Comparing G: multivariate analysis of genetic variation in multiple populations |
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Authors: | J D Aguirre E Hine K McGuigan M W Blows |
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Institution: | 1.School of Biological Sciences, The University
of Queensland, Brisbane, Australia |
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Abstract: | The additive genetic variance–covariance matrix (G) summarizes the
multivariate genetic relationships among a set of traits. The geometry of G
describes the distribution of multivariate genetic variance, and generates genetic
constraints that bias the direction of evolution. Determining if and how the multivariate
genetic variance evolves has been limited by a number of analytical challenges in
comparing G-matrices. Current methods for the comparison of G typically share
several drawbacks: metrics that lack a direct relationship to evolutionary theory, the
inability to be applied in conjunction with complex experimental designs, difficulties
with determining statistical confidence in inferred differences and an inherently
pair-wise focus. Here, we present a cohesive and general analytical framework for the
comparative analysis of G that addresses these issues, and that incorporates and
extends current methods with a strong geometrical basis. We describe the application of
random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the
decomposition of the multivariate breeders equation, all within a Bayesian framework. We
illustrate these methods using data from an artificial selection experiment on eight
traits in Drosophila serrata, where a multi-generational pedigree was available
to estimate G in each of six populations. One method, the tensor, elegantly
captures all of the variation in genetic variance among populations, and allows the
identification of the trait combinations that differ most in genetic variance. The tensor
approach is likely to be the most generally applicable method to the comparison of
G-matrices from any sampling or experimental design. |
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Keywords: | genetic variance G-matrix tensor Bayesian MCMC |
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