When does heterogeneity average out in coarse-grained ecological communities?
Luo, M.; Savage, V.; Song, C.
Show abstract
Ecological coarse-graining of individuals or species into aggregate variables, such as total biomass or regional abundance, is common practice, yet differences among species can still influence aggregate dynamics. We propose a metric for quantifying this irreducible dynamical heterogeneity. For small fluctuations near a stable equilibrium, we compare the aggregate fluctuation spectrum of the full dynamical system with that of the best Ornstein-Uhlenbeck model having the same dimension as the aggregate. The remaining spectral mismatch quantifies the dynamical effects of hidden differences that the fitted aggregate model cannot capture. For weakly interacting random community models at fixed collective interaction strength, we show that increasing species richness can either reduce or increase this heterogeneity, depending on how species interact. Our framework helps understand when ecological and evolutionary differences average out versus when their dynamical effects persist.
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