This guest post is by Michael Blum, Eric Bazin, and Nicolas Duforet-Frebourg on their preprint Genome scans for detecting footprints of local adaptation using a Bayesian factor model, available from the arXiv here.

Finding genomic regions subject to local adaptation is a central part of population genomics, which is based on genotyping numerous molecular markers and looking for outlier loci. Most common approaches use measures of genetic differentiation such as Fst. There are many software implementing genome scans based on statistics related to Fst (BayeScan, DetSel, FDist2 , Lositan), and they contribute to the popularity of this approach in population genomics.

However, there are different statistical and computational problems that may arise with approaches based on Fst or related measures. The first problem arises because methods related to Fst assume the so-called F-model, which corresponds to a particular covariance structure for gene frequencies among populations (Bierne et al. 2013). When spatial structure departs from the assumption of the F-model, it can generate many false positives. A second potential problem concerns the computational burden of some Bayesian approaches, which can become an obstacle with large number of SNPs. The last problem is that individuals should be grouped into populations in advance whereas working at the scale of individuals is desirable because it avoids defining populations.

Using a Bayesian factor model, we address the three aforementioned problems. Factor models capture population structure by inferring latent variables called factors. Factor models have already been proposed to ascertain population structure (Engelhardt and Stephens 2010). Here we extend the framework of factor model in order to identify outlier loci in addition to the ascertainment of population structure. Our approach is not the first one to account for deviations to the assumptions of the F-model (Bonhomme et al. 2010, Günther and Coop 2013) but it does not require to define populations by contrast to the previous approaches. Using simulations, we show that factor model can achieve a 2-fold or more reduction of false discovery rate compared to the Fst-related approaches. We also analyze the HGDP human dataset to provide an example of how factor models can be used to detect local adaptation with a large number of SNPs. The Bayesian factor model is implemented in the PCAdapt software and we would be happy to answer to comments or questions regarding the software.

To explain why the factor model generates less false discoveries, we can introduce the notions of mechanistic and phenomenological models. Mechanistic models aim to mimic the biological processes that are thought to have given rise to the data whereas phenomenological models seek only to best describe the data using a statistical model. In the spectrum between mechanistic and phenomenological model, the F-model would stand close to mechanistic models whereas factor models would be closer to the phenomenological ones. Mechanistic models are appealing because they provide quantitative measures that can be related to biologically meaningful parameters. For instance, the parameters of the F-model measures genetic drift that can be related to migration rates, divergence times or population sizes. By contrast, phenomenological models work with mathematical abstractions such as latent factors that can be difficult to interpret biologically. The downside of mechanistic models is that violation of the modeling assumption can invalidate the proposed framework and generate many false discoveries in the context of selection scan. The F-model assumes a particular covariance matrix between populations which is found with star-like population trees for instance. However, more complex models of population structure can arise for various reasons including non-instantaneous divergence or isolation-by-distance, and they will violate the mechanistic assumptions and make phenomenological models preferable.

Michael Blum, Eric Bazin, and Nicolas Duforet-Frebourg

This guest post is by Matthieu Foll and Laurent Excoffier on their preprint (with co-authors) Hierarchical Bayesian model of population structure reveals convergent adaptation to high altitude in human populations, arXived here.

Background

Since the seminal paper of Lewontin and Krakauer (1973), Fst-based genome scan methods had to struggle with the confounding effect of population structure. These methods started to be very popular with the FDIST software implemented by Beaumont and Nichols (1996), which was based on an island model. At that time it was proposed that the island model was robust to different demographic scenario (recent divergence and growth, isolation by distance or heterogeneous levels of gene flow between populations). A Bayesian version of this model (generally called the F-model) in which populations can receive unequal number of migrants has then been proposed (Beaumont and Balding 2004; Foll and Gaggiotti 2008), and implemented in the BayeScan software (http://cmpg.unibe.ch/software/BayeScan/), which is now quite widely used.

However, all these models assume that migrant genes originate from a unique and common migrant pool. We started to realize that this assumption could lead to a massive amount of false positive when we tried to analyze the HGDP data, where this assumption was clearly not supported. To overcome this problem, we proposed an extension of Beaumont and Nichols’s (1996) based on a hierarchical island model (Excoffier et al. 2009) in which populations were assigned to different groups or regions. An island model was assumed in each group, and the group themselves were assumed to follow an island model. This new method was then implemented in Arlequin (Excoffier and Lischer 2010).

