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An important problem in evolutionary genomics is to investigate whether acertain trait measured on each sample is associated with the samplephylogenetic tree. The phylogenetic tree represents the shared evolutionaryhistory of the samples and it is usually estimated from molecular sequence dataat a locus or from other type of genetic data. We propose a model for traitevolution inspired by the Chinese Restaurant Process that includes a parameterthat controls the degree of preferential attachment, that is, the tendency ofnodes in the tree to subtend from nodes of the same type. This model with nopreferential attachment is equivalent to a structured coalescent model withsimultaneous migration and coalescence events and serves as a null model. Wederive a test for phylogenetic binary trait association with linearcomputational complexity and empirically demonstrate that it is more powerfulthan some other methods. We apply our test to study the phylogeneticassociation of some traits in swordtail fish, breast cancer, yellow fever virusand influenza A H1N1 virus. R package implementation of our methods isavailable at $\texttt{https://github.com/jyzhang27/CRPTree}$.

CRP-Tree: A phylogenetic association test for binary traits