The problem of assessing landmark error in geometric morphometrics: theory, methods, and modifications.

Geometric morphometric methods rely on the accurate identification and quantification of landmarks on biological specimens. As in any empirical analysis, the assessment of inter- and intra-observer error is desirable. A review of methods currently being employed to assess measurement error in geometric morphometrics was conducted and three general approaches to the problem were identified. One such approach employs Generalized Procrustes Analysis to superimpose repeatedly digitized landmark configurations, thereby establishing whether repeat measures fall within an acceptable range of variation. The potential problem of this error assessment method (the "Pinocchio effect") is demonstrated and its effect on error studies discussed. An alternative approach involves employing Euclidean distances between the configuration centroid and repeat measures of a landmark to assess the relative repeatability of individual landmarks. This method is also potentially problematic as the inherent geometric properties of the specimen can result in misleading estimates of measurement error. A third approach involved the repeated digitization of landmarks with the specimen held in a constant orientation to assess individual landmark precision. This latter approach is an ideal method for assessing individual landmark precision, but is restrictive in that it does not allow for the incorporation of instrumentally defined or Type III landmarks. Hence, a revised method for assessing landmark error is proposed and described with the aid of worked empirical examples.