The nature of size fluctuations is crucial in forecasting future population persistence, independently of whether the variability stems from external forces or from the dynamics of the population renewal process. The risk of intercepting zero is highly dependent on the way the variance of the population size relates to its mean. The minimum population size required for a population not to go extinct can be determined by a scaling equation relating the variance to the arithmetic mean. By the use of a derived expression for the harmonic mean defined by the parameters of the scaling equation we show how it is possible to separate the domains of persistence from those of extinction and to facilitate the identification of populations on the brink of extinction.