Evolutionary Inference for Function-valued Traits: Gaussian Process Regression on Phylogenies

TL;DR

This paper introduces a flexible Bayesian model combining Gaussian processes with phylogenetic assumptions to analyze function-valued traits, enabling ancestral function prediction and evolutionary rate comparison.

Contribution

It extends Gaussian process regression and phylogenetic models to handle functional data within a Bayesian framework, allowing for nonparametric inference on evolutionary processes.

Findings

Successfully models function-valued traits with phylogenetic correlation

Enables ancestral function prediction and evolutionary rate comparison

Extends existing models to nonparametric Bayesian functional data analysis

Abstract

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical model for such data, by combining assumptions from phylogenetics with Gaussian processes. We describe its use as a nonparametric Bayesian prior distribution, both for prediction (placing posterior distributions on ancestral functions) and model selection (comparing rates of evolution across a phylogeny, or identifying the most likely phylogenies consistent with the observed data). Our work is integrative, extending the popular phylogenetic Brownian Motion and Ornstein-Uhlenbeck models to functional data and Bayesian inference, and extending Gaussian Process regression to phylogenies. We provide a brief illustration of the application of our method.