Wildfire, landscape diversity and the Drossel-Schwabl model

How simple can a model be that still captures essential aspects of wildfire ecosystems at large spatial and temporal scales? The Drossel-Schwabl model (DSM) is a metaphorical forest-fire model developed to reproduce only one pattern of real systems: a frequency distribution of fire sizes resembling a power law. Consequently, and because it appears oversimplified, it remains unclear what bearings the DSM has in reality. Here, we test whether the DSM is capable of reproducing a pattern that was not considered in its design, the hump-shaped relation between the diversity of succession stages and average annual area burnt. We found that the model, once reformulated to represent succession, produces realistic landscape diversity patterns. We investigated four succession scenarios of forest-fire ecosystems in the USA and Canada. In all scenarios, landscape diversity is highest at an intermediate average annual area burnt as predicted by the intermediate disturbance hypothesis. These results show that a model based solely on the dynamics of the fuel mosaic has surprisingly high predictive power with regard to observed statistical properties of wildfire systems at large spatial scales. Parsimonious models, such as the DSM can be used as starting points for systematic development of more structurally realistic but tractable wildfire models. Due to their simplicity they allow analytical approaches that further our understanding under increasing complexity.