Evaluation of redundancy analysis to identify signatures of local adaptation

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 paper 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. Additionally, 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., 2013). The RDA-based approach identifies the main selective gradient contrasting southern and coastal populations to northern and continental populations in the northwestern American coast.