A Comparison of Semilandmarking Approaches in the Analysis of Size and Shape

Landmarks are commonly used to investigate how objects vary in form. However, many objects present few identifiable landmarks. To remedy this, several approaches have been developed to densely match points between surfaces lacking readily identifiable landmarks. These matched points are termed semilandmarks. The investigator has to make choices about which approach to use and the eventual locations and density of semilandmarks. In studies of growth or evolution of biological material, landmarks represent points that, from prior knowledge, are equivalent in each individual at each stage of developmental or evolutionary transformation. Their differences in relative location over time describe the transformation. However, semilandmarks are located on specimens using algorithms that do not pay regard to development or evolution, and so the consequences of using semilandmarks on resulting analyses of developmental or evolutionary differences in form are unclear. In this study, we compare results among analyses based on landmarks and semilandmarks with each other and with analyses based only on landmarks. We find that while there is some consistency among findings from different semilandmarking approaches, there are also some differences, and that results from such analyses should be considered as approximations of reality that require cautious interpretation.Often, few landmarks can be reliably identified in analyses of form variation and covariation. Thus, 'semilandmarking' algorithms have increasingly been applied to surfaces and curves. However, the locations of semilandmarks depend on the investigator's choice of algorithm and their density. In consequence, to the extent that different semilandmarking approaches and densities result in different locations of semilandmarks, they can be expected to yield different results concerning patterns of variation and co-variation. The extent of such differences due to methodology is, as yet, unclear and often ignored. In this study, the performance of three landmark-driven semilandmarking approaches is assessed, using two different surface mesh datasets (ape crania and human heads) with different degrees of variation and complexity, by comparing the results of morphometric analyses. These approaches produce different semilandmark locations, which, in turn, lead to differences in statistical results, although the non-rigid semilandmarking approaches are consistent. Morphometric analyses using semilandmarks must be interpreted with due caution, recognising that error is inevitable and that results are approximations. Further work is needed to investigate the effects of using different landmark and semilandmark templates and to understand the limitations and advantages of different semilandmarking approaches.