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Abstract
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.
Highlights
Specialty section: This article was submitted to Infectious Diseases, a section of the journal Frontiers in Microbiology
What is the use of mathematical modeling in biology? The answer likely depends on the background of the responder as mathematicians or physicists may have a different answer than biologists, and the answer may depend on the researcher’s definition of a “model.” In some cases models are useful for estimation of parameters underlying biological processes when such parameters are not directly measurable
By measuring the number of T lymphocytes over time and by utilizing a simple model, assuming exponential growth, we can estimate the rate of expansion of T cell populations (De Boer et al, 2001)
Summary
What is the use of mathematical modeling in biology? The answer likely depends on the background of the responder as mathematicians or physicists may have a different answer than biologists, and the answer may depend on the researcher’s definition of a “model.” In some cases models are useful for estimation of parameters underlying biological processes when such parameters are not directly measurable. By varying model assumptions one can vary model predictions and subsequently by comparing predictions to experimental observations, sets of assumptions which generate predictions consistent and inconsistent with the data can be identified This is the core of mathematical modeling which can provide profound insights into biological processes. One of the earlier models assumed that memory precursors proliferate during the infection and produce terminally differentiated, nondividing effector T cells, which die following clearance of the infection (Wodarz et al, 2000; Bocharov et al, 2001; Wodarz and Nowak, 2002; Fearon et al, 2006) While this model was used to explain several biological phenomena, later studies have shown that this model failed to accurately explain experimental data on the dynamics of CD8 T cell response to lymphocytic choriomengitis virus (Antia et al, 2005; Ganusov, 2007). This has not been formally done, two alternative mechanisms (predator-prey and seasonality) may be reasonable explanations of the hare-lynx dynamics in Canada
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