Approximating spatial interactions in a model of forest dynamics
Résumé
Developments in forest dynamics modelling have led to complex individual-tree distance-dependent models. Questions that arise are: how might such complex models be approximated (possibly through aggregation techniques) to obtain distribution-based models; and, when are such approximated models “equivalent” to the complex models from which they are derived. The approximation process usually involves replacing distance-dependent tree interactions by distance-independent interactions. We used a “toy model” that is derived from an individual-based distancedependent model of a forest in French Guiana to address these methodological questions. This toy model (model I) was defined in two forms; first a short-range tree interaction (1 m); second for a long-range tree interaction (30 m). Mean-field approximations were used to convert model I into an individual-tree distance-independent model (model II) and into a distribution-based model (model III). If the starting model is model I(long-range), models II and III are shown to be equivalent to each other. Model II is also found to be “consistent” with model I(long-range). Hence, for the toy model considered, long-range interactions can be disregarded, and have no influence on forest growth predictions. On the other hand, model I(short-range) is not equivalent with models II or III. Even so, it was found to be possible to obtain, by ad hoc methods, a distribution-based model (model IV) which, by taking into account the spatial structure generated by short-range interactions, is “consistent” with model I(short range)