VISUALIZING LARGE-SCALE TRENDS USING TIME-VARYING CHANGE-VS-ANCESTOR PLOTS

The change-vs-ancestor plot is a valuable tool for visualizing within-lineage trends, particularly complex and subtle examples of such trends. In such a plot, the x-axis represents the ancestral value of some characteristic (e.g., body size), and the y-axis represents the change or difference in that characteristic between its ancestral and descendant values (i.e., the descendant value minus the ancestral value). The plot thus shows how different ancestors differ in their degree of change. Large-scale trends, such as Cope’s rule, can occur when the average change in a change-vs-ancestor plot is non-zero. Previous work has shown that trends can also occur even when the average change is zero, as long as the variance around the average varies for different ancestral values. Here we demonstrate that trends can also occur when the pattern in a change-vs-ancestor plot varies over time. In particular, trends can occur due to a shifting dynamic equilibrium. In such a situation, ancestors and descendants are at or close to equilibrium at any given time, but trends are produced when the equilibrium point shifts over time. This mechanism allows for trends toward larger or smaller size in diverse clades without requiring that all taxa be either above or below a clade-specific optimum size. We demonstrate this effect using a dataset of body sizes of Mesozoic foraminifera.