Understanding the dynamics of wildfire regimes is crucial for both regional forest management and predicting global interactions between fire regimes and climate. Accordingly, spatially explicit modeling of forest fire ecosystems is a very active field of research, including both generic and highly specific models. There is, however, a second field in which wildfire has served as a metaphor for more than 20 years: statistical physics. So far, there has been only limited interaction between these two fields of wildfire modeling. Here we show that two typical generic wildfire models from ecology are structurally equivalent to the most commonly used model from statistical physics. All three models can be unified to a single model in which they appear as special cases of regrowth-dependent flammability. This local "ecological memory" of former fire events is key to self-organization in wildfire ecosystems. The unified model is able to reproduce three different patterns observed in real boreal forests: fire size distributions, fire shapes, and a hump-shaped relationship between disturbance intensity (average annual area burned) and diversity of succession stages. The unification enables us to bring together insights from both disciplines in a novel way and to identify limitations that provide starting points for further research.
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