Scale invariant spatio-temporal patterns of field vole density

1. Recent characterizations of the spatial scale of population dynamics have typically considered patterns at a single scale and ignored the possibility that different patterns may arise at different scales. In this study we assessed population densities of field voles with cyclic dynamics in northern England at 147 sites from three spatial scales on five occasions over a 2.5-year period.

2. The scale over which densities were similar was estimated by comparing the variance of density at the three scales (< 1 km(2), 10 km(2), and 70 km(2)) and by using autocorrelation techniques. Closer sites were more similar in density than more distant sites and the autocorrelations suggested that sites up to within 8-20 km had more similar densities and higher population synchrony than the average similarity for all the sampling sites.

3, A generalized additive model fitted to all the data showed that the data supported the hypothesis of a travelling wave of vole densities moving through the study area. The model assumed that the wave moved at a constant speed and in a uniform direction. Estimates of the wave's speed (14 km year(-1)) and direction (travelling in a direction of 66<degrees> from north) were consistent with the estimates which had previously been calculated from a time series of vole densities covering a much smaller spatial area but a longer temporal scale.

4. The spatio-temporal pattern of vole densities detected over a small spatial scale therefore appears to extend over much larger scales and occurs despite the fragmentation of suitable vole habitat at local (a few square kilometres) and regional (hundreds of square kilometres) scales.