**
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* *D*^{2/3},
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 (*R*^{2} = 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.

**Key words:**
allometry; diameter; elastic similarity model; environmental impacts; height;
stocking** **

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