## Introduction

Metabolic Scaling Theory (MST) has proven immensely stimulating to plant ecologists because it provides ‘a quantitative, predictive framework for understanding the structure and dynamics of an average idealized forest’ (Enquist, West & Brown 2009). Proponents of this ‘zeroth-order’ theory maintain that it enables useful generalizations to be made about tree growth by focusing attention on two key processes – the optimization of water transport through the xylem and the biomechanics of stem wood (West, Enquist & Brown 2009). Yet its sweeping generalizations and bold assumptions have also generated debate and drawn much criticism (Muller-Landau *et al.* 2006; Reich *et al.* 2006). The counterargument is that other processes that contribute to resource capture, transportation and metabolism have a significant influence on tree growth, and that their omission, or superficial treatment, gives rise to mismatches between MST predictions and empirical realities (e.g. Reich *et al.* 2006; Muller-Landau *et al.* 2006; Coomes and Allen 2007a,b).

Here, we consider whether one of MST’s central claims is supported by data. Enquist *et al.* (1999) argued that tree stem diameter growth *dD*/*dt* scales with stem diameter (*D*) according to a power function:

They emphasized that the scaling exponent, α, was equal to 1/3, arguing that differences in the life history of species affected the scaling coefficient, β, but had little influence on α. In the face of much criticism, Enquist *et al.* have recently conceded that scaling exponents can vary greatly among species, and have shifted their position to arguing that MST ‘predicts a basin of attraction, around which actual biological networks cluster’ (Price, Enquist & Savage 2007). We interpret this phrase as meaning that MST is useful in predicting the average value of α taken across species.

Enquist *et al.* (1999) demonstrated support for their theory by modelling the growth of 45 tree species found in a Costa Rican forest, for which stem diameters had been measured and re-measured 20 years later. To estimate α and β, they integrated the growth function given in eqn 1 to get:

where *D*_{0} and *D*_{t} are stem diameter measurements made on a tree during an initial census and after time interval *t*. If the MST prediction that α = 1/3 is correct, then it follows that:

Enquist *et al.* (1999) used Reduced Major Axis (RMA) regression to fit straight lines through scatterplots of *D*_{0}^{2/3} vs. *D*_{t}^{2/3} for each species. Note that RMA regression is identical in all but name to Standardized Major Axis (SMA) line-fitting, and we use the latter terminology for the reasons set out in Warton *et al.* (2006). SMA line-fitting is a least-squares method that differs from linear regression only in the direction in which errors from the line are measured and is regarded as the most appropriate approach when the purpose of a study is to describe how two size variables are related (Warton *et al.* 2006). Enquist *et al.* (1999) reasoned that the slope of the fitted line (*m*) would only be equal to 1.000 if α was equal to 1/3. Testing whether slopes differ significantly from 1.000 provides a reasonable way of testing the hypothesis that α = 1/3, but it is important to note that it does not provide an estimate of α. In other words, it identifies species whose growth curves deviate from the MST prediction, but is unable to quantify the degree of deviation.

Analysis of the Costa Rican data set using this method produced apparently compelling evidence in support of MST (Enquist *et al.* 1999). For 40 of the 45 species examined, the 95% confidence intervals (CIs) of slope estimates overlapped with 1.0, suggesting that α = 1/3 was consistent with data for the vast majority of species. Lines fitted to *D*_{0}^{2/3} vs. *D*_{t}^{2/3} using linear regression had high *r*^{2} values – 0.95 on average – conveying an impression that these inferences carried statistical weight. In addition, the cross-species mean of the slope estimates was 1.038, with a CI of 1.01–1.08. Although the confidence intervals indicated a departure from the null hypothesis, Enquist *et al.* (1999) passed this off as ‘essentially not different from the predicted value of 1.0’ and who could deprive them of such an indulgence when the mean slope was so remarkably close to 1.00? The conclusions drawn from these analyses seem compelling and have been repeated in several subsequent papers (Enquist, West & Brown 2009). However, we take issue with the way the results were interpreted and illustrate our concerns by revisiting the Costa Rican data set.