Pritchard, Stephens, and Donnelly on Population Structure

In essentially any species, genetic similarity among individuals is structured by the existence of subgroups and geographic isolation. For researchers, understanding this population structure can be of direct interest, a necessary waystation to further analyses, or a confounding nuisance. Regardless of the motivation, understanding population structure is an essential step for population genetic analysis. In 2000, Pritchard, Stephens, and Donnelly published one of the most widespread and important frameworks for addressing this task: the model-based clustering method known as STRUCTURE (Pritchard et al. 2000).

The birth of the method owes much to having the right expertise in a room. In September of 1998, Pritchard arrived for a postdoc in Oxford just as a workshop at the Newton Institute in Cambridge was starting. At the time, he was finishing up work on a test for cryptic population structure in disease association studies (Pritchard and Rosenberg 1999) and had become interested in clustering related individuals. At the workshop, he shared these interests with his new advisor Peter Donnelly and fellow postdoc, Matthew Stephens. Donnelly was deeply experienced with Bayesian models in genetics, including models for forensic samples of uncertain origins (e.g., Balding and Donnelly 1995), and Matthew had written his PhD dissertation on Bayesian clustering using Markov chain Monte Carlo techniques (Stephens 2000). Bringing these backgrounds together, they hashed out the first model on a board within a couple of hours. Then, Pritchard implemented it with the help of Stephens over the next several days. The prototype worked well, and there were no real changes from what was written out in the first meeting to what was ultimately published (J. K. Pritchard and P. Donnelly, personal communication).

The novelty was in taking a Bayesian approach that assigns individuals to source populations or allows them to have proportional assignment of their ancestry to multiple populations (the “admixture model”). Their work followed that of those who had developed likelihood-based individual assignment to populations (Paetkau et al. 1995; Rannala and Mountain 1997), population mixture models (Smouse et al. 1990), and Bayesian models of cryptic population structure (Foreman et al. 1997; Roeder et al. 1998). The resulting STRUCTURE method had a tremendous impact in human genetics, evolutionary genetics, and molecular ecology, and went on to be highly cited and awarded (Noor 2013). The admixture model is also used widely in machine learning where it is known as latent Dirichlet allocation (Blei et al. 2003). In addition, in the late 1990s, coalescent-based approaches dominated population genetic methods, and in this milieu the impact of STRUCTURE reinforced that relatively simple models can have tremendous utility.

After the initial publication, Pritchard and colleagues extended the work to include addressing ancestry along chromosomes (Falush et al. 2003), dominant markers and null alleles (Falush et al. 2007), and prior group information (Hubisz et al. 2009). Others developed extensions that, for instance, carry out assignment to hybrid categories (Anderson and Thompson 2002) or assume a spatial distribution for populations (Guillot et al. 2005; François et al. 2006; Durand et al. 2009; François and Durand 2010). Most recently there have been improvements to computational speed. Likelihood-based approaches (Tang et al. 2005; Alexander et al. 2009) and variational approximations (Raj et al. 2014) now make it feasible to analyze thousands of individuals (Novembre 2014).

One persistent challenge with applying STRUCTURE is inferring the number of source populations (K). Increasing the value of K adds parameters, which can lead to overfitting the data, and so model-choice procedures are necessary to estimate K. Numerous procedures have been proposed (Evanno et al. 2005; Huelsenbeck and Andolfatto 2007), though the conventional wisdom is that reproducible inference of K is a difficult problem, with less stability than conventional parameter estimation (e.g., Gilbert et al. 2012). Pritchard, Stephens, and Donnelly were prescient and acknowledged problems in the inference and interpretation of K. They have long advocated instead using STRUCTURE as an exploratory tool and inspecting results from a range of values of K.

Another challenge is that STRUCTURE has become, in some sense, a victim of its own success. It is applied by default in most studies without consideration of whether the underlying model is relevant. For example, if applied to a geographic continuum, the method will infer source populations that are vaguely spatial but have no real interpretation as source populations in an admixed sample (e.g., Witherspoon et al. 2007). A recent paper captures the care needed with its colorful title: “A tutorial on how (not) to over-interpret STRUCTURE/ADMIXTURE bar plots” (Falush et al. 2016). All this being said, the need for careful interpretation is ubiquitous in population genetics, and the extra attention on the STRUCTURE method is warranted because of its widespread use. Looking forward, we can expect new methods for studying population structure will continue to leverage the principles of individual-based analysis and proportional ancestry so nicely deployed by Pritchard, Stephens, and Donnelly.