The G-Matrix as One Piece of the Phenotypic Evolution Puzzle

In quantitative genetics, a single term, the genetic covariance matrix (G-matrix), is used to encompass all important associations between traits, whether due to pleiotropy or gametic disequilibrium. As noted by Polly (2008) some quantitative geneticists have argued that the G-matrix is a sufficient descriptor of the ways in which underlying development influences phenotypic evolution, while many other researchers find these models unsatisfactory. To see why G-matrix models are sufficient sometimes, but not always, we need to look to a more general formulation, phenotype landscape theory, of which quantitative genetics is one special case. A phenotype landscape is a plot of some trait as a function of a set of underlying genetic or environmental factors. Such landscapes have recently started to be constructed for particular traits, either through the synthesis of detailed developmental studies (Nijhout et al. 2006) or through Quantitative Trait Locus analysis (Rice 2008). Evolution on the landscape is described by a set of vectors, termed Q vectors, each of which corresponds to a different set of interactions between the underlying factors or a different property of the shape of the distribution of underlying variation. There are potentially a very large number of Q vectors, and an exact description of how a population evolves over a phenotype landscape requires specifying all of them. One of these vectors, Q1, describes the effects of directional selection on an uncurved landscape in terms of only the variances and covariances of the distribution of underlying genetic variation. Q1 is thus essentially the same as the G-matrix model. The fact that the G-matrix is only one of many terms that jointly describe phenotypic evolution raises the question of why it is ever useful by itself. The answer is