Inferring continuous and discrete population genetic structure across space

Abstract

These authors contributed equally to this work. AbstractA 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 twodimensional 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. 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. Author summaryOne of the first steps in the analysis of genetic data, and a principal mission of biology, is to describe and categorize natural variation. A continuous pattern of differentiation (isolation by distance), where individuals found closer together in space are, on average, more genetically similar than individuals sampled farther apart, can confound attempts to categorize natural variation into groups. This is because current statistical methods for assigning individuals to discrete clusters cannot accommodate spatial patterns, and so are forced to use clusters to describe what is in fact continuous variation. As isolation by distance is common in nature, this is a substantial shortcoming of existing methods. In this study, we introduce a new statistical method for categorizing natural genetic variation -one that describes variation as a combination of continuous and discrete patterns. We demonstrate that this method works well and can capture patterns in population genomic data without resorting to splitting populations where they can be described by continuous patterns of variation.

Landscape drivers of genomic diversity and divergence in woodland Eucalyptus

“…However, unlike previous studies, we found no support for strong discrete genetic structure. As seen in simulated and empirical studies of continuously distributed species (Bradburd et al, 2017;Frantz et al, 2009), we found statistical support for discrete population structure only when IBD was not incorporated into models of population structure. This conflation of IBD and discrete structure cements the conclusion that accurate determination of population structure in widespread species should use methods that can jointly estimate isolation by distance and discrete population structure.…”

“…Traditional model-based genetic clustering methods like STRUCTURE (Pritchard et al, 2000) and ADMIXTURE (Alexander et al, 2009) were designed to detect discrete population structure, therefore they may perform poorly for continuously distributed natural populations in which isolation by distance is the primary driver of genetic structure (Frantz et al, 2009). ConStruct addresses this limitation by jointly modeling the effects of both continuous isolation by distance and discrete population structure on inter-sample relationships (Bradburd et al, 2017). As we expected continuously distributed landscape features to contribute to inter-sample genetic distances, we used conStruct to simultaneously test for discrete and continuous population structure.…”

“…The second layer in such models had no strong signal of IBD. This second layer could describe a small contribution of inter-species introgression to extant genetic diversity, or could represent "homogeneous minimum layer membership", an artifact produced by conStruct when there are significant levels of missing data (Bradburd et al, 2017). ConStruct models that did not allow continuous isolation by distance required at least two populations to achieve similar predictive accuracy ( fig.…”

“…Continuous isolation by distance can lead to support for discrete population structure in analysis with genetic clustering methods like STRUCTURE and ADMIXTURE (Frantz et al, 2009). However, recent methodological developments now allow joint estimation of IBD and discrete structure (conStruct; Bradburd et al, 2017). Spatial autocorrelation of environmental variables makes disentangling their effects from IBD challenging, and older methods like partial Mantel tests are beset with several flaws (e.g., assumption of linearity, high Type I error rate; Guillot and Rousset, 2013).…”

“…in E. salubris; Steane et al, 2015). In any case, given the likely conflation of IBD and discrete population structure by traditional genetic clustering methods (Bradburd et al, 2017;Frantz et al, 2009), the relative extent of IBD and discrete structure remains an open question in many species. Correlation between genetic variation and environment has been observed in many forms, including IBE (e.g.…”