Extending the Geometric Approach for Studying Biomechanical Motions

Whether it is swimming, walking, eating, or jumping, motions are a fundamental way in which organisms interact with their environment. Understanding how morphology contributes to motion is a primary focus of kinematic research and is necessary for gaining insights into the evolution of functional systems. However, an element that is largely missing from traditional analyses of motion is the spatial context in which they occur. We explore an application of geometric morphometrics (GM) for analyzing and comparing motions to evaluate the outputs of biomechanical linkage models. We focus on a common model for oral jaw mechanics of perciform fishes, the fourbar linkage, using GM to summarize motion as a trajectory of shape change. Two traits derived from trajectories capture the total kinesis generated by a linkage (trajectory length) and the kinematic asynchrony (KA) of its mobile components (trajectory nonlinearity). Oral jaw fourbar data from two subfamilies of Malagasy cichlids were used to generate form-function landscapes, describing broad features of kinematic diversity. Our results suggest that kinesis and KA have complex relationships with fourbar morphology, each displaying a pattern in which different shapes possess equivalent kinematic trait values, known as many-to-one mapping of form-to-function. Additionally, we highlight the observation that KA captures temporal differences in the activation of motion components, a feature of kinesis that has long been appreciated but was difficult to measure. The methods used here to study fourbar linkages can also be applied to more complex biomechanical models and broadly to motions of live organisms. We suggest that they provide a suitable alternative to traditional approaches for evaluating linkage function and kinematics.