Robust Ecosystem Demography (RED): Emergent simplicity of tree size distributions.

Understanding how the terrestrial biomass will respond to climate perturbations is currently a large source of uncertainty within ESMs (Sitch et al., 2008). Cohort based models have been a recent development of DGVMs that can improve representation of size dependent interactions between the environment and species normally seen in individual based models while removing stochastic characteristics within global runs (Fisher et al., 2018) .

RED partitions the population of a PFT into size classes, of an appropriate variable (biomass, basal diameter) across the physiological range. Using a biomass/basal-diameter spaced advection equation that accounts for size dependent scaling of the structural growth and mortality across the classes, we are able to model how the population evolves over time.

By assuming a power scaling size-growth relationship with constant mortality, RED derives a quasi-Weibull distribution for the forest steady state. When compared to forest inventory data the solution provides a realistic fit (Moore et al., 2018). By applying a boundary condition limiting seedlings to open space, RED can derive solutions for the total vegetation fraction, biomass, and other variables by only knowing two parameters - the background ratio of mortality and growth and the fraction of NPP going into seedling production. From this, we have shown that RED can obtain realistic global outputs for biomass densities and evalutory metrics.

The analytical solutions derived from the foundational equations and assumptions of RED suggests an inherent simplicity of the forest structure, with low competition between trees, strong competition for seedlings, and size-independent mortality. Divergence from the analytical solution could indicate a historic disturbance. As RED allows for representation of asymmetrical mortality and growth, disturbances in which size is important can be dynamically simulated. The theory and model allows for potential insights into how ecosystems will respond to future increases in CO2 and disturbances.