Linking the ball-and-cup analogy and ordination trajectories to describe ecosystem stability, resistance, and resilience

Abstract

The ball-and-cup diagram for conceptualizing ecosystem stability, resistance, and resilience is often presented as a ball rolling around within and between two or more cups. This analogy has a long history in ecology and has been used to illustrate ecosystem changes over time where the magnitude of changes required to push the ball from one cup to another represents a regime shift to an alternative state. Another approach for visualizing ecosystem stability, resistance, and resilience involves ordinations of repeated measures of community data or environmental variables and tracking trajectories over time in ordination space. Interestingly, the two approaches have not been linked in a meaningful way. Here, we provide a conceptual link between trajectories of ecological change in ordination space to the ball-and-cup analogy and show how distance-based measures calculated from ordination scores can be used to quantitatively classify and evaluate the relative stability and resilience of ecological systems.