Weak-Form Inference for Hybrid Dynamical Systems in Ecology

TL;DR

This paper introduces a data-driven weak-form equation learning method to model hybrid ecological systems, capturing interactions between short-term continuous dynamics and long-term discrete changes using sparse data.

Contribution

It presents a novel approach for inferring coupled hybrid dynamical equations in ecology, enabling analysis of multi-scale population behaviors from limited measurements.

Findings

Successfully applied to ecological models of epizootics in moth populations.

Accurately estimates parameters from sparse, intermittent data.

Reveals interdependencies between short-term and long-term ecological variables.

Abstract

Species subject to predation and environmental threats commonly exhibit variable periods of population boom and bust over long timescales. Understanding and predicting such behavior, especially given the inherent heterogeneity and stochasticity of exogenous driving factors over short timescales, is an ongoing challenge. A modeling paradigm gaining popularity in the ecological sciences for such multi-scale effects is to couple short-term continuous dynamics to long-term discrete updates. We develop a data-driven method utilizing weak-form equation learning to extract such hybrid governing equations for population dynamics and to estimate the requisite parameters using sparse intermittent measurements of the discrete and continuous variables. The method produces a set of short-term continuous dynamical system equations parametrized by long-term variables, and long-term discrete equations parametrized by short-term variables, allowing direct assessment of interdependencies between the two time scales. We demonstrate the utility of the method on a variety of ecological scenarios and provide extensive tests using models previously derived for epizootics experienced by the North American spongy moth (Lymantria dispar dispar).