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A tale of two matrices: multivariate approaches in evolutionary biology
Author(s) -
BLOWS M. W.
Publication year - 2007
Publication title -
journal of evolutionary biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 128
eISSN - 1420-9101
pISSN - 1010-061X
DOI - 10.1111/j.1420-9101.2006.01164.x
Subject(s) - biology , selection (genetic algorithm) , univariate , multivariate statistics , bivariate analysis , evolutionary biology , quantitative genetics , multivariate analysis , variance (accounting) , covariance , covariance matrix , statistics , genetic variation , mathematics , genetics , computer science , machine learning , accounting , gene , business
Two symmetric matrices underlie our understanding of microevolutionary change. The first is the matrix of nonlinear selection gradients ( γ ) which describes the individual fitness surface. The second is the genetic variance–covariance matrix ( G ) that influences the multivariate response to selection. A common approach to the empirical analysis of these matrices is the element‐by‐element testing of significance, and subsequent biological interpretation of pattern based on these univariate and bivariate parameters. Here, I show why this approach is likely to misrepresent the genetic basis of quantitative traits, and the selection acting on them in many cases. Diagonalization of square matrices is a fundamental aspect of many of the multivariate statistical techniques used by biologists. Applying this, and other related approaches, to the analysis of the structure of γ and G matrices, gives greater insight into the form and strength of nonlinear selection, and the availability of genetic variance for multiple traits.