Academic journal article Genetics

Inferring Continuous and Discrete Population Genetic Structure across Space

Academic journal article Genetics

Inferring Continuous and Discrete Population Genetic Structure across Space

Article excerpt

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A fundamental quandary in the description of biological diversity is the fact that diversity shows both discrete and continuous patterns. For example, reasonable people can disagree about whether two populations are separate species because the process of speciation is usually gradual, and so there is no set point in the continuous divergence of populations when they unambiguously become distinct species. The issue of identifying meaningful biological subunits extends below the species level, as patterns of phenotypic and genetic diversity within and among populations are shaped by continuous migration and drift, as well as by more discrete events, such as rapid expansions, bottlenecks, rare long-distance migration, and separation by geographic barriers. Both discrete and continuous components are required to accurately describe most species' patterns of genetic relatedness.

From a practical standpoint, we often need to identify somewhat separable populations from which individuals are sampled (Wright 1949), even while acknowledging continuous processes. Delineating populations is useful for systematics and for informing conservation priorities (Moritz 1994; Waples 1998; Moritz et al. 2002). Furthermore, we often need to identify subsets of individuals resulting from reasonably coherent evolutionary histories for downstream analyses to learn about population history and adaptation. Conversely, the substantial information available from continuous, geographic differentiation (e.g., adaptation along a climatic gradient) can be confounded by discrete historical processes (e.g., admixture), requiring methods that can disentangle the two.

There have been many methods proposed to characterize population genetic structure, including generating population phylogenies (Cavalli-Sforza and Piazza 1975; Pickrell and Pritchard 2012), dimensionality-reduction approaches such as principal components analysis (Menozzi et al. 1978; Price et al. 2006; Novembre and Stephens 2008; Meirmans 2009), and model-based clustering approaches (e.g., Pritchard et al. 2000; Corander et al. 2003; Falush et al 2003; Guillot et al 2005; Huelsenbeck and Andolfatto 2007; Alexander et al. 2009; Hubisz et al. 2009; Lawson et al. 2012; Raj et al. 2014; Caye et al. 2018). Each of these methods performs best in particular situations, but many can give misleading results when applied to data that show a continuous pattern of differentiation, as that produced by geographic isolation by distance (Wright 1943; Novembre and Stephens 2008; Frantz et al. 2009). Here, we will focus on model-based clustering, the most widely used class of approaches for population delineation. (We note that the problem of identifying population clusters is distinct from, though of course related to, the problem of detecting barriers to gene flow between populations, (e.g., Barton 2008; Bradburd etal. 2013; Petkova etal. 2016; Ringbauer et al. 2018). Existing model-based clustering methods model each individual's genotypes as random draws from a set of underlying, unobserved population clusters, each with a characteristic set of allele frequencies, which are estimated. These underlying frequencies are identical for all individuals assigned to a cluster, regardless of their spatial location. Spatial information has been incorporated into some of these methods, by, for example, placing spatial priors on cluster membership (Guillot et al. 2005; Caye et al. 2018), but this does not address the underlying issue that these methods assume that allele frequencies are constant in a cluster across the species' range.

Isolation by distance refers to a pattern of increasing genetic differentiation with geographic separation, which occurs when geographically restricted dispersal allows genetic drift to build up differentiation between distant locations (Wright 1943). Theoretical work, mostly derived from "stepping-stone" models (Kimura and Weiss 1964; Sawyer 1976; Shiga 1988), gives us some analytical predictions for isolation by distance (Malécot 1969; Slatkin 1985; Epperson 2003), and some theory has been derived for continuous space (Nagylaki 1978; Nagylaki and Barcilon 1988; Barton et al. …

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