Research Article Comparing covariance matrices: random skewers method compared to the common principal components model

By James M. Cheverud, G. Marroig. 2007

140 citations recorded by the source corpus.

Comparisons of covariance patterns are becoming more common as interest in the evolution of relationships between traits and in the evolutionary phenotypic diversification of clades have grown. We present parallel analyses of covariance matrix similarity for cranial traits in 14 New World Monkey genera using the Random Skewers (RS), T-statistics, and Common Principal Components (CPC) approaches. We find that the CPC approach is very powerful in that with adequate sample sizes, it can be used to detect significant differences in matrix structure, even between matrices that are virtually identical in their evolutionary properties, as indicated by the RS results. We suggest that in many instances the assumption that population covariance matrices are identical be rejected out of hand. The more interesting and relevant question is, How similar are two covariance matrices with respect to their predicted evolutionary responses? This issue is addressed by the random skewers method described here.

Subfields: Genetics, Geometry and Topology, Paleontology

View Paper: https://www.semanticscholar.org/paper/a5d2eb15f1de5c4436f69fbf4fbae153552d9865

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In Genetics

In Geometry and Topology

In Paleontology

Citations in the corpus

The Evolution of Modularity in the Mammalian Skull II: Evolutionary Consequences (2009, methodology): “…accomplish this fusion of morphological integration studies with evolutionary quantitative genetics is to use analytical tools suited for V/CV matrices, like the random skewers (RS) approach which is based on the multivariate response to selection equation (Lande 1979; Cheverud and Marroig 2007).”
Integration and Evolvability in Primate Hands and Feet (2009, methodology): “The statistical significance of this index can be evaluated against a null hypothesis of no common orientation between selection and response vectors, by comparing it against the distribution of vector correlations among 10000 pairs of random p-element vectors (Cheverud and Marroig 2007).”
The Evolution of Modularity in the Mammalian Skull I: Morphological Integration Patterns and Magnitudes (2009, methodology): “…and Matrix Repeatability Covariance patterns were compared among mammalian orders using the random skewers method, in which the evolutionary responses of each pair of V/CV matrices to 1,000 random selection vectors (normalized to a length of one) are compared (Cheverud and Marroig 2007).”
Comparing sample bias correction methods for species distribution modeling using virtual species (2021, methodology): “…was assessed with the random skewers method of covariance similarity (Cheverud 1996) in the package phytools (Revell 2012) in R 3.3.2 (R Core Team 2020), by measuring the collinearity between two random selection vectors, each operating on a single covariance matrix (Cheverud and Marroig 2007).”
Measuring and comparing evolvability and constraint in multivariate characters (2008, methodology): “They termed this method random skewers (Cheverud, 1996; Cheverud & Marroig, 2007).”