What abundance correlations actually measure in stochastic ecological communities
Abundance correlations cannot reveal ecological interactions without an assumption about the covariance of environmental noise. A natural biological expectation is that similar species respond similarly to environmental fluctuations, generating positive correlations. Yet the same species also tend to overlap more strongly in resource use and therefore compete more intensely, generating negative correlations. The simplest plausible benchmark is thus to take environmental-response correlations proportional to niche overlap. We show that, under this assumption and across a broad class of stochastic community models, the two effects cancel exactly: equal-time abundance correlations vanish, independently of interaction strength, heterogeneity, and system size. Away from this matched point, the observed correlations measure primarily the mismatch between shared environmental response and competition, rather than the interaction matrix itself. Correlations can recover information about niche overlap when competitive feedback is delayed relative to environmental forcing, but the inference then depends on a resource-response timescale that is generally not determined by the abundance time series alone. When stochasticity enters through the mechanism that generates similarity itself--for example, through fluctuating shared resources--nonzero correlations may persist, but they reflect yield-depletion mismatch rather than niche overlap. Abundance correlations therefore report how environmental variability reaches the community at least as much as they report who competes with whom.