Modeling Moose-Wolf interactions in Isle Royale National Park using sparseidentification of nonlinear dynamics.

Building the mathematical models to study the dynamics of prey-predator relationship in ecology is a long standing research topic. The only connection that has been established between real data and ecological models is through parameter estimation. Till date, only a few studies have attempted to formulate ecological models directly from real data without prior knowledge of the underlying structure of the system being modeled. Present work is an attempt in this direction. The ecological study of the moose (Alces alces) and wolf (Canis lupus) populations of Isle Royale National Park (USA) is the longest running large mammal prey-predator study in the world. In this study, we formulate mathematical models of moose and wolf dynamics from yearly reported population data from 1959 to 2019 using sparse identification of nonlinear dynamical systems (SINDy) algorithm. We have used SINDy and Ensemble SINDy (E-SINDy) algorithms with model selection techniques on the park data. We have performed global uncertainty and sensitivity analysis of the best obtained model. The findings suggest that the mathematical models obtained using E-SINDy method is a close representation of the moose-wolf relationship in Isle Royale.