Inferring Models with Alternative Stable States from Independent Observations

Multiple attractors and alternative stable states are defining features of scientific theories in ecology and evolution, implying that abrupt regime shifts can occur and that outcomes can be hard to reverse. Here we describe a statistical inferential framework that uses independent, noisy observations with low temporal resolution to support or refute multiple attractor process models. The key is using initial conditions to choose among a finite number of expected outcomes using a nonstandard finite mixture methodology. We apply the framework to contemporary issues in social-ecological systems, coral ecosystems, and chaotic systems, showing that incorporating history allows us to statistically infer process models with alternative stable states while minimizing false positives. Further, in the presence of disturbances and oscillations, alternative stable states can help rather than hamper inference. The ability to infer models with alternative stable states across natural systems can help accelerate scientific discoveries, change how we manage ecosystems and societies, and place modern theories on firmer empirical ground.