New approaches to modelling cross-sectional area to height allometry in four Mediterranean pine species

Crown dynamics affect tree cross-sectional growth by responding to individual traits and stand history and features, i.e. species, stocking, thinning, site quality or climatic conditions. Under this assumption we analysed two simple models that relate cross-sectional growth to the growth of stem length above the cross section in four species of Mediterranean pines. Cross-sectional growth was measured at breast height. The first model (Model 0) has no parameters, and specifies an isometric relationship between cross-sectional area and stem length. The second model (Model α), which was formulated to analyse Model 0, has one parameter. Neither of the two simple models requires knowledge of crown length, though Model 0 derives – under an assumption of constant crown length – from a more general model that relates cross-sectional growth to crown length dynamics. A mixed-effects modelling strategy was selected to fit Model α in order to incorporate fixed effects of species, and random effects to account for factors like ontogeny (tree effect), stand history (plot effect) and climatic conditions (growth period). Results indicate that Model α predicts better than Model 0 when the single parameter is expanded to take into account all these effects and indicate that the constant ratio between cross-sectional area and the length of stem predicted by Model 0 is one possible value within a ratio that changes over time as function of ontogeny, stand history and climatic conditions. On average the ratio is positive, indicating greater cross-sectional growth than height growth showing greater variation in stem formation. Inter-specific analysis indicated a less asymmetric behaviour in competition for pine species growing in water-stress environment