Watt, M.S., Kirschbaum, M.U.F. (2011). Moving beyond simple linear allometric relationships between tree height and diameter. Ecological Modelling 222: 3910-3916.
Abstract. Allometric relationships are used across a broad range of ecological disciplines as they provide a convenient means of scaling height (H) as a function of diameter (D). In these functions, it is commonly assumed that log transformed diameters and heights are linearly related, with a constant slope across environmental gradients. It is also widely thought that the elastic similarity model, in which H D2/3, holds true for all tree species, as this is a functional relationship that describes mechanical stability under self weight. Despite the wide use of these functions, little research has undertaken a rigorous intra-species evaluation of the applicability of these functions or the underlying theory. Here, we evaluate the applicability of these models to measurements from Pinus radiata plots covering broad intra and inter-stand environmental variation, and refine these models to make them more generally applicable. We used observations from 84 plots situated throughout New Zealand that had been measured repeatedly throughout stand development.
The slope of the relationship between H and D ranged from 0.73 − 1.43 between the 84 plots. This range clearly violates the assumptions underlying both allometric relationships and the elastic similarity model. A large proportion of the variation in plot level slope (R2 = 0.72) was found to be explained by significant positive relationships with stand density, degree of topographical exposure, ratio of soil carbon to nitrogen, and air temperature. There was also a significant increase in H/D with increasing age. Addition of a slope sub-model and an age modifier into a standard allometric relationship significantly improved the model fit to the data without unduly complicating the model form. We discuss implications of this research in the context of allometric scaling theory and offer an alternative theory that accounts for the observed results.
allometry; diameter; elastic similarity model; environmental impacts; height;