Model convergence and state variable update in forest gap models

During the last 25 years, models of the JABOWA/FORET type ('gap models') were increasingly applied to study forest succession. By adding more and more details, they have grown to rather complex systems, but little is known about the importance of the numerous ecological processes included in the models and about their exact mathematical properties from a systems theoretical point of view. Based on the stochastic gap model FORECE developed for European forests we analysed two generally relevant aspects of gap models: (1) the sample size needed to reliably compute the statistical properties of the model behaviour; (2) inconsistencies in the mechanism used to update the state variables. It was found that 150-200 simulation runs are required to warrant the convergence of the average species-specific biomass values. This sample size is considerably larger than that used in most previous studies. The analysis of the mechanism used for updating the state variables revealed that it does not conform to the requirements of systems theory. A new consistent update mechanism is presented, which even leads to more efficient calculations. While the FORECE model produces only minor differences of the simulated species-specific biomass values when using the old vs. the new update mechanism, the frequency distribution of stem numbers may be affected significantly. It is concluded that rigorous systems theoretical and statistical investigations of the properties of forest gap models are required to render the application of those models more robust. It is proposed to revise the update mechanism for the state variables in the existing forest gap models as outlined in the present study. The design of future simulation studies with these models should be improved so as to sample sufficiently large numbers of about 200 simulation runs.