Sample size and sampling error in geometric morphometric studies of size and shape

Geometric morphometric studies are increasingly becoming common in systematics and palaeontology. The samples in such studies are often small, due to the paucity of material available for analysis. However, very few studies have tried to assess the impact of sampling error on analytical results. Here, this issue is addressed empirically using repeated randomized selection experiments to build progressively smaller samples from an original dataset of similar to 400 vervet monkey (Cercopithecus aethiops) skulls. Size and shape parameters (including mean size and shape, size and shape variances, angles of allometric trajectories) that are commonly used in geometric morphometric studies, are estimated first in the original sample and then in the random subsamples. Estimates are then compared to give an indication of what is the minimum desirable sample size for each parameter. Mean size, standard deviation of size and variance of shape are found to be fairly accurate even in relatively small samples. In contrast, mean shapes and angles between static allometric trajectories are strongly affected by sampling error. If confirmed in other groups, our findings may have substantial implications for studies of morphological variation in present and fossil species. By performing rarefaction analyses like those presented in our study, morphometricians can be easily provided with important clues on how a simple but crucial factor like sample size can alter results of their studies.