A beta distribution-based moment closure enhances the reliability of trait-based aggregate models for natural populations and communities

Ecological communities are complex adaptive systems that exhibit remarkable feedbacks between their biomass and trait dynamics. Trait-based aggregate models cope with this complexity by focusing on the temporal development of the community’s aggregate properties such as its total biomass, mean trait and trait variance. They are based on particular assumptions about the shape of the underlying trait distribution, which is commonly assumed to be normal. However, ecologically important traits are usually restricted to a finite range, and empirical trait distributions are often skewed or multimodal. As a result, normal distribution-based aggregate models may fail to adequately represent the biomass and trait dynamics of natural communities. We resolve this mismatch by developing a new moment closure approach assuming the trait values to be beta-distributed. We show that the beta distribution captures important shape properties of both observed and simulated trait distributions, which cannot be captured by a Gaussian. We further demonstrate that a beta distribution-based moment closure can strongly enhance the reliability of trait-based aggregate models. We compare the biomass, mean trait and variance dynamics of a full trait distribution (FD) model to the ones of beta (BA) and normal (NA) distribution-based aggregate models, under different selection regimes. This way, we demonstrate under which general conditions (stabilizing, fluctuating or disruptive selection) different aggregate models are reliable tools. All three models predicted very similar biomass and trait dynamics under stabilizing selection yielding unimodal trait distributions with small standing trait variation. We also obtained an almost perfect match between the results of the FD and BA models under fluctuating selection, promoting skewed trait distributions and ongoing oscillations in the biomass and trait dynamics. In contrast, the NA model showed unrealistic trait dynamics and exhibited different alternative stable states, and thus a high sensitivity to initial conditions under fluctuating selection. Under disruptive selection, both aggregate models failed to reproduce the results of the FD model with the mean trait values remaining within their ecologically feasible ranges in the BA model but not in the NA model. Overall, a beta distribution-based moment closure strongly improved the realism of trait-based aggregate models.