Equilibrium forest demography explains the distribution of tree sizes across North America

The distribution of tree sizes within a forest strongly influences how it will respond to disturbances and environmental changes such as future climate change and increases in atmospheric CO2. This means that global vegetation models must include variation in tree size to accurately represent carbon sinks, such as that seen in North America. Here we use an analytical model of large-scale forest demography which assumes tree growth varies as a power of tree diameter whilst tree mortality is independent of size. The equilibrium solutions of this model are able to accurately reproduce the tree-size distributions, for 61 species and four plant functional types, measured across North America, using just a single species-specific fitting parameter, μ, which determines the ratio of mortality to growth. The predictions of metabolic scaling theory for tree-size distributions are also tested and found to deviate significantly from observations and that maybe explained by the assumptions made about how individual trees fill the available space. We show that equilibrium forest demography implies a single curve that relates mean tree diameter to μ, and that this can be used to make reasonable estimates of the whole dataset mean trunk diameter by fitting only to the larger trees. Our analysis suggests that analytical solutions such as those in this paper may have a role in aiding the understanding and development of next-generation Dynamic Global Vegetation Models based on ecosystem demography.