Multivariate Phylogenetic Comparative Methods: Evaluations, Comparisons, and Recommendations.

Area of Science:

• Evolutionary Biology
• Phylogenetics
• Quantitative Genetics

Background:

• Phylogenetic comparative analyses of multivariate data are increasingly used.
• Existing methods have not been thoroughly evaluated for their mathematical properties and limitations.

Purpose of the Study:

• To review mathematical requirements for multivariate phylogenetic methods.
• To evaluate existing methods against these requirements.
• To identify robust approaches for analyzing macroevolutionary patterns in multivariate data.

Main Methods:

• Mathematical property review of multivariate methods.
• Evaluation of full multivariate likelihood methods.
• Assessment of methods summarizing trait dimensions separately (e.g., SURFACE).
• Analysis of pairwise composite likelihood methods.
• Examination of algebraic generalizations using covariance matrix traces.

Main Results:

• Full likelihood methods are limited by trait dimensionality and model complexity.
• Methods assuming trait independence (e.g., SURFACE) show high misspecification.
• Pairwise composite likelihood methods are sensitive to data orientation and trait covariation.
• Algebraic generalizations demonstrate robustness to trait covariation, dimensionality, and data orientation.
• Permutation tests with algebraic generalizations yield acceptable statistical power and Type I error rates.

Conclusions:

• Full likelihood and pairwise composite likelihood methods, as well as methods assuming trait independence, should be avoided for multivariate phylogenetic comparative analyses.
• Algebraic generalizations of phylogenetic comparative methods are recommended for assessing macroevolutionary patterns in multivariate data.
• Future research should focus on developing highly multivariate Ornstein-Uhlenbeck models and model comparison approaches.