AbstractCoral reefs are among the many communities believed to exhibit regime shifts between alternative stable states, single-species dominance, and coexistence. Proposed drivers of regime shifts include changes in grazing, spatial clustering, and ocean temperature. Here we distill the dynamic regimes of coral-macroalgal interaction into a three-dimensional geometry, akin to thermodynamic phase diagrams of state transitions, to facilitate analysis. Specific regime-shifting forces can be understood as bifurcation vectors through the cubic regime geometry. This geometric perspective allows us to understand multiple forces simultaneously in terms of the stability and persistence of interacting species. For example, in a coral-macroalgae community, grazing on macroalgae can lead to alternative stable states when there is no spatial clustering (e.g., high habitat connectivity). However, with spatial clustering, grazing can lead to coexistence because of elevated local intraspecific competition. The geometrical analysis of regime shifts is applicable to any two-species communities and can help conservation efforts navigate complexity and abrupt changes.
Three-dimensional light sculpting using a geometric analysis
