Statistical Models in Morphometric: Are They Realistic? Syst

Abstract.—This analysis considers the validity of the assumptions of the Gaussian perturbation model as applied to landmark data collected for morphometric analyses. The primary conclusion is that the assumption of homoscedasticity is unrealistic when applied to biological data sets. We also point out some important difficulties associated with alternate models. [Perturbation models; models for linear distances.] Morphometrics is the quantitative anal-ysis of size and shape. Recent years are marked by the development of new statis-tical methods and models for the study of size, shape and also shape differences be-tween populations of forms (e.g., Book-stein et al. 1985, Bookstein 1986, 1989a, b, and references therein; Goodall and Bose, 1987). We focus here on methods used to analyze landmark data. A statistical model that is commonly used in the development of statistical procedures is the Gaussion perturbation model. A basic assumption of this model as proposed by Bookstein (1984) is that variability around each landmark is constant throughout the object. The purpose of this paper is to examine this assumption using actual data sets col-lected for morphometric analyses. Our conclusion is that real data sets do not nec-essarily concur with the assumption of constant variability local to landmarks. We also point out difficulties associated with some alternate models suggested in the lit-erature. Our results underscore the need for developing models which are more flexible, and consequently more realistic. Though technical in nature, we feel the conclusions of this paper are important for biologists and scientists who use these models for morphometric analysis