PT  - JOURNAL ARTICLE
AU  - David J. Warne
AU  - Ruth E. Baker
AU  - Matthew J. Simpson
TI  - Using experimental data and information criteria to guide model selection for reaction–diffusion problems in mathematical biology
AID  - 10.1101/444679
DP  - 2018 Jan 01
TA  - bioRxiv
PG  - 444679
4099  - http://biorxiv.org/content/early/2018/10/16/444679.short
4100  - http://biorxiv.org/content/early/2018/10/16/444679.full
AB  - Reaction–diffusion models describing the movement, reproduction and death of individuals within a population are key mathematical modelling tools with widespread applications in mathematical biology. A diverse range of such continuum models have been applied in various biological contexts by choosing different flux and source terms in the reaction–diffusion framework. For example, to describe collective spreading of cell populations, the flux term may be chosen to reflect various movement mechanisms, such as random motion (diffusion), adhesion, haptotaxis, chemokinesis and chemotaxis. The choice of flux terms in specific applications, such as wound healing, is usually made heuristically, and rarely is it tested quantitatively against detailed cell density data. More generally, in mathematical biology, the questions of model validation and model selection have not received the same attention as the questions of model development and model analysis. Many studies do not consider model validation or model selection, and those that do often base the selection of the model on residual error criteria after model calibration is performed using nonlinear regression techniques. In this work, we present a model selection case study, in the context of cell invasion, with a very detailed experimental data set. Using Bayesian analysis and information criteria, we demonstrate that model selection and model validation should account for both residual errors and model complexity. These considerations are often overlooked in the mathematical biology literature. The results we present here provide a clear methodology that can be used to guide model selection across a range of applications. Furthermore, the case study we present provides a clear example where neglecting the role of model complexity can give rise to misleading outcomes.