Abstract

It is now well documented that biology needs morphometrics. Morphometrics can provide useful and often unexpected information about development and growth, functional—especially mechanical—adaptation, and evolutionary difference and relationship. Such studies often apply coordinate data from anatomical landmarks. Recently semi-landmarks and sliding landmarks increase information content, especially of apparently featureless regions . Yet, how we landmark our materials limits the results we get and the questions we ask. Here we show different landmarking schemes leading to different equivalences between specimens and different results. Geometric morphometric methods often treat landmarks as points on rubber sheets. Distortions of the sheets are often visualized by techniques like thin plate splines showing changes or differences as stretches or contractions. The statistics of morphometrics can handle these. Further consideration of anatomical landmarks, however, implies that real biologies are sometimes more complex. Sometimes two-dimensional rubber sheets of anatomies contain cusps or holes representing appearances or disappearances of structures. In three dimensions, equivalent rubber blocks may show not only appearances or disappearances but also reversals of positions of structures. Such phenomena are generally ignored in landmarks and analyses. We show that in some cases morphometrics can take account of such matters. But we also suggest that sometimes these modifications from elastic analogues are so complex that new methods may be required for our morphometric packages. It is in this sense that improvement of morphometrics needs deeper understanding of biology