Abstract. Predicting the response of forests to climate and land-use change depends on models that can simulate the time-varying distribution of different tree sizes within a forest – so-called forest demography models. A necessary condition for such models to be trustworthy is that they can reproduce the tree-size distributions that are observed within existing forests worldwide. In a previous study, we showed that demographic equilibrium theory (DET) is able to fit tree-diameter distributions for forests across North America, using a single site-specific fitting parameter (μ) which represents the ratio of the rate of mortality to growth for a tree of a reference size. We use a form of DET that assumes tree-size profiles are in a steady state resulting from the balance between a size-independent rate of tree mortality and tree growth rates that vary as a power law of tree size (as measured by either trunk diameter or biomass). In this study, we test DET against ForestPlots data for 124 sites across Amazonia, fitting, using maximum likelihood estimation, to both directly measured trunk diameter data and also biomass estimates derived from published allometric relationships. Again, we find that DET fits the observed tree-size distributions well, with best-fit values of the exponent relating growth rate to tree mass giving a mean of ϕ=0.71 (0.31 for trunk diameter). This finding is broadly consistent with exponents of ϕ=0.75 (ϕ=1/3 for trunk diameter) predicted by metabolic scaling theory (MST) allometry. The fitted ϕ and μ parameters also show a clear relationship that is suggestive of life-history trade-offs. When we fix to the MST value of ϕ=0.75, we find that best-fit values of μ cluster around 0.25 for trunk diameter, which is similar to the best-fit value we found for North America of 0.22. This suggests an as yet unexplained preferred ratio of mortality to growth across forests of very different types and locations.

Abstract. A significant proportion of the uncertainty in climate projections arises from uncertainty in the representation of land carbon uptake. Dynamic global vegetation models (DGVMs) vary in their representations of regrowth and competition for resources, which results in differing responses to changes in atmospheric CO2 and climate. More advanced cohort-based patch models are now becoming established in the latest DGVMs. These models typically attempt to simulate the size distribution of trees as a function of both tree size (mass or trunk diameter) and age (time since disturbance). This approach can capture the overall impact of stochastic disturbance events on the forest structure and biomass – but at the cost of increasing the number of parameters and ambiguity when updating the probability density function (pdf) in two dimensions. Here we present the Robust Ecosystem Demography (RED), in which the pdf is collapsed onto the single dimension of tree mass. RED is designed to retain the ability of more complex cohort DGVMs to represent forest demography, while also being parameter sparse and analytically solvable for the steady state. The population of each plant functional type (PFT) is partitioned into mass classes with a fixed baseline mortality along with an assumed power-law scaling of growth rate with mass. The analytical equilibrium solutions of RED allow the model to be calibrated against observed forest cover using a single parameter – the ratio of mortality to growth for a tree of a reference mass (μ0). We show that RED can thus be calibrated to the ESA LC_CCI (European Space Agency Land Cover Climate Change Initiative) coverage dataset for nine PFTs. Using net primary productivity and litter outputs from the UK Earth System Model (UKESM), we are able to diagnose the spatially varying disturbance rates consistent with this observed vegetation map. The analytical form for RED circumnavigates the need to spin up the numerical model, making it attractive for application in Earth system models (ESMs). This is especially so given that the model is also highly parameter sparse.

Vegetation is subject to multiple pressures in the 21st century, including changes in climate, atmospheric composition and human land-use. Changes in vegetation type, structure, and function also feed back to the climate through their impact on the surface-atmosphere fluxes of carbon and water. Dynamic Global Vegetation Models (DGVMs), are therefore key component of the latest Earth System Models (ESMs). Model projections for the future land carbon sink still span a wide range, in part due to the difficulty of representing complex ecosystem and biogeochemical processes at large scales (i.e. grid lengths ≈ 100km). The challenge for developers of DGVMs is therefore to find an optimal balance between detailed process representation and the ability to scale-up. We categorise DGVMs into four groups; Individual, Average Area, Two Dimensional Cohort and One Dimensional Cohort models. From this we review popular methods used to represent dynamic vegetation within the context of Earth System modelling. We argue that the minimum level of complexity required to effectively model changes in carbon storage under changing climate and disturbance regimes, requires a representation of tree size distributions within forests. Furthermore, we find that observed size distributions are consistent with Demographic Equilibrium Theory, suggesting that One Dimensional Cohort models with a focus on tree size, offer the best balance between computational tractability and realism for ESM applications.

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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 5 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, 10 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 15 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. also assumed the same growth scaling as MST. In this study we test two versions of DET, one with the MST growth scaling and another where the assumed power law scaling of growth has an exponent that is also allowed to vary as a fitting parameter.So this study will test which of the models is the best choice for trunk diameter distributions, for mass distributions and for also for total biomass density prediction for the Amazon. 2 Theory 5 2.1 Demographic Equilibrium Theory (DET)The distribution of tree sizes in a forest can be understood in terms of how the growth and mortality of the trees vary with tree size (Kohyama et al., 2003;Coomes et al., 2003; Muller-Landau et al., 2006b). For a given size class (i.e. range of tree size), then trees smaller than that ra...