Euclidean distance matrix analysis: a coordinate-free approach for comparing biological shapes using landmark data.

For problems of classification and comparison in biological research, the primary focus is on the similarity of forms. A biological form can be conveniently defined as consisting of size and shape. Several approaches for comparing biological shapes using landmark data are available. Lele (1991a) critically discusses these approaches and proposes a new method based on the Euclidean distance matrix representation of the form of an object. The purpose of this paper is to extend this new methodology to the comparison of groups of objects. We develop the statistical versions of various concepts introduced by Lele (1991a) and use them for developing statistical procedures for testing the hypothesis of shape difference between biological forms. We illustrate the use of this method by studying morphological differences between normal children and those affected with Crouzon and Apert syndromes and craniofacial sexual dimorphism in Cebus apella.     

Cranial growth in the squirrel monkey (Saimiri sciureus): a quantitative analysis using three dimensional coordinate data.

Improvements in data gathering technology have made it possible to quickly and accurately digitize large numbers of objects. The three dimensional coordinates of 44 homologous landmarks were obtained from a sample of 104 squirrel monkey (Saimiri sciureus) crania. After sorting by sex, the crania were assigned to one of four dental age groups. Two quantitative methods, Euclidean distance matrix analysis (EDMA) and finite element scaling analysis (FESA), were used to study craniofacial form change during growth within each sex. Form differences between the sexes at each developmental age were also examined. Both sexes show a small amount of cranial growth overall; however, there are areas of substantial local growth. These areas include the anterior neurocranium and basicranium, the basioccipital, and the anterior palate. Sexual dimorphism in the craniofacial complex is minimal. The most dimorphic regions are the orbitonasal portion of the lower face, the cranial base, and the palate.     

On the risks of using dendrograms to measure functional diversity and multidimensional spaces to measure phylogenetic diversity: a comment on Sobral et al. (2016)

Sobral et al. (Ecology Letters, 19, 2016, 1091) reported that the loss of bird functional and phylogenetic diversity due to species extinctions was not compensated by exotic species introductions. Here, we demonstrate that the reported changes in biodiversity were underestimated because of methodological pitfalls.