Multivariate analyses such as principal component analysis were among the first statistical methods employed to extract information from genetic markers. From their early applications to current innovations, these approaches have proven to be efficient for the analysis of the genetic variability in various contexts such as human genetics, conservation and adaptation studies. However, because multivariate analysis is a wide and diversified area of statistics, choosing a method appropriate to both the data and to the question being asked can be difficult. Moreover, some particularities of genetic markers need to be taken into account when using multivariate methods. As a consequence, multivariate analyses are often used as black boxes, which results in frequent mistakes in the literature. In this review, we provide a critical analysis of the application of multivariate methods to genetic markers, using a general framework that unifies all these methods for the sake of clarity. First, we focus on some common mistakes in these applications and ways to avoid these pitfalls. We then detail the most critical particularities of allele frequencies that demand adaptations of multivariate methods, and we propose solutions to the subsequent problems. Finally, we tackle several questions of interest in which multivariate analysis has a great role to play, such as the study of the typological coherence of different genetic markers, or the investigation of spatial genetic patterns.
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