Quantifying asymmetry in non-symmetrical morphologies, with an example from Cetacea

Abstract

1. Three-dimensional measurements of morphology are key to gaining an understanding of a species biology and to answering subsequent questions regarding the processes of ecology (or palaeoecology), function, and evolution. However, the collection of morphometric data is often focused on methods designed to produce data on bilaterally symmetric morphologies which may mischaracterise asymmetric structures. 2. Using 3D landmark and curve data on 3D surface meshes of specimens, we present a method for first quantifying the level of asymmetry in a specimen and second, accurately capturing the morphology of asymmetric specimens for further geometric analyses. 3. We provide an example of the process from initial landmark placement, including details on how to place landmarks to quantify the level of asymmetry, and then on how to use this information to accurately capture the morphology of asymmetric morphologies or structures. We use toothed whales (odontocetes) as a case study and include examples of the consequences of mirroring landmarks and curves, a method commonly used in bilaterally symmetrical specimens, on asymmetric specimens. 4. We conclude by presenting a step-by-step method to collecting 3D landmark data on asymmetric specimens. Additionally, we provide code for placing landmarks and curves on asymmetric specimens in a manner designed to both save time and ultimately accurately quantify morphology. This method can be used as a first crucial step in morphometric analyses of any biological specimens by assessing levels of asymmetry and then if required, accurately quantifying this asymmetry. The latter not only saves the researcher time, but also accurately represents the morphology of asymmetric structures.