Modelling diameter class distribution with a second-order matrix model

Matrix models of forest dynamics rely on four hypotheses: independence hypothesis, Markov’s hypothesis, Usher’s hypothesis, and temporal homogeneity hypothesis. We investigate the consequences of relaxing Markov’s hypothesis, allowing the state of the tree at time t to depend on its states at time t−1 and t−2. The methodology for building and testing the relevance of second-order matrix model is thus proposed. The derivation of second-order transition probabilities turns to be sensitive to the width of the diameter classes. A strategy for choosing diameter classes is proposed. A second-order matrix model is then built for a tropical rain-forest in French Guiana. A different behaviour is detected between small (dbh ≤30 cm) and large trees, the smaller trees being more sensitive to their past history: small trees that have well grown have a tendency to grow well again, and small trees that have not grown tend to have a higher probability to die. The widths of the diameter classes that are selected are much less than the widths usually retained, that favour first-order selection.