Genetic variance–covariance matrices: a critique of the evolutionary quantitative genetics research program

This paper outlines a critique of the use of the genetic variance–covariance matrix (G), one of the central concepts in the modern study of natural selection and evolution. Specifically, I argue that for both conceptual and empirical reasons, studies of G cannot be used to elucidate so-called constraints on natural selection, nor can they be employed to detect or to measure past selection in natural populations – contrary to what assumed by most practicing biologists. I suggest that the search for a general solution to the difficult problem of identifying causal structures given observed correlation’s has led evolutionary quantitative geneticists to substitute statistical modeling for the more difficult, but much more valuable, job of teasing apart the many possible causes underlying the action of natural selection. Hence, the entire evolutionary quantitative genetics research program may be in need of a fundamental reconsideration of its goals and how they correspond to the array of mathematical and experimental techniques normally employed by its practitioners. Introduction: the emergence of a new field? Very little philosophy of biology has yet been focused on evolutionary quantitative genetics, despite the fact that the field has seen a renaissance during the past decade, with several new textbooks (e.g., Falconer and Mackay 1996; Roff 1997; Pigliucci and Preston 2004) and a plethora of empirical papers in major biological journals such as Evolution, Genetics, Journal of Evolutionary Biology, etc. One concept in particular has emerged as crucial for the quantitative genetic study of complex (multivariate) phenotypes: the so-called genetic variance–covariance matrix, G. This is thought of and calculated as an actual matrix summarizing the genetic portion of the phenotypic variance of a series of morphological, life history, or behavioral characteristics, as well as all possible pairwise (genetic) covariances between said characteristics (Figure 1). The basic idea is that G describes the degree to which the ‘genetic architecture’ (i.e., how traits are genetically connected to each other) determines the response of a population to natural selection. Suppose, for example, that there happens to be a positive genetic covariance between phenotypic traits X and Y (Figure 2a). Theory (and intuition) then predict that, other things being equal, if selection favors, say, an increase in trait X, trait Y will also be ‘lifted’ upwards as an indirect result of its covariance (or correlation, which is a Biology and Philosophy (2006) 21:1–23 Springer 2006 DOI 10.1007/s10539-005-0399-z