Voles and lemmings: Chaos and uncertainty in fluctuating populations

Turchin (Oikos 68, 167-172 (1993)) provided point estimates of the dominant Lyapunov exponent suggesting that chaos occurs in microtines north of 60 degrees N. Falck et al. (Proc. R. Soc. Lond. B 261, 159-165 (1995)) proposed to use bootstrapping methodology to investigate the uncertainty associated with the reported estimates. Based on this, Falck et al. (1995) found no reason to conclude that the northern populations are chaotic. The methodology employed, and the conclusions reached, were criticized by Turchin (Proc. R. Sec. Lend. B 262, 357-361 (1995)). Here we discuss the critique as well as analyse the new data set introduced by Turchin (1995). In addition to analysing pooled data for all microtines at seventeen localities (as Turchin does), we also analyse data for each species at the sites separately. As an integral part of our response, we address some fundamental statistical and biological issues. We reach the same conclusion as earlier: there is no statistical evidence to conclude that northern microtine populations are characterized by chaotic dynamics.