Missing the third dimension in geometric morphometrics: how to assess if 2D images really are a good proxy for 3D structures?

Procrustean geometric morphometrics has made large use of 2D images for studying three-dimensional structures such as mammalian bones or arthropod exoskeleta. This type of use of 2D data is still widespread today and will likely remain common for several years due to its simplicity, efficiency and low cost. However, using 2D pictures to measure morphological variation in a 3D object is an approximation that inevitably implies measurement error. Despite this being an obvious problem, which was emphasized since the early days of the first applications of geometric morphometrics to biology, whether 2D is a good proxy for 3D has been a rather neglected topic in the literature until very recently. In this paper, using marmot mandibles and crania as an example, I show how to assess the potentially crucial impact of 'missing the third dimension' in 2D landmarks and suggest a new method to test the accuracy of these data: the method is simple and can be easily performed in a user-friendly free software such as MorphoJ. This test is complimentary to other more exploratory analyses, that can also be performed using free programs and might offer a routine protocol to estimate the goodness of the 2D to 3D approximation in geometric morphometrics. Example data and a fully worked out MorphoJ project are provided for readers to learn how to replicate the analysis.