Under Skewed Offspring Distribution Among Individuals in a Population

Coalescent Processes When the Distribution of Offspring Number Among Individuals Is Highly Skewed

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