Using Experimental Data and Information Criteria to Guide Model Selection for Reaction-Diffusion Problems in...

Area of Science:

• Mathematical Biology
• Population Dynamics
• Mathematical Modeling

Background:

• Reaction-diffusion models are widely used in mathematical biology to describe population dynamics, including movement, reproduction, and death.
• Current practices in selecting these models often rely on heuristic choices for flux and source terms and prioritize residual error over comprehensive validation.
• Model validation and selection are underexplored areas in mathematical biology compared to model development and analysis.

Purpose of the Study:

• To present a model selection case study using a detailed experimental dataset on cell invasion.
• To demonstrate the importance of accounting for both residual errors and model complexity in model selection and validation.
• To propose a straightforward methodology for guiding model selection in mathematical biology.

Main Methods:

• Utilized a detailed experimental dataset on cell invasion.
• Employed Bayesian analysis for model calibration and comparison.
• Applied information criteria to evaluate model performance.

Main Results:

• Model selection and validation must consider both residual errors and model complexity.
• Neglecting model complexity can lead to misleading outcomes in biological modeling.
• The proposed methodology provides a clear framework for model selection.

Conclusions:

• A robust methodology for model selection in mathematical biology is presented, emphasizing the balance between data fit and model complexity.
• The study highlights the limitations of relying solely on residual error criteria for model selection.
• The findings are applicable to a broad range of reaction-diffusion models and biological contexts.