Differences between sliding semi-landmark methods in geometric morphometrics, with an application to human craniofacial and dental variation

Over the last decade, geometric morphometric methods have been applied increasingly to the study of human form. When too few landmarks are available, outlines can be digitized as series of discrete points. The individual points must be slid along a tangential direction so as to remove tangential variation, because contours should be homologous from subject to subject whereas their individual points need not. This variation can be removed by minimizing either bending energy (BE) or Procrustes distance (D) with respect to a mean reference form. Because these two criteria make different assumptions, it becomes necessary to study how these differences modify the results obtained. We performed bootstrapped-based Goodall's F-test, Foote's measurement, principal component (PC) and discriminant function analyses on human molars and craniometric data to compare the results obtained by the two criteria. Results show that: (1) F-scores and P-values were similar for both criteria; (2) results of Foote's measurement show that both criteria yield different estimates of within- and between-sample variation; (3) there is low correlation between the first PC axes obtained by D and BE; (4) the percentage of correct classification is similar for BE and D, but the ordination of groups along discriminant scores differs between them. The differences between criteria can alter the results when morphological variation in the sample is small, as in the analysis of modern human populations.