CHAOS IN MICROTINE POPULATIONS

On the basis of nonlinear time-series analysis of vole data, Turchin ( 1993) proposed that there is a latitudinal shift from stability to cha os in the dynamics of vole populations. Falck et al. (1995) question s everal aspects of the approach I used. In particular, they point out t hat no measure of uncertainty has been calculated for each point estim ate of the dominant Lyapunov exponent (a positive Lyapunov exponent im plies chaos, while a negative one implies stability). In this note I r espond to the criticisms of Falck et al. (1995). As part of my respons e, I analyse fluctuations of pooled numbers of microtine rodents at al l European locations for which I currently have data. Treating each ge ographic location as a replicate, I show that the mean Lyapunov expone nt is significantly greater than zero in northern populations (latitud e greater than 60 degrees N).