Probability distribution of allometric coefficients and Bayesian estimation of aboveground tree biomass

Allometric biomass equations are widely used to predict aboveground biomass in forest ecosystems. A major limitation of these equations is that they need to be developed for specific local conditions and species to minimize bias and prediction errors. This variability in allometries across sites and species contradicts universal scaling rules that predicts constant coefficients for plants. A large number of biomass equations have been developed over the years, which provides an opportunity to synthesize parameter values and estimate their probability distributions. These distributions can be used as a priori probabilities to develop new equations for other species or sites. Here we found the distribution of the parameters a and b of the allometry between aboveground biomass (M) and diameter at breast height (D), ln (M) = a + bln(D), well approximated by a bivariate normal. We propose a method to develop new biomass equations based on prior information of parameter distributions and apply it to a dataset of tropical trees. The method we propose outperforms the classical statistical approach of least-square regression at small sample sizes. With this method it is possible to obtain similar significant values in the estimation of parameters using a sample size of 6 trees rather than 40-60 trees in the classical approach. Further, the Bayesian approach suggests that allometric scaling coefficients should be studied in the framework of probability distributions rather than fixed parameter values.