Mapping the Regional Transition to Cyclicity in Clethrionomys rufocanus: Spectral Densities and Functional Data Analysis

We study the regional transitions in dynamics of the gray-sided vole, Clethrionomys rufocanus, within Hokkaido, Japan. The data-set consists of 225 time series of varying length (most from 23 to 31 years long) collected between 1962 and 1992 by the Forestry Agency of the Japanese Government. To see clearly how the periodic behavior changes geographically, we estimate the spectral density functions of the growth rates of all populations using a log-spline method. We subsequently apply functional data analysis to the estimated densities. The functional data analysis is, in this context, analogous to a principal component analysis applied to curves. We plot the results of the analysis on the map of Hokkaido, to reveal a clear transition from relatively stable populations in the southwest and west to populations undergoing 3-4 year cycles in the northeast and east. The degree of seasonality in the vegetation and the rodent demography appear to be strongest in the cyclic area. We briefly speculate that the destabilization of the rodent dynamics is linked to increased seasonalforcing on the trophic interactions in which the gray-sided voles are involved.