TESTING FOR DEVELOPMENTAL CONSTRAINTS: CARPAL FUSIONS IN URODELES.

Abstract

By definition a developmental constraint is a bias on the production of phenotypic variation caused by the action of developmental processes (Maynard Smith et al., 1985). While there have been many philosophical speculations about the nature of the underlying phenomena and about the impact of developmental constraints on evolution, attempts to measure these biases have been extremely rare. Gould (1989) succeeded in showing an actual constraint at work with his analysis of variation in land snails of the genus Cerion. A sharp transition between juvenile button-like growth and later dome-like growth acts in concert with a-probably ecological -constraint on final size, to produce an allometric transition from very flat shells, where the period of juvenile growth is prolonged relative to the period of dome-like growth, to very high shells, where the conditions are reversed. Gould termed this interplay between ecological restrictions, which set up the dimensions of the frame (size of the adult shell) and variations in the size of pieces (whorls), the jigsawconstraint. Because the growth of a shell is a smooth and continuous process, even if there is a succession of different modes of growth, conventional multivariate statistics can be applied fairly easily. However, heterochrony and differential growth are not the only important evolutionary events: qualitative differences and discontinuous jumps are clearly important (Alberch, 1982; Oster and Alberch, 1983). The analysis of phenomena showing discontinuous jumps usually results in data on the frequencies of different varieties. This would make the chi-square test or other related tests (cf. Sokal and Rohlf, 1981; Chap. 17) natural candidates for statistical evaluation of different developmental hypotheses. Unfortunately developmental hypotheses are just qualitative predictions and not sufficiently accurate to stand quantitative analysis. Most often we wish to determine whether a developmental hypothesis is better than the null hypothesis in which varieties are equally distributed. Hence, a test that provides an index of similarity between developmental hypothesis and empirical data and checks against the null hypothesis discussed above is the most desirable tool for analysis. Mantel's test of quadratic assignment offers these desirable properties (Mantel, 1967): first an index of similarity between two vectors or matrices (say A and B) is calculated (usually the Pearson product-moment correlation coefficient).