Fixed point sensitivity analysis of interacting structured populations.

Area of Science:

• Population Ecology
• Mathematical Biology
• Theoretical Ecology

Background:

• Sensitivity analysis is crucial for understanding structured populations, historically focusing on linear models and single populations.
• Recent advancements extend sensitivity analysis to nonlinear models and interacting populations.
• A gap exists in general methods for analyzing sensitivity in structured communities.

Purpose of the Study:

• To derive a general mathematical expression for the sensitivity of equilibrium abundances in communities of interacting structured populations.
• To develop a method applicable to arbitrary functions of stage class abundances and model parameters.
• To explore the implications of this sensitivity analysis within niche theory.

Main Methods:

• Derivation of a general mathematical framework for sensitivity analysis.
• Application of the method to a two-species model with ontogenetic niche shifts and two stage classes (juveniles, adults).
• Testing the robustness of the theory against violations of equilibrium and perturbation assumptions.

Main Results:

• A fully general method for calculating the sensitivity of equilibrium abundances in structured population communities.
• Demonstration of the method's robustness, even when assumptions of point equilibrium and infinitesimal perturbations are relaxed.
• Interpretation of community sensitivity in terms of niche composition and niche segregation.

Conclusions:

• The derived method provides a powerful and robust tool for sensitivity analysis in complex ecological communities.
• The framework connects population structure, community interactions, and niche theory.
• This approach enhances understanding of how perturbations affect community dynamics and stability.