Spatial asynchrony and periodic travelling waves in cyclic populations of field voles

We demonstrate evidence for the presence of travelling waves in a cyclic population of field voles in northern Britain by fitting simple, empirical models to spatially referenced time series data. Population cycles were broadly synchronous at all sites, but use of Mantel correlations suggested a strong spatial pattern along one axis at a projection line 72 degrees from North. We then fitted a generalized additive model to log population density assuming a fixed-form travelling wave in one spatial dimension for which the density at each site was offset in time by a constant amount from a standard density-time curve. We assumed that the magnitude of this offset would be proportional to the spatial separation between any given site and the centroid of the sampling sites, where separation is the distance between sites in a fixed direction. After fitting this model, we estimated that the wave moved at an average speed of 19 km yr-1, heading from West to East at an angle of 78 degrees from North. Nomadic avian predators which could synchronize populations over large areas are scarce and the travelling wave may be caused by density-dependent dispersal by field voles and/or predation by weasels, both of which act at a suitably small spatial scale.