The occasional perils of reflection (across the midline; in geometric morphometrics)

Manually collecting landmark data on a large biological sample takes a long time. Several options exist to speed data collection, though each strategy introduces problems or raises concerns of its own. For bilaterally symmetric structures (e.g., crania), some recent papers recommend limiting landmark collection to one side and the midline, then \"mirror-reflecting\" landmarks across the midline to produce an approximation of the true bilateral configuration. However, where the midline is narrow relative to the bilateral anatomy, net midline landmark deviations from the mid-sagittal axis or plane will distort the mirror-reflected configuration. Here, I test whether this is a substantive concern at the scale of real biology. To do so, I simulate small amounts of mediolateral error on the mean shape from a sample of human mandibles (n = 178), then compare the distribution of simulated forms to variation in the data. I also test how faithfully mirror-reflected configurations replicate bilateral shape and size relationships. In both analyses, midline deviations from symmetry create striking distortions. I go on to show that incorporating a small number of landmarks from the opposite side of the mandible produces far more accurate estimates of bilateral shape than does mirror reflection. Mirror reflection is clearly inappropriate for these data and is likely suspect in all cases of narrow midline morphology.