Opening Pandora's box: caveats with using toolbox-based approaches in mathematical modeling in biology

Abstract

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Mathematical modeling is a powerful method to understand how biological systems work. By creating a mathematical model of a given phenomenon one can investigate which model assumptions are needed to explain the phenomenon and which assumptions can be omitted. Creating an appropriate mathematical model (or a set of models) for a given biological system is an art, and classical textbooks on mathematical modeling in biology go into great detail in discussing how mathematical models can be understood via analytical and numerical analyses. In the last few decades mathematical modeling in biology has grown in size and complexity, and along with this growth new tools for the analysis of mathematical models and/or comparing models to data have been proposed. Examples of tools include methods of sensitivity analyses, methods for comparing alternative models to data (based on AIC/BIC/etc.), and mixed-effect-based fitting of models to data. I argue that the use of many of these “toolbox” approaches for the analysis of mathematical models has negatively impacted the basic philosophical principle of the modeling—to understand what the model does and why it does what it does. I provide several examples of limitations of these toolbox-based approaches and how they hamper generation of insights about the system in question. I also argue that while we should learn new ways to automate mathematical modeling-based analyses of biological phenomena, we should aim beyond a mechanical use of such methods and bring back intuitive insights into model functioning, by remembering that after all, modeling is an art and not simply engineering. “Getting something for nothing is impossible; there is always a price to pay.” Louis Gross.“There is not such a thing as a free lunch.”

Keywords

• mathematical modeling
• sensitivity analysis
• model selection
• AIC
• mixed-effect modeling