Detecting dynamic system regime boundaries with Fisher information: the case of ecosystems

Abstract

Abstract: The direct measurement of the resilience (resistance to disturbances) of an ecosystem’s current regime (or “alternative stable state”) remains a key concern for managing human impacts on these ecosystems and their risk of collapse. Approaches which utilize statistics or information theory have demonstrated utility in identifying regime boundaries. Here, we use Fisher information to establish the limits of the resilience of a dynamic regime of a predator–prey system. This is important because previous studies using Fisher information focused on detecting whether a regime change has occurred, whereas here we are interested in determining how much an ecological system can vary its properties without a regime change occurring. We illustrate the theory with simple two species systems. We apply it first to a predator–prey model and then to a 60-year wolf–moose population dataset from Isle Royale National Park in Michigan, USA. We assess the resilience boundaries and the operating range of a system’s parameters without a regime change from entirely new criteria for Fisher information, oriented toward regime stability. The approach allows us to use system measurements to determine the shape and depth of the “cup” as defined by the broader resilience concept. Graphic abstract: The direct measurement of the resilience (resistance to disturbances) of an ecosystem’s current regime remains a key concern for managing human impacts on these ecosystems and their risk of collapse. Here, we use Fisher information to establish the limits of stability of a dynamic regime of a predator–prey system. The region of stability is represented by the “floor of the canyon” in the adjacent graphic. While the theory is illustrated with an ecosystem example, it is applicable in its present form to dynamic systems in general.[Figure not available: see fulltext.].