Inferring Models with Alternative Stable States from Independent Observations

Abstract

14 Multiple attractors and alternative stable states are defining features of scientific theories 15in ecology and evolution, implying that abrupt regime shifts can occur and that outcomes can be 16 hard to reverse. Here we describe a statistical inferential framework that uses independent, noisy 17 observations with low temporal resolution to support or refute multiple attractor process models. 18The key is using initial conditions to choose among a finite number of expected outcomes using 19 a nonstandard finite mixture methodology. We apply the framework to contemporary issues in 20 social-ecological systems, coral ecosystems, and chaotic systems, showing that incorporating 21 history allows us to statistically infer process models with alternative stable states while 22 minimizing false positives. Further, in the presence of disturbances and oscillations, alternative 23 stable states can help rather than hamper inference. The ability to infer models with alternative 24 stable states across natural systems can help accelerate scientific discoveries, change how we 25 manage ecosystems and societies, and place modern theories on firmer empirical ground. 26 27Keywords: bifurcation, alternative stable states, P-value, coral reef, Lorenz system, conservation 28 behaviour, multiple attractors, regression, finite mixture model 29 30 the process model. For the statistical translation, we employ a finite mixture model (McLachlan,