## 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.