A tale of two matrices: multivariate approaches in evolutionary biology
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....
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description | 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. |
doi_str_mv | 10.1111/j.1420-9101.2006.01164.x |
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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.</description><subject>Biological Evolution</subject><subject>Data Interpretation, Statistical</subject><subject>genetic constraints</subject><subject>genetic variance‐covariance matrix</subject><subject>Genetic Variation</subject><subject>Multivariate Analysis</subject><subject>nonlinear selection</subject><subject>Quantitative Trait, Heritable</subject><subject>Selection, Genetic</subject><subject>stabilizing selection</subject><issn>1010-061X</issn><issn>1420-9101</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqNkD1PwzAQhi0EolD4C8gTW4LtOG6MxFCqUkCVWEBis5zkAq6cusRJP_49Dq1g5ZY7yc97Pj0IYUpiGupmEVPOSCQpoTEjRMSEUsHj7RE6-304DjOhJCKCvg_QufcLQgKUpqdoQEeMSJmJMzQb41ZbwK7C7cbhWreNKcDf4rqzrVnrxugWsF6tGqeLT_DYLDGsne1a45a62eHcOOs-dhfopNLWw-WhD9Hbw_R18hjNX2ZPk_E8KniW8EhWNOEsYbRkZVlVesTyUaJ5ypNUFiyFTI9kVpS5BAqiTGWAEi24YLrKSR8eouv93nDQVwe-VbXxBVirl-A6r0TGKZOpDGC2B4vGed9ApVaNqcPFihLVS1QL1btSvSvVS1Q_EtU2RK8Of3R5DeVf8GAtAHd7YGMs7P69WD1P7_sp-QaKVIB5</recordid><startdate>200701</startdate><enddate>200701</enddate><creator>BLOWS, M. 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W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4834-9f1342321d2ddffa72b73a454359c25e8a798cdb9e1e6d59ddf3a6462afb09f13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Biological Evolution</topic><topic>Data Interpretation, Statistical</topic><topic>genetic constraints</topic><topic>genetic variance‐covariance matrix</topic><topic>Genetic Variation</topic><topic>Multivariate Analysis</topic><topic>nonlinear selection</topic><topic>Quantitative Trait, Heritable</topic><topic>Selection, Genetic</topic><topic>stabilizing selection</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>BLOWS, M. W.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Journal of evolutionary biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>BLOWS, M. W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A tale of two matrices: multivariate approaches in evolutionary biology</atitle><jtitle>Journal of evolutionary biology</jtitle><addtitle>J Evol Biol</addtitle><date>2007-01</date><risdate>2007</risdate><volume>20</volume><issue>1</issue><spage>1</spage><epage>8</epage><pages>1-8</pages><issn>1010-061X</issn><eissn>1420-9101</eissn><abstract>Two symmetric matrices underlie our understanding of microevolutionary change. 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subjects | Biological Evolution Data Interpretation, Statistical genetic constraints genetic variance‐covariance matrix Genetic Variation Multivariate Analysis nonlinear selection Quantitative Trait, Heritable Selection, Genetic stabilizing selection |
title | A tale of two matrices: multivariate approaches in evolutionary biology |
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