Empirical cycle

The role of mathematical models in the empirical cycle of quantitative science is not always recognized appropriately in the eyes of a theoretical biologist. This is because modellers not always start with explicit assumptions to derive mathematical models, before they start coding and do computer simulation studies. Empirically oriented workers are also not always fully aware of the implicit assumptions they make wile interpreting measurements, and the human brain has strong limitations to evaluate non-linear interactions between factors without using models. This can lead to problems in the single most important aspect in the use of models: Models are not an aim but a mean to gain a deeper understanding of underlying mechanisms.

This diagram shows the various steps in the empirical cycle (or rather spiral), starting from the white box. Red arrows should be followed on negative results, green arrows on positive ones.

An implied conclusion is that many models don't need to be tested against empirical data, because they should be rejected on more basic grounds. The failure of a model to describe experimental results adequatly does not imply that (some of) the underlying mechanistic assumptions are flawed; all models are simplifications of "reality", and some confounding factor possibly needs to be incorporated to repair the lack of fit. This is the reason why model development and experimental research should be done simultaneously and in close interaction.

A model that is based on unrealistic assumptions can survive tests against experimental data. This is the reason why models that fail to describe experimental results are more useful for improving insight. This only applies to models that are constructed following the rules as illustrated in the diagram. Models without assumptions from which they are derived are useless; the list of assumptions should be such that the model can be derived mathematically. This list then represents our (current) insight into the problem. It is the story behind the model that is most relevant, not the model itself.