Abstract
A classic problem in population genetics is the characterization of discrete population structure in the presence of continuous patterns of genetic differentiation. Especially when sampling is discontinuous, the use of clustering or assignment methods may incorrectly ascribe differentiation due to continuous processes (e.g., geographic isolation by distance) to discrete processes, such as geographic, ecological, or reproductive barriers between populations. This reflects a shortcoming of current methods for inferring and visualizing population structure when applied to genetic data deriving from geographically distributed populations. Here, we present a statistical framework for the simultaneous inference of continuous and discrete patterns of population structure. The method estimates ancestry proportions for each sample from a set of two-dimensional population layers, and, within each layer, estimates a rate at which relatedness decays with distance. This thereby explicitly addresses the "clines versus clusters" problem in modeling population genetic variation, and remedies some of the overfitting to which nonspatial models are prone. The method produces useful descriptions of structure in genetic relatedness in situations where separated, geographically distributed populations interact, as after a range expansion or secondary contact. We demonstrate the utility of this approach using simulations and by applying it to empirical datasets of poplars and black bears in North America.
Highlights
A fundamental quandary in the description of biological diversity is the fact that diversity shows both discrete and continuous patterns
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)
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)
Summary
A fundamental quandary in the description of biological diversity is the fact that diversity shows both discrete and continuous patterns. 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). This problem can be compounded if sampling is done unevenly or discretely across a population or species’ range, and has given rise to a debate in the population genetic literature about how best to describe sets of individuals using continuous clines and discrete clusters (e.g., Serre and Pääbo 2004; Rosenberg et al 2005)
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