Evaluating the Fidelity of Data-Driven Predator-Prey Models: A Dynamical Systems Analysis

In empirical predator-prey systems, understanding the inherent dynamics typically comes from analyzing a structural model fitted to observation data. However, determining an appropriate model structure and its parameters is often complex and highly uncertain. A promising alternative is to learn the model structure directly from time series data of both predator and prey. This study explores the capability of a data-driven algorithm, Sparse Identification of Nonlinear Dynamics (SINDy), to accurately capture the dynamics of a predator-prey system. We apply SINDy to derive a Learned Model (LM) from data generated by a Reference Model (RM), whose predator-prey dynamics are well understood. The study compares the dynamics of the LM to the RM using criteria such as equilibrium points, stability, sensitivity, and bifurcation analysis. Our results demonstrate general consistency between the RM and LM dynamics, though notable differences remain. We discuss the implications of these differences in the broader context of using learned models to uncover the inherent drivers of predator-prey dynamics and ecological implications. 2010 MSC37M05, 37N25, 92B05, 92D25, 92D40, 65L05, 37G15 HighlightsO_LIEvaluates data-driven models ability to replication of predator-prey dynamics using SINDy framework C_LIO_LILearned Model captures core dynamics but shows parameter sensitivity and bifurcation differences C_LIO_LIAnalysis reveals need for extensive data for effective model learning C_LIO_LISuggests combining data-driven methods with biological priors to improve model accuracy C_LI