Population biologists have long been interested in the variability of natural populations(1-6). One approach to dealing with ecological complexity is to reduce the system to one or a few species, for which meaningful equations can be solved Here we explore an alternative approach(7,8) by studying the statistical properties of a data set containing over 600 species, namely the North American breeding bird survey(9). The survey has recorded annual species abundances over a 31-year period along more than 3,000 observation routes(10). We now analyse the dynamics of population variability using this data set, and find scaling features in common with inanimate systems composed of strongly interacting subunits(11). Specifically, we find that the distribution of changes in population abundance over a one-year interval is remarkably symmetrical, with long tails extending over six orders of magnitude. The variance of the population over a time series increases as a power-law with increasing time lag, indicating long-range correlation in population size fluctuations(12). We also find that the distribution of species lifetimes (the time between colonization and local extinction) within local patches is a power-law with an exponential cutoff imposed by the finite length of the time series. Our results provide a quantitative basis for modelling the dynamics of large species assemblages.