Academic journal article Genetics

Coalescence and Linkage Disequilibrium in Facultatively Sexual Diploids

Academic journal article Genetics

Coalescence and Linkage Disequilibrium in Facultatively Sexual Diploids

Article excerpt

(ProQuest: ... denotes formulae omitted.)

COALESCENT theory is a powerful mathematical framework that is used to determine how natural selection and demographic history affect genetic diversity (Kingman 1982; Rosenberg and Nordborg 2002; Hein et al. 2005; Wakeley 2009). Traditional coalescent models assume that the population is obligately sexual, but there has been less attention on creating models that account for different reproductive modes. While the coalescent with self-fertilization has been extensively studied (Nordborg 1997, 2000; Nordborg and Donnelly 1997; Nordborg and Krone 2002), little theory exists on coalescent histories in organisms with other mixed reproductive systems.

Previous theory has investigated genetic diversity in facultatively sexual diploid organisms, which reproduce via a mixture of sexual and parthenogenetic reproduction (Brookfield 1992; Burt et al. 1996; Balloux et al. 2003; Bengtsson 2003; Ceplitis 2003). A general result arising from this work is that when an organism exhibits very rare population-level rates of sex [s# O(1/N), for s the probability of sex and population size N], they will exhibit "allelic sequence divergence" where both alleles within a diploid individual accumulate distinct polymorphisms from each other (Mark Welch and Meselson 2000; Butlin2002). Hartfield etai. (2016) subsequently investigated a coalescent model of facultative sexuals and quantified how the presence of gene conversion can reduce within-individual diversity to less than that expected in sexual organisms, contrary to the effects of allelic sequence divergence. Hence these results provide a potential explanation as to why allelic divergence is not widely observed in empirical studies of facultatively sexual organisms (reviewed in Hartfield 2016).

However, this analysis only modeled the genetic history at a single, nonrecombining locus. Here, genealogies only greatly differed from those in obligately sexual organisms at very low frequencies of sex [s # O(1/N)\. As a consequence, methods to estimate the frequency of sex can only do so based on the degree of allelic sequence divergence, and are expected to be ineffective if the frequency of sex is > 1/N and/or gene conversion is prevalent (Ceplitis 2003; Hartfield et al. 2016). In contrast, many facultatively sexual organisms exhibit much higher occurrences of sex. Pea aphids reproduce sexually about once every 10-20 generations (Jaquiéry et al. 2012), while Daphnia undergo 1 sexual generation and 5-20 asexual generations a year (Haag et al. 2009). The wild yeast Saccharomyces paradoxus has an outcrossing frequency of 0.001; while low, this value is four orders of magnitude higher than 1/Ne (Tsai et al. 2008). If we wish to create a general coalescent model that can be used to estimate rates of sexual reproduction in species undergoing more frequent sex, then we need to increase the power of this coalescent analysis to consider how patterns of genetic diversity at multiple loci are affected with facultative sex.

This is achievable by considering how genealogies of multiple sites correlate along a chromosome. Two completely linked sites will reach a common ancestor in the past at the same time, so will share the same gene genealogy. However, if a recombination event (e.g., via meiotic crossing over) were to separate the sites, each subsegment may have different genetic histories (Hudson 1983). Breaking apart correlations between sites is reflected with lower linkage disequilibrium, which can be measured from genomic data (Griffiths 1981; Hudson and Kaplan 1985; Hudson 1990; Simonsen and Churchill 1997; McVean 2002). Gene conversion can also break apart correlations between sites through transferring genetic material across DNA strands (Wiuf and Hein 2000).

As meiotic crossing over occurs during sexual reproduction, one may expect that the extent to which linkage disequilibrium is broken down should scale with the probability of sex (see Nordborg 2000 for a related argument for the coalescent with self-fertilization). …

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