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Jagged lines: five realizations of a stochastic logistic model. The model is a diffusion process representing a logistic "skeleton" with environmental "noise". Unimodal smooth line: theoretical gamma probability distribution of population abundance represents the equilibrium (stationary distribution) of the stochastic model. Smooth sigmoid line: solution trajectory of the deterministic logistic model. See: Dennis, B. & Costantino, R. F. 1988. Analysis of steady-state populations with the gamma abundance model: applications to Tribolium. Ecology 69: 1200-1213.