Abstract
Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Given a dataset of function-valued traits generated by evolution, we develop a practical statistical approach to infer ancestral function-valued traits, and estimate the generative evolutionary process. We do this by combining dimension reduction and phylogenetic Gaussian process regression, a nonparametric procedure which explicitly accounts for known phylogenetic relationships. We test the methods' performance on simulated function-valued data generated from a stochastic evolutionary model. The methods are applied assuming that only the phylogeny and the function-valued traits of taxa at its tips are known. Our method is robust and applicable to a wide range of function-valued data, and also offers a phylogenetically aware method for estimating the autocorrelation of function-valued traits.
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