Distribution of animal population fluctuations

We show that the fluctuations of a variety of animal (insect, mammal and fish) populations are well-modeled by stable (Lévy) distributions, a family of distributions which includes the Gaussian. Our findings together with the finding [A.P. Allen, B.-L. Li, E.L. Charnov, Ecol. Lett. 4 (2001) 1–3] that bird population fluctuations are well-modeled by Gaussian distributions suggest the hypothesis that, in general, animal population fluctuations are well-modeled by stable distributions. If the hypothesis is confirmed, the stable law for the distribution of animal population fluctuations would be useful for animal population modeling, prediction and management.

Research highlights
► The fluctuations of a variety of animal populations are stable distributed.
► Our findings and a previous finding suggest this behavior is universal.
► Such a universal law would have important ecological implications.