Note that alternative ways to deal with complex genetic structure have also been proposed (Coop et al. 2010; Bonhomme et al. 2010; Fariello et al. 2013; Günther and Coop 2013), but the main message people took from these papers was that methods aiming at identifying loci under selection can be quite sensitive to some hidden (or unaccounted) population structure and should be used with caution. Hermisson (2009) even rather provocatively asked: “Who believes in whole-genome scans for selection?”

One radical way to deal with the problem of complex genetic structure is to reduce the number of sampled populations to just two (Vitalis et al. 2001). This leads to a GWAS-like strategy where people sample two populations living in contrasting environments (playing the role of cases and controls in GWAS) with potentially different selection pressures. However, other problems occur when doing so: (i) having only two populations leads to a reduction in power, (ii) related to this first point, one generally needs to sample a larger number of individuals to have sufficient power, (iii) the comparison of results obtained from different pairs of populations can be problematic, especially when one is interested in detecting convergent selection by looking at the overlap in lists of candidate genes. In the last few years, studies comparing pairs of populations living in different environments have accumulated. Typically, each pairwise comparison produced a set of candidate loci, and people often used some informal criterion to identify “repeated outliers” based on the number of times they were identified in the different tests performed (see Nosil et al. 2008 or Paris et al. 2010 for example).

A new hierarchical F-model

We started to think that the introduction of a Bayesian F-model dealing with a hierarchical population structure could solve some of these problems. We therefore introduced a hierarchical F-model where populations are assigned to different groups. In each group the genetic structure is modeled with a classical F-model, and the group themselves are modeled with a higher-level F-model. One advantage is that the Beaumont and Balding (2004) decomposition of Fst as population- and locus-specific effects can be done in each group separately as well as between groups. This allows the identification of selection at different levels: within a specific group of populations, or at a higher level (among groups). Here again, an interesting question is to identify loci responding similarly to selection in several groups. In order to look at that particular case, we explicitly included a convergent selection model were at any given locus all groups share the same locus-specific effect. Posterior probabilities of all possible models of selection are then evaluated using a Reversible Jump MCMC algorithm.

Adaptation to high altitude

We applied this new method to the very interesting case of high altitude adaptation in humans. We reanalyzed a published large SNP dataset (Bigham et al. 2010) including two populations living at high altitude in the Andes and in Tibet, as well as two lowland related populations from Central-America and East Asia. One of the most striking results we find is that convergent selection is much more common than previously found based on separate analyses in the two continents. We checked with simulations that this was in fact expected: being able to analyze the four populations together is indeed more powerful than performing two separate pairwise tests. In addition to confirming several known candidate genes and biological processes involved in high altitude adaptation, we were able to identify additional new genes and processes under convergent selection. In particular, we were very excited to find two specific biological pathways that could have evolved to counter the toxic levels of fatty acids and the neuronal excitotoxicity induced by hypoxia in both continents. Interestingly, several genes included in these pathways had been identified in high altitude Ethiopians (Scheinfeldt et al. 2012; Alkorta-Aranburu et al. 2012; Huerta-Sánchez et al. 2013), suggesting that these pathways could represent a striking example of convergent adaptation in three continents.

Conclusion

Our hierarchical F-model appears very flexible and can cope with a variety of sampling strategies to identify adaptation. Whereas we have considered only two groups of two populations in our paper, it is worth noting that our method can handle more than two groups and more than two populations per group. An alternative sampling scheme to detect selection could for instance to contrast several genetically related high altitude populations to several related lowland populations (see e.g. Pagani et al. 2011). Our method could also deal with such a sampling scheme, but this time, one would focus on the decomposition of the genetic differentiation between the groups (i.e. Fct). In summary, our approach allows the simultaneous analysis of populations living in contrasting environments in several geographic regions. It can be used to specifically test for convergent adaptation, and this approach is more powerful than previous methods contrasting pairs of populations separately.

Matthieu Foll and Laurent Excoffier

References

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