1.3 Model development process and validation

Mathematical modeling in biology is a powerful tool for understanding complex systems. It involves defining problems, formulating hypotheses, and constructing equations to represent biological processes. From predator-prey interactions to population growth, these models help scientists make predictions and gain insights.

Developing a mathematical model is an iterative process. It requires careful data collection, model validation, and refinement. By analyzing outputs, comparing results to biological knowledge, and incorporating new data, researchers can continually improve their models to better reflect real-world phenomena.

Model Development Process

Steps of mathematical model development

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• Define biological problem identifying system components and determining scope and boundaries (predator-prey interactions)
• Formulate hypotheses developing conceptual models and identifying key variables and relationships (population growth rates)
• Choose mathematical framework considering differential equations, discrete models, or stochastic models (Lotka-Volterra equations)
• Construct model defining variables and parameters and writing equations or algorithms (birth rates, death rates)
• Analyze model determining steady states and conducting stability analysis (carrying capacity)
• Implement model computationally choosing software or programming language and developing code (MATLAB, Python)

Data for model parameterization

• Determine necessary data types including time series data, spatial data, and population-level data (species abundance over time)
• Identify data sources from experimental studies, field observations, and literature reviews (mark-recapture studies)
• Assess data quality and quantity considering sample size requirements and measurement accuracy (statistical power analysis)
• Consider data preprocessing needs such as normalization and outlier detection (log transformation)
• Plan for data collection designing experiments and developing sampling strategies (transect surveys)

Model Validation and Refinement

Methods of model validation

• Recognize validation purpose ensuring model accuracy and reliability and building confidence in predictions
• Apply statistical validation techniques using goodness-of-fit tests and residual analysis (R-squared, residual plots)
• Perform sensitivity analysis identifying influential parameters and assessing model robustness (local and global sensitivity)
• Use cross-validation methods applying k-fold cross-validation and leave-one-out cross-validation
• Compare model predictions to independent data sets assessing predictive power (hindcasting, forecasting)

Interpretation of model simulations

• Analyze model outputs identifying trends and patterns and recognizing unexpected behaviors (population cycles)
• Compare results to biological knowledge assessing plausibility and identifying potential discrepancies
• Quantify uncertainty in model predictions calculating confidence intervals and performing error propagation analysis
• Relate model results to original research questions addressing hypotheses and evaluating practical implications
• Communicate findings effectively creating clear visualizations and summarizing key insights (phase plots, time series graphs)

Iterative process of model refinement

• Recognize need for continuous improvement acknowledging model limitations and identifying areas for refinement
• Incorporate new data updating parameter estimates and expanding model scope if necessary (including additional species)
• Refine model structure adding or removing variables and modifying relationships between components
• Reassess model assumptions challenging initial hypotheses and considering alternative formulations (density-dependent vs density-independent growth)
• Evaluate trade-offs in model complexity balancing accuracy and simplicity and considering computational efficiency
• Document model versions and changes maintaining version control and tracking improvements over time (Git repositories)