Structural sensitivity of a tri-trophic food chain model in a parameter plane

Area of Science:

• Ecological modeling
• Mathematical biology
• Systems ecology

Background:

• Biological models are essential for understanding ecological processes like species interactions and disease spread.
• Model predictive capability hinges on parameterization, specifically the choice of mathematical functions.
• Structural sensitivity, where similar functions yield different predictions, is a key challenge in ecological modeling.

Purpose of the Study:

• To investigate the structural sensitivity of a tri-trophic food chain model.
• To compare the impact of three distinct trophic functions (Holling type-II, Ivlev, trigonometric) on model dynamics.
• To analyze how functional form influences the organization of periodic structures within the model's parameter plane.

Main Methods:

• Utilized bifurcation diagrams to analyze model stability and transitions.
• Employed isospike diagrams to visualize spatial patterns in model dynamics.
• Applied Lyapunov exponent diagrams to quantify system chaos and predictability.
• Examined a tri-trophic food chain model with Holling type-II, Ivlev, and trigonometric functional responses.

Main Results:

• The choice of functional form significantly impacts the organization of periodic structures in the parameter plane.
• Diverse dynamical behaviors were observed within a fixed parameter range solely due to variations in functional form.
• Species survival and the nature of population oscillations are demonstrably influenced by the selected trophic functions.
• Even minor differences in functional response curves lead to substantial qualitative and quantitative changes in food chain dynamics.

Conclusions:

• Structural sensitivity is a critical consideration in ecological modeling, affecting model predictions and interpretations.
• The selection of appropriate functional responses is paramount for accurately representing food chain dynamics and species interactions.
• Future ecological modeling efforts must carefully account for the influence of functional form on system behavior to enhance predictive power.