Identifying Heritable Communities of Microbiome by Root-Unifrac and Wishart Distribution
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We introduce a method to identify heritable microbiome communities when the input is a pairwise dissimilarity matrix among all samples. Current methods target each taxon individually and are unable to take advantage of their phylogenetic relationships. In contrast, our approach focuses on community heritability by using the root-Unifrac to summarize the microbiome samples through their pairwise dissimilarities while taking the phylogeny into account. The resulting dissimilarity matrix is then transformed into an outer product matrix and further modeled through a Wishart distribution with the same set of variance components as in the univariate model. Directly modeling the entire dissimilarity matrix allows us to bypass any dimension reduction steps. An important contribution of our work is to prove the positive definiteness of such outer product matrix, hence the applicability of the Wishart distribution. Simulation shows that this community heritability approach has higher power than existing methods to identify heritable groups of taxa. Empirical results on the TwinsUK dataset are also provided.
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