Exploring Factor Analysis for Dimension Reduction in the Context of Traits on a Phylogenetic Tree

• Activity Number: 450
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 3:05 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Max Tolkoff* and Marc A. Suchard
• Companies: and UCLA
• Keywords: Factor Analysis ; Phylogenetics

Abstract

Frequently in evolutionary biology we are interested in how different quantitative traits of an organism evolve together over time, especially when adjusting for shared evolutionary history. Previous methods rely on modeling quantitative traits as undergoing a high dimensional, correlated Brownian diffusion down a phylogenetic tree. In order to improve the scalability of these models, we develop a phylogenetic factor analysis model on these quantitative traits assuming that the relatively low dimensional factors, rather than the traits themselves, undergo independent Brownian diffusion down a phylogenetic tree. We apply this method to real world problems in columbine flowers development, rat morphometry, and reproduction patterns of fish of the family Poeciliidae. For the flowers we efficiently infer evolution patterns that are consistent with previous research, but with less posterior uncertainty. For the gerbil morphometry problem with hundreds of quantitative traits, we successfully recover low-dimesnional evolutionary patterns in this small n, large p setting as well as simultaneously, with the help of DNA sequence data, draw inference on the phylogenetic tree itself.