Meeting Abstract
One advantage of geometric morphometric methods (GMMs) is an ability to visualize data. Yet classical GMMs cannot fulfill all visualization needs. One example is shape trajectories, temporally-ordered sets of shapes. While GMMs can visualize comparisons between shapes within trajectories, visualizations to compare trajectories themselves are challenging. Here we introduce a method to visualize how two regularly sampled, globally stable shape trajectories differ. First, an autoregressive-moving average model is fit to each trajectory. These models describe how a shape relates to previous shapes in the trajectory, how a shape deviates from the other two components (i.e., the “shock”), and how a shape relates to previous shapes’ shocks. Since the shocks are assumed to follow a normal distribution with mean zero, the shocks’ covariance matrices are estimable. Next, the researcher creates two simulated trajectories. The first shapes in each are identical to one of the original trajectories’ mean shapes, and the initial shocks are zero. The difference between the mean shapes is then visualized. Next, a shock for the next shapes in the simulations is drawn from a normal distribution with mean zero and one of the estimated covariance matrices. Based on this shock and the models, the simulations’ next shapes are calculated and a comparison is visualized. The process of generating shocks, calculating new shapes, and visualizing comparisons continues for a desired number of shapes. Finally, each comparison is merged into an animation. The animation reflects the original trajectories as the simulations show roughly how the original trajectories would appear had the same conditions (i.e., shocks) influenced both. The merits and drawbacks of this method are discussed.
