From formulae, via models to theories: Dynamic Energy Budget theory illustrates requirements

As sciences mature, they transition from observation and description to explanation and prediction. This transition is associated with qualitative changes in the way quantitative mathematical formulations are constructed and interpreted, resulting in a ‘theory’. Such transitions from phenomenology to theory are happening in biology but the heuristic framework involved is rarely articulated. We here describe how the use of models in research sets model requirements, using Dynamic Energy Budget (DEB) theory to illustrate the more elaborate ones. We first make the distinction between mathematical formulae and models based on their relation to the abstract and real worlds. We then explain how the transition from models to theory affects model construction and parameter estimation, and discuss the concept of parameter estimation-in-context using the database Add_my_Pet on animal energetics. The transition comes with the need to develop auxiliary and meta- theory and to work with multiple datasets, implying constraints for the loss function that is used for parameter estimation. Finally, we discuss the extra requirements for general explanatory models: they need to be explicit on relevant general principles and to be embedded in a wider scientific context. We also discuss how we see theory’s relationship to observation and prediction change in the future as we use it to deal with theoretical and applied problems in biology.