Quantitative genetics of geometric shape: heritability and the pitfalls of the univariate approach.

There is considerable interest in the evolution of morphological traits, and morphometric studies in combination with the multivariate theory of quantitative genetics can provide a detailed understanding of the variation and evolutionary potential of these traits. For both morphometrics and quantitative genetics, new and improved techniques have been established recently (e.g., Dryden and Mardia 1998; Lynch and Walsh 1998). The combination of these two approaches makes it possible to study genetic variation with explicit reference to the geometry of the structure under investigation and to interpret the results in their anatomical context. Examples include studies using classical quantitative genetic designs (e.g., Arnqvist and Thornhill 1998; Currie et al. 2000; Klingenberg and Leamy 2001) and analyses of quantitative trait loci (Zimmerman et al. 2000; Klingenberg et al. 2001; Workman et al. 2002). In a recent paper, Monteiro et al. (2002) proposed a univariate estimate of heritability for shape based on Procrustes distance, a measure of the extent of difference between pairs of landmark configurations. The method extracts a univariate heritability estimate from the inherently multidimensional shape data by assuming the model of isotropic variation (Goodall 1991), which presumes that there is an equal amount of nondirectional variation at each landmark and that the landmarks are independent of one another. Monteiro et al. (2002, pp. 565, 569) suggest that this univariate heritability estimate can be used to assess whether the relative amount of genetic versus phenotypic variation differs among populations in space and time, and to examine whether nonexisting shapes should be explained by selection or developmental constraints. They illustrate their method with a case study of shape variation in honeybee wings. The assumptions of the isotropic model, on which the method of Monteiro et al. (2002) is based, are often unrealistic—even in the authors’ own dataset. Moreover, these assumptions also have strong implications for the comparison of shape variation among populations and for the study of genetic constraints. Another difficulty is that the experimental design of the case study of Monteiro et al. (2002) is not large enough to characterize the genetic variation in