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

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 (inline-formulaμ) 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 inline-formulaϕ=0.71 (0.31 for trunk diameter). This finding is broadly consistent with exponents of inline-formulaϕ=0.75 (inline-formula $M4inlinescrollmathml\mathrm{italic \varphi }=normal 1/normal 3$ 42pt14ptsvg-formulamathimg8f39ef606946bf9e7e0963b396242328 bg-17-1013-2020-ie00001.svg42pt14ptbg-17-1013-2020-ie00001.png for trunk diameter) predicted by metabolic scaling theory (MST) allometry. The fitted inline-formulaϕ and inline-formulaμ parameters also show a clear relationship that is suggestive of life-history trade-offs. When we fix to the MST value of inline-formulaϕ=0.75, we find that best-fit values of inline-formulaμ cluster around inline-formula0.25 for trunk diameter, which is similar to the best-fit value we found for North America of inline-formula0.22. This suggests an as yet unexplained preferred ratio of mortality to growth across forests of very different types and locations.

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Moore, Jonathan R. / Argles, Arthur P. K. / Zhu, Kai / et al: Validation of demographic equilibrium theory against tree-size distributions and biomass density in Amazonia. 2020. Copernicus Publications.

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