If we take the speculations of Yule presented at the Third International Conference of Genetics (Yule 1906) on the relationship between the biometrical and Mendelian approaches to heredity as the foundations upon which the field of quantitative genetics is based, then we have just passed the 100th birthday of quantitative genetics. On the other hand, the 1918 publication of Fisher might be taken as the real beginnings of quantitative genetics as we know it (for a detailed account of Yule's musings in relation to Fisher's contribution see Tabery 2004), in which case the centenary of quantitative genetics birth is but a few years away. No matter which date we take, the fact remains that quantitative genetics has been around for a long time, during which it has developed with a very large statistical foundation that is still in the process of being tested. Early work focused on the contribution of quantitative genetics to animal and plant breeding but the work of Russell Lande in the 1970s promoted the use of quantitative genetics by those interested in evolutionary biology. A significant difference between the interests of the breeder versus the evolutionary biologist is that whereas the breeder frequently is concerned with the improvement of a single trait (or two traits combined into a single index), the evolutionary biologist is generally faced with addressing the evolution of multiple traits simultaneously. This change in focus has raised issues of methodology and approach that are still being worked out: the purpose of this perspective is to suggest that a singular contribution that quantitative genetics can make to our understanding of organic evolution is in the area of multivariate trait evolution and that the new fields of research in genomics such as QTL and microarray analyses are contributing to, and benefiting from, a quantitative genetic perspective.

The most general form in which quantitative genetics is used in evolutionary biology is given by the equation , where is the change in trait means, **G** is the genetic variance–covariance matrix, **P**^{−1} is the inverse of the phenotypic variance–covariance matrix, and **S** is the vector of selection differentials. An alternate and equivalent formulation of this equation is , where is the response of the *i*th of *n* traits, *h _{j}* is the square root of the heritability of the

*j*th trait,

*r*

_{Aij}is the genetic correlation between traits

*i*and

*j*, and β

_{j}is the selection gradient on the

*j*th trait. I shall refer to these equations as the multivariate breeder's equation. In this perspective I shall highlight five issues that bear upon the present and future contributions of quantitative genetics to our understanding of evolutionary change:

- 1The utility of a quantitative genetic approach to measuring genetic variation: In this section I outline the utility of a quantitative genetic perspective in describing and analyzing genetic variation at two very different levels of resolution, namely genetic variation in natural populations and genetic variation at the level of DNA transcription.
- 2Do the results of QTL analyses support the assumptions of quantitative genetics? As a general descriptor in the two circumstances discussed in section 1, the quantitative genetic parameters may be useful in themselves, but what we really desire is that the approach can actually be used to predict evolutionary change. In this case we need to consider whether the basic assumptions of quantitative genetics are likely to be sufficiently accurate or robust for at least short-term prediction and then whether selection on multiple traits has produced results consistent with the multivariate breeder's equation. To address the question of the number of loci and the distribution of their effects, I use information recently obtained from QTL analyses, at present possibly the premier method for investigating such questions.
- 3What is the importance to quantitative genetics of identifying specific genes? Recently there has been an enormous effort put into elucidating the molecular basis of variation with attention being given to identifying genes of major effect. Given that quantitative genetics focuses upon the totality of genomic expression of a trait as expressed in a statistical description, does such research have any messages for quantitative genetics?
- 4Testing predictions of the multivariate breeder's equation. In the fourth section I consider whether artificial selection on multiple traits or evolutionary changes in wild populations can be reasonably predicted by the multivariate breeder's equation.
- 5The evolution of the phenotypic and genetic variance covariance matrices. Application of the multivariate breeder's equation assumes that the variance–covariance matrices remain constant. In this section I examine this proposition and suggest that the present hypothesis-testing approaches should be replaced by an interval-estimation perspective.