  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.
