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A METHOD FOR ASSESSING PHYLOGENETIC LEAST SQUARES MODELS FOR SHAPE AND OTHER HIGH‐DIMENSIONAL MULTIVARIATE DATA
Author(s) -
Adams Dean C.
Publication year - 2014
Publication title -
evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.84
H-Index - 199
eISSN - 1558-5646
pISSN - 0014-3820
DOI - 10.1111/evo.12463
Subject(s) - multivariate statistics , phylogenetic tree , phylogenetic comparative methods , biology , context (archaeology) , statistics , trait , statistical power , statistical hypothesis testing , type i and type ii errors , covariance , sample size determination , parametric statistics , regression , generalized least squares , evolutionary biology , mathematics , computer science , genetics , paleontology , estimator , gene , programming language
Studies of evolutionary correlations commonly use phylogenetic regression (i.e., independent contrasts and phylogenetic generalized least squares) to assess trait covariation in a phylogenetic context. However, while this approach is appropriate for evaluating trends in one or a few traits, it is incapable of assessing patterns in highly multivariate data, as the large number of variables relative to sample size prohibits parametric test statistics from being computed. This poses serious limitations for comparative biologists, who must either simplify how they quantify phenotypic traits, or alter the biological hypotheses they wish to examine. In this article, I propose a new statistical procedure for performing ANOVA and regression models in a phylogenetic context that can accommodate high‐dimensional datasets. The approach is derived from the statistical equivalency between parametric methods using covariance matrices and methods based on distance matrices. Using simulations under Brownian motion, I show that the method displays appropriate Type I error rates and statistical power, whereas standard parametric procedures have decreasing power as data dimensionality increases. As such, the new procedure provides a useful means of assessing trait covariation across a set of taxa related by a phylogeny, enabling macroevolutionary biologists to test hypotheses of adaptation, and phenotypic change in high‐dimensional datasets.