Validation of demographic equilibrium theory against tree-size distributions and biomass density in Amazonia

Abstract. Understanding the relative abundance of trees of different sizes is an important part of predicting the response of forests to changes in climate, land-use and disturbance events. Two competing theories of forest size-distributions are demographic equilibrium theory (DET), based on scaling of mortality and growth with size, and metabolic scaling theory (MST), based scaling size with metabolic rates and how trees fill space. Recently, it was shown that for US forests DET is a much better model than MST, even using the same growth scaling with size. Studies comparing DET and MST have so far focused on trunk diameter, but tree mass and the associated forest mass per unit area (biomass density) are much more relevant to climate. In this study, we extend by fitting both DET and MST to mass data for the Amazon rainforest. The conversion via allometry from trunk diameter data to mass leads to an artefact in the mass distribution, which can be corrected by excluding smaller trees. We derive equations to calculate the total forest biomass density from the mass distribution equation, for both models, and these can be used as an indicator of goodness of model fit to the data. The models were fitted to the data, using Maximum Likelihood Estimation, at the forest plot, regional and continental scale. The fits for both diameter and mass demonstrate that MST is rarely a good fit for Amazon size-distributions and that DET is much better and can estimate biomass density, at the forest plot scale, with a mean error of 6 % (10 % if DET allometry fixed to MST) of its true value, compared to 139 % for MST. The median of the fitted growth scaling power for all the 124 plots is very close to the MST allometry values, implying MST allometry is a mean scaling, around which smaller forest plots cluster. At the larger regional scale, the error in the biomass density estimate of DET reduces to 2 % or less and it is less than 1 % for the whole continent. This suggests that models based on DET, such as the relatively simple Robust Ecosystem Demography model (RED), are a good basis for a next-generation dynamic global vegetation model, and that Amazonian forests remain close to demographic equilibrium on large-scales, despite climate change and significant anthropogenic disturbance.