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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 2018-01-01, Vol.67 (1), p.14-31
Main Author: Adams, Dean C
Other Authors: Collyer, Michael L
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: England: Oxford University Press
ID: ISSN: 1063-5157
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
format: Article
creator:
  • Adams, Dean C
  • Collyer, Michael L
subjects:
  • Comparative analysis
  • Data processing
  • Datasets
  • Evolution
  • Mathematical models
  • Mathematics
  • Matrix
  • Multivariate analysis
  • Phylogenetics
  • Phylogeny
  • Principal components analysis
  • REGULAR ARTICLES
  • Statistics
ispartof: Systematic biology, 2018-01-01, Vol.67 (1), p.14-31
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 ill-conditioned 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.
language: eng
source:
identifier: ISSN: 1063-5157
fulltext: no_fulltext
issn:
  • 1063-5157
  • 1076-836X
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descriptionRecent 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 ill-conditioned 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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subjectComparative analysis ; Data processing ; Datasets ; Evolution ; Mathematical models ; Mathematics ; Matrix ; Multivariate analysis ; Phylogenetics ; Phylogeny ; Principal components analysis ; REGULAR ARTICLES ; Statistics
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1The Author(s) 2017. Published by Oxford University Press on behalf of the Systematic Biology. All rights reserved. For Permissions, please email: journals.permissions@oup.com 2017
2The Author(s) 2017. Published by Oxford University Press on behalf of the Systematic Biology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
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abstractRecent 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 ill-conditioned 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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