Population dynamics, synchrony, and environmental quality of Hokkaido voles lead to temporal and spatial Taylor's laws.

Taylor's law (TL) asserts that the variance in a species' population density is a power-law function of its mean population density: log(variance) = a + b × log(mean). TL is widely verified. We show here that empirical time series of density of the Hokkaido gray-sided vole, Myodes rufocanus, sampled 1962-1992 at 85 locations, satisfied temporal and spatial forms of TL. The slopes (b ± standard error) of the temporal and spatial TL were estimated to be 1.613 ± 0.141 and 1.430 ± 0.132, respectively. A previously verified autoregressive Gompertz model of the dynamics of these populations generated time series of density which reproduced the form of temporal and spatial TLs, but with slopes that were significantly steeper than the slopes estimated from data. The density-dependent components of the Gompertz model were essential for the temporal TL. Adding to the Gompertz model assumptions that populations with higher mean density have reduced variance of density-independent perturbations and that density-independent perturbations are spatially correlated among populations yielded simulated time series that satisfactorily reproduced the slopes from data. The slopes (b ± standard error) of the enhanced simulations were 1.619 ± 0.199 for temporal TL and 1.575 ± 0.204 for spatial TL.