Evaluation of redundancy analysis to identify signatures of local adaptation

Abstract

Ordination is a common tool in ecology that aims at representing complex biological information in a reduced space. In landscape genetics, ordination methods such as principal component analysis (PCA) have been used to detect adaptive variation based on genomic data. Taking advantage of environmental data in addition to genotype data, redundancy analysis (RDA) is another ordination approach that is useful to detect adaptive variation. This study aims at proposing a test statistic based on RDA to search for loci under selection. We compare redundancy analysis to pcadapt, which is a nonconstrained ordination method, and to a latent factor mixed model (LFMM), which is a univariate genotype-environment association method. Individual-based simulations identify evolutionary scenarios where RDA genome scans have a greater statistical power than genome scans based on PCA. By constraining the analysis with environmental variables, RDA performs better than PCA in identifying adaptive variation when selection gradients are weakly correlated with population structure. In addition, we show that if RDA and LFMM have a similar power to identify genetic markers associated with environmental variables, the RDA-based procedure has the advantage to identify the main selective gradients as a combination of environmental variables. To give a concrete illustration of RDA in population genomics, we apply this method to the detection of outliers and selective gradients on an SNP data set of Populus trichocarpa (Geraldes et al., ). The RDA-based approach identifies the main selective gradient contrasting southern and coastal populations to northern and continental populations in the north-western American coast.

Climate‐associated genetic variation in Fagus sylvatica and potential responses to climate change in the French Alps

“…The statistical approach we used to investigate the drivers of local adaptation in F. sylvatica is based on redundancy analysis (RDA) and is just starting to show its potential in the field of genetics of adaptation (Capblancq et al, 2018; Forester, Jones, Joost, Landguth, & Lasky, 2016; Forester, Lasky, Wagner, & Urban, 2017; De Kort et al, 2014; Lasky et al, 2012; Steane et al, 2014). RDA has shown great potential in identifying the signatures of selection and adaptive loci, both in comparison with other genome scan methods (Capblancq et al, 2018; Forester et al, 2017) and in different types of environments (Forester et al, 2016). Such multivariate approaches are thought to be more efficient in detecting multi‐loci selection since they consider the potential co‐variation among genetic markers (Rellstab, Gugerli, Eckert, Hancock, & Holderegger, 2015).…”

“…Specific loci associated with environmental adaptation were searched using a method derived from RDA and following the procedure proposed in Capblancq, Luu, Blum, Bazin, and Umr (2018). This method starts using a classical RDA procedure, and an outlier locus is detected when its projection in the K first axis of the RDA (principal component) does not follow the projection of the majority of the loci along the same K principal component.…”

“…This method starts using a classical RDA procedure, and an outlier locus is detected when its projection in the K first axis of the RDA (principal component) does not follow the projection of the majority of the loci along the same K principal component. More precisely, outliers correspond to loci for which the Mahalanobis distance (i.e., the distance estimated between the z ‐scores of the locus on the K first principal component and the mean of all the loci z ‐scores on the same set of principal components) is extreme relative to the distribution of the Mahalanobis distances of all loci (Capblancq et al, 2018, Luu, Bazin, & Blum, 2017). A p ‐value is then obtained for each locus after a transformation of the Mahalanobis distances (see the procedure in Luu et al, 2017).…”

Genome‐wide association analyses reveal polygenic genomic architecture underlying divergent shell morphology in SpanishLittorina saxatilisecotypes

“…Recent applications of multivariate ordination methods such as redundancy analysis have shown promise in finding multilocus adaptation while accounting for both population structure and polygenic interactions among loci (Capblancq, Luu, Blum, & Bazin, ; Forester et al, ). These methods have recently been shown to outperform mixed‐model‐based methods, as well as Random Forest, a machine‐learning‐based method, in uncovering loci associated with environmental variation (Capblancq et al, ; Forester et al, ). We acknowledge that although the RDA has performed better in simulation studies and appeared here to better match expectations from theory, the identification of a larger number of highly divergent trait‐associated loci does not guarantee that all these associations are true.…”

Predicting the success of an invader: Niche shift versus niche conservatism

“…Genotype-environment associations (GEA) were performed for testing association between each of the 6,506 SNPs and the six environmental variables. We used two GEA: the univariate latent factor mixed model (LFMM; Frichot, Schoville, Bouchard, & François, 2013) implemented in the LEA package v1.4.0 in R (Frichot & François, 2015), and the multivariate approach based on redundancy analysis (RDA; Capblancq, Luu, Blum, & Bazin, 2018;Forester, Lasky, Wagner, & Urban, 2018) using rda in the vegan package v2.4-5 in R (Legendre & Legendre, 2012;Oksanen et al, 2017). The univariate GEA method LFMM tests for association between each SNP allele frequency and a single environmental predictor (Frichot et al, 2013).…”