Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations
Recent years have seen increased interest in phylogenetic comparative analyses of multivariate data sets, but to date the varied proposed approaches have not been extensively examined. Here we review the mathematical properties required of any multivariate method, and specifically evaluate existing... Full description
Journal Title:  Systematic biology 20180101, Vol.67 (1), p.1431 
Main Author:  Adams, Dean C 
Other Authors:  Collyer, Michael L 
Format:  Electronic Article 
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English 
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Publisher:  England: Oxford University Press 
ID:  ISSN: 10635157 
Link:  https://www.ncbi.nlm.nih.gov/pubmed/28633306 
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recordid:  cdi_proquest_miscellaneous_1912195661 
title:  Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations 
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ispartof:  Systematic biology, 20180101, Vol.67 (1), p.1431 
description:  Recent years have seen increased interest in phylogenetic comparative analyses of multivariate data sets, but to date the varied proposed approaches have not been extensively examined. Here we review the mathematical properties required of any multivariate method, and specifically evaluate existing multivariate phylogenetic comparative methods in this context. Phylogenetic comparative methods based on the full multivariate likelihood are robust to levels of covariation among trait dimensions and are insensitive to the orientation of the data set, but display increasing model misspecification as the number of trait dimensions increases. This is because the expected evolutionary covariance matrix (V) used in the likelihood calculations becomes more illconditioned as trait dimensionality increases, and as evolutionary models become more complex. Thus, these approaches are only appropriate for data sets with few traits and many species. Methods that summarize patterns across trait dimensions treated separately (e.g., ) incorrectly assume independence among trait dimensions, resulting in nearly a 100% model misspecification rate. Methods using pairwise composite likelihood are highly sensitive to levels of trait covariation, the orientation of the data set, and the number of trait dimensions. The consequences of these debilitating deficiencies are that a user can arrive at differing statistical conclusions, and therefore biological inferences, simply from a dataspace rotation, like principal component analysis. By contrast, algebraic generalizations of the standard phylogenetic comparative toolkit that use the trace of covariance matrices are insensitive to levels of trait covariation, the number of trait dimensions, and the orientation of the data set. Further, when appropriate permutation tests are used, these approaches display acceptable Type I error and statistical power. We conclude that methods summarizing information across trait dimensions, as well as pairwise composite likelihood methods should be avoided, whereas algebraic generalizations of the phylogenetic comparative toolkit provide a useful means of assessing macroevolutionary patterns in multivariate data. Finally, we discuss areas in which multivariate phylogenetic comparative methods are still in need of future development; namely highly multivariate Ornstein–Uhlenbeck models and approaches for multivariate evolutionary model comparisons. 
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identifier:  ISSN: 10635157 
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