How to make use of ordination methods to identify local adaptation: a comparison of genome scans based on PCA and RDA

Ordination is a common tool in Ecology that aims at representing complex biological information on a reduced space. For instance, it is frequently used to study geographic distribution pattern of species diversity and to study the link between ecological variable such as temperature, drought, etc, and the species turnover. Recently, ordination methods such as PCA have been used as a framework 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 useful to detect adaptive variation. These methodologies are specially used in Landscape Genomic where one wants to study the link between environmental variable and the distribution pattern of genome wide diversity, especially its adaptive component. This paper aims at proposing a test based on RDA approaches to search for genes under selection and to compare it to the PCA method implemented in the pcadapt package. Individual based simulations identify evolutionary scenarios where RDA genome scan has a greater statistical power than PCA genome scan. By constraining the analysis with environmental variables, RDA performs better than PCA on identifying adaptive variation when selection gradients are weakly correlated with population structure. Additionally, we show that RDA is efficient to identify the main selective gradients among a set of environmental variables. Finally, to give a concrete illustration of RDA in population genomics, we apply this method to the detection of outliers and selective gradients on a SNP data set of Populus trichocarpa in North America (Geraldes et al, 2013). RDA-based approach identifies the main selective gradient that corresponds to a temperature gradient contrasting southern and coastal populations to northern and continental populations in North Western American coast.