QUANTITATIVE GENETICS OF DEVELOPMENT: GENETIC CORRELATIONS AMONG AGE-SPECIFIC TRAIT VALUES AND THE EVOLUTION OF ONTOGENY.

Abstract

It has recently been re-emphasized, by Gould (1977) and others, that evolution of adult forms takes place through the evolution of ontogenies. Direct selection at any age results in a correlated response at all other life history stages. This selection alters growth curves, or causes the evolution of ontogeny. Lande (1982) has presented a quantitative genetic model for the evolution of ontogenetically varying traits which clearly defines the parameters required for an analysis of ontogeny and evolution: (1) the genetic variance/covariance matrix; (2) the phentoypic variance/ covariance matrix; and (3) the vector of selection differentials. Genetic covariances or correlations among age-specific trait values quantitatively describe the genetic link between expressions of the same trait at different points in ontogeny. These genetic links between age-specific trait values are the result of pleiotropy, in this case the effects of one gene on the phenotype as expressed at more than one age, and linkage disequilibrium. The general effects of genetic variation on growth curves may be summarized using two parameters, curve height and curve shape (see Fig. 1). The average height of the curve can be defined as the average value of a trait over the ontogenetic period under consideration or the area under the growth curve divided by the length of the growth period. When there are only height differences between two growthi curves, the two curves will be parallel. Differences in curve shape, or the rate of growth at all ages, can be quantified independent of height, by standardizing the curves so that they have the same average height, or enclose the same area, and then calculating the absolute value of the area remaining between curves and dividing by the length of the growth period (see Fig. 1). This curve shape measure does not specify particular shapes but rather gives a general measure of differences in growth rates to compare with the independent measure of curve height differences. Specific curve shapes are presented without summarization. When heritabilities and phenotypic variances are the same at all ages, one can discern the independent effects of genetic correlations among age-specific trait values on ontogenetic variation and evolution. For example, in Figure 2 the ancestral ontogeny is displayed as a horizontal line (A) for purposes of illustration. Selection on the adult, or any other age, when the genetic correlations between ages are all 1.000, results in the descendant ontogeny, curve B. Note that the average height of the curve has changed but not its shape. When all the genetic correlations are one, the spectral decomposition of the age-specific traits correlation matrix includes only one non-zero eigenvalue equal to 'n,' the number of traits represented in the matrix, and an associated isometric eigenvector with loadings of 1/\Vn for each trait. This vector measures variation in growth curve height independent of variation in curve shape. Any deviation of the correlations