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

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.

Some New Results of a Fractional Von Bertalanffy Model

“…Research has been done to convert deterministic growth models to their stochastic counterparts because deterministic models are in fact insufficient to explain the dynamical process of population expansion (Shabana (2019) and references therein). Researchers have expanded the Von Bertalanffy model in numerous investigations (Lee (2020); Garcia (1983); Konig (2019)). On the other hand, the only models that have been extended to their stochastic counterpart to date are the logistic and Gompertz models (Shabana (2019) and references therein); Al-Saffar (2017); Al-Saffar (2020)).…”

Fisher information approach to understand the Gompertz model

“…Further comparison is conducted based on changes in information during growth between the Logistic growth model and Gompertz growth model [13]. In order to achieve regime change, an ecological system must be able to change its properties to a great extent [6]. The purpose of this article is to study the effects of oscillatory modulations on the parameters and examine sustainability by using Fisher information.…”