Abstract
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.