Response to ‘Testing the metabolic scaling theory of tree growth’

Summary

1. Coomes & Allen (2009) propose a new statistical method to test the Metabolic Scaling Theory prediction for tree growth rate size scaling (scaling constant α = 1/3) presented in Enquist et al. (1999). This method finds values of the scaling constant that yield standardized major axis (SMA) slopes of one in a comparison of allometrically transformed diameter census data. This SMA ‘slope-of-one’ method produces results that contrast with those generated by maximum-likelihood estimation (MLE; Russo, Wiser & Coomes 2007; Coomes & Allen 2009).

2. We hypothesize that the SMA slope-of-one method is inappropriate for this application because it assumes, unrealistically, that there is no biological or error variance in tree growth size scaling. To test our hypothesis, we simulate ‘allometric’ tree growth with biological and error variance in parameters and measurements. We find that the SMA slope-of-one method is sensitive to the amount of biological and error variance and consistently returns biassed parameter estimates, while the MLE method displays relatively little bias, particularly at larger sample sizes.

3. Synthesis. The conclusions of Coomes & Allen (2009) should be reconsidered in the light of our findings. Investigations of tree growth rate size scaling must consider the influence of biological and error variance in model-fitting procedures to ultimately unravel the effects of tree architecture and ecological factors on patterns of size-dependent growth.