Predator Prey Scavenger Model using Holling's Functional Response of Type III and Physics-Informed Deep Neural Networks

2024-12-24

AI Summary

Traditional Lotka–Volterra models fail to capture complex trophic interactions involving scavengers. Method: We propose a novel three-species dynamical model integrating predators, prey, and scavengers, incorporating a type-III Holling functional response and—uniquely—the scavengers’ dependence on deceased predators. To estimate parameters robustly while preserving ecological interpretability, we develop a hybrid approach combining physics-informed neural networks (PINNs) with the BFGS optimization algorithm, effectively mitigating gradient explosion. Contribution/Results: Applied to American forest observational data, our method achieves high-accuracy parameter inversion. Jacobian stability analysis and multi-scenario simulations confirm model validity; prediction errors are significantly lower than those of purely data-driven approaches. This work establishes a new paradigm for modeling multi-trophic ecosystems by unifying mechanistic ecological theory with advanced computational inference.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka-Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling's functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden-Fletcher-Goldfarb-Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. Future research work includes minimization of error induced by parameters, bifurcation analysis, and sensitivity analysis of the parameters.

Problem

• Predator-prey dynamics
• Ecological modeling
• Decomposer ecosystem

Innovation

• Nonlinear Mathematical Model
• Deep Neural Networks with Physical Knowledge
• Stability Analysis