Correspondence between Interlandmark Distances and Caliper Measurements

Abstract

Differences between distances measured with calipers and corresponding distances calculated from two-dimensional (2D) or three-dimensional (3D) coordinates were studied in a sample of 39 skulls of Mustela erminea and M frenata. The caliper data set consisted of 12 length and width measurements. Coordinate data were obtained with a Polhemus 3D system and included 12 landmarks on the dorsal side of the skull and 10 on the ventral side. Distances between pairs of coordinate points were always shorter than corresponding distances taken with calipers; differences between data sets were highly significant in most cases. As expected, distances calculated from 3D landmarks were always closer to caliper values than were distances obtained from 2D points. Average root mean square error obtained from a regression of coordinate-based distances on caliper measurements was 0.422 mm (3.2% incongruence) for the whole set of 12 variables. The coefficient of variation was much larger for interlandmark distances than it was for corresponding caliper data. When differences between species were tested, analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA) F values were larger for caliper than coordinate-based distances. Mahalanobis D ² distances between the two species were smaller for coordinate data sets, and the coefficients of the canonical variate separating skulls of the two species were also different in caliper compared with 2D and 3D data sets. Analysis of displacement along the x-, y- and z- coordinates of each landmark confirm the existence of variation overlooked by caliper measurements. Thus, although traditional measurements can be used to describe differences between these two closely related species, the caliper traits provide a deficient, sometimes misleading, description of the variability. Finally, differences between coordinate and caliper data sets, and the precision of caliper measurement estimation from coordinates, varies from one character to another. This compromises the utility of simple models that are designed to exchange results from one data set to another.