Landmark morphometrics and the analysis of variation

This chapter discusses the standard approaches that have been used to estimate variation in landmark data and explains why these methods do not properly estimate variation in biological forms. Though some of these approaches have become rather mathematically involved, their suitability to the realities of biological data has not improved in parallel. The chapter presents a generalized model for variation in landmark data. It has been shown that only certain features of this model can be consistently estimated. This model and the estimators are used in morphometric analysis as the basis for parametric bootstrapping procedures to test for differences in form using landmark data. Recognizing the limitation of the ability to estimate only certain features of this general model of variation, it discusses the need for the development of less general models that may reasonably characterize variation in landmark data. The chapter shows how biological knowledge pertaining to the organisms under study can be used to impose certain constraints on the models of variance-covariance structure. It suggests ways to integrate such constraints into the proposal of several less generalized models, some statistically convenient but biologically improbable, others less streamlined statistically but more biologically reasonable.