Before revision: The remarkable empirical finding that extensive fine-scale diversity is stable on long time scales, despite selective pressures, has spurred the study of several models, which can explain species formationand stability. However, the focus has been more on the possible mechanisms which sustain coexistence, rather than on their universality and robustness. We thus consider a model that includes generic forms of many-body non-linear interactions, which are non-local and depend on a set of parameters. Despite the complicated dynamics, we are able to aptly identify a region in the parameter space where the dynamics manifests universal and robust features which extend to the weakly non-linear regime.
After revision: The remarkable empirical finding that extensive fine-scale diversity is stable on long time scales, despite selective pressures, has spurred the study of several models, which can explain pattern formation. The modulations of patterns, occurring on long spatial and temporal scales, can not be captured by linear approximation analysis. Here, we show that, starting from a general model with long range couplings displaying patterns, the spatio-temporal evolution of large scale modulations at the onset of instability is ruled by the well-known Ginzburg-Landau equation, independently of the weakly non-linear regime.