The abundance of a species population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a well-defined double-exponential (Laplace) distribution. This striking regularity allows us to devise a stochastic model despite seemingly irregular variations in population abundances. The model identifies the effect of reduced growth at low population density as a key factor missed in current approaches of population variability analysis and without which extinction risks are severely underestimated. The model also allows us to separate the effect of demographic stochasticity and show that single-species growth rates are dominantly determined by stochasticity common to all species. This dominance---and the implications it has for interspecies correlations, including co-extinctions---emphasizes the need of ecosystem-level management approaches to reduce the extinction risk of the individual species themselves.
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