Phylogenetic factor analysis

Phylogenetic comparative methods explore the relationships between quantitative traits adjusting for shared evolutionary history. This adjustment often occurs through a Brownian diffusion process along the branches of the phylogeny that generates model residuals or the traits themselves. For high-dimensional traits, inferring all pair-wise correlations within the multivariate diffusion is limiting. To circumvent this problem, we propose phylogenetic factor analysis (PFA) that assumes a small unknown number of independent evolutionary factors arise along the phylogeny and these factors generate clusters of dependent traits. Set in a Bayesian framework, PFA provides measures of uncertainty on the factor number and groupings, combines both continuous and discrete traits, integrates over missing measurements and incorporates phylogenetic uncertainty with the help of molecular sequences. We develop Gibbs samplers based on dynamic programming to estimate the PFA posterior distribution, over t...