Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations

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Collyer, Michael
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Ecology, Evolution and Organismal Biology

The Department of Ecology, Evolution, and Organismal Biology seeks to teach the studies of ecology (organisms and their environment), evolutionary theory (the origin and interrelationships of organisms), and organismal biology (the structure, function, and biodiversity of organisms). In doing this, it offers several majors which are codirected with other departments, including biology, genetics, and environmental sciences.

The Department of Ecology, Evolution, and Organismal Biology was founded in 2003 as a merger of the Department of Botany, the Department of Microbiology, and the Department of Zoology and Genetics.

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As leaders in statistical research, collaboration, and education, the Department of Statistics at Iowa State University offers students an education like no other. We are committed to our mission of developing and applying statistical methods, and proud of our award-winning students and faculty.
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Recent years have seen increased interest in phylogenetic comparative analyses of multivariate datasets, 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 dataset, 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 datasets with few traits and many species. Methods that summarize patterns across trait dimensions treated separately (e.g., SURFACE) 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 dataset, and the number of trait dimensions. The consequences of these debilitating deficiencies is 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 dataset. 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, while 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.


This is a pre-copyedited, author-produced version of an article accepted for publication in Systematic Biology following peer review. The version of record, Dean C. Adams, Michael L. Collyer; Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations, Systematic Biology, Volume 67, Issue 1, January 2018, Pages 14–31 is available online at: doi: 10.1093/sysbio/syx055. Posted with permission.

Sun Jan 01 00:00:00 UTC 2017