The increasing availability of multidimensional phenotypic data in large cohorts of genotyped individuals requires efficient methods to identify genetic effects on multiple traits. Permutational multivariate analysis of variance (PERMANOVA) offers a powerful non-parametric approach. However, it relies on permutations to assess significance, which hinders the analysis of large datasets. Here, we derive the limiting null distribution of the PERMANOVA test statistic, providing a framework for the fast computation of asymptotic p values. Our asymptotic test presents controlled type I error and high power, often outperforming parametric approaches. We illustrate its applicability in the context of QTL mapping and GWAS.
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