A theory of demographic optimality in forests

Carbon uptake by the land is a key determinant of future climate change. Unfortunately, Dynamic Global Vegetation Models have many unknown internal parameters which leads to significant uncertainty in projections of the future land carbon sink. By contrast, observed forest inventories in both Amazonia and the USA show strikingly common tree-size distributions, pointing to a simpler modelling paradigm. The curvature of these size-distributions is related to the ratio of mortality to growth in Demographic Equilibrium Theory (DET). We extend DET to include recruitment limited by competitive exclusion from existing trees. From this, we find simultaneous maxima of tree density and biomass in terms of respectively the ratio of mortality to growth and the proportion of primary productivity allocated to reproduction, an idea we call Demographic Optimality (DO). Combining DO with the ratio of mortality to growth common to the US and Amazon forests, results in the prediction that about an eighth of productivity should be allocated to reproduction, which is broadly consistent with observations. Another prediction of the model is that seed mortality should decrease with increasing seed size, such that the advantage of having many small seeds is nullified by the higher seed mortality. Demographic Optimality is therefore consistent with the common shape of tree-size distributions seen in very different forests, and an allocation to reproduction that is independent of seed size.