Measuring Evolutionary Constraints Through the Dimensionality of the Phenotype: Adjusted Bootstrap Method to Estimate Rank of Phenotypic Covariance Matrices |
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Authors: | Mihaela Pavlicev Günter P Wagner James M Cheverud |
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Institution: | (1) Department of Anatomy and Neurobiology, Washington University, St. Louis, MO 63110, USA;(2) Department of Ecology and Evolution, Yale University, New Haven, CT, USA;(3) Present address: CEES, Department of Biology, University of Oslo, Blindern, P.O. Box 1066, Oslo, Norway |
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Abstract: | The potential and direction of phenotypic evolution is constrained by the distribution of genetic variation for the traits
as described by the phenotypic (P) and genetic covariance matrices (G). The rank of the covariance matrix reflects the number of independent variational dimensions of the phenotype. Covariance
matrices with less than full rank indicate lack of variation in some directions of the phenotype space and thus are an indication
of absolute evolutionary constraints. Because selection acts upon phenotypic variation, the rank of P represents the upper limit of the dimensionality in G, relevant for selection response. The limitations of current methods to estimate matrix rank motivated us to analyze and
adjust a bootstrap method and evaluate its performance by simulation. The results show that the modified bootstrap method
(ABRE) gives reliable and rather conservative rank estimates when the sample size is sufficient for the number of variables
studied (the sample size is at least five-fold the number of variables). Applying the method to various datasets suggests
high phenotypic dimensionality in all cases. The analysis thus provides no evidence for absolute evolutionary constraints.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. |
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Keywords: | Evolutionary constraint Phenotypic evolution Dimensionality Morphological integration Evolvability |
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