Sparse precision matrix estimation in phenotypic trait evolution models

Phylogenetic trait evolution models allow for the estimation of evolutionary correlations between a set of traits observed in a sample of related organisms. By directly modeling the evolution of the traits on a phylogenetic tree in a Bayesian framework, the model's structure allows us to control for shared evolutionary history. In these models, relevant correlations are assessed through a post-process procedure based on the high posterior density interval of marginal correlations. However, the selected correlations alone may not provide all available information regarding trait relationships. Their association structure, in contrast, is likely to express some sparsity pattern and provide straightforward information about direct associations between traits. In order to employ a model-based method to identify this association structure we explore the use of Gaussian graphical models (GGM) for covariance selection. We model the precision matrix with a G-Wishart conjugate prior, which results in sparse precision estimates. We evaluate our approach through Monte Carlo simulations and applications that examine the association structure and evolutionary correlations of phenotypic traits in Darwin's finches and genomic and phenotypic traits in prokaryotes. Our approach provides accurate graph estimates and lower errors for the precision and correlation parameter estimates, especially for conditionally independent traits, which are the target for sparsity in GGMs.