Optimal size of predictive models

This work focuses on models for ecosystems, like lakes and coastal areas. The objective has been to discuss the optimization problem, i.e., the balance between an increasing generality as dynamic and empirical/statistical models account for more processes and factors, and the increase in predictive uncertainty associated with this growth. The apparent predictive power, expressed for example by the r2-value (coefficient of determination between model-predicted values and empirical values), may increase with the number of x-variables (dependent variables) accounted for in predictive models. However, every x-variable and/or rate in a predictive model has a certain uncertainty due to the fact that there are always problems associated with sampling, transport, storage, analyses, etc. Uncertainties in x-variables may be added or multiplied in the model predictions. The optimal size of predictive models is therefore generally achieved for a (surprisingly) small number of dependent variables. The results presented here indicate that predictive models should not have more than two to six x-variables (or compartments). It is, however, evident that there may be many specific cases when more x-variables would do more good than harm, but it is important to note that the potential model uncertainty would then also increase.