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

Abstract

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.

Synchrony affects Taylor’s law in theory and data

“…Their example is consistent with our work and illustrates the value of our general results for understanding TL in specific systems. Using 31 y of population density data for the gray-sided vole, Myodes rufocanus, at 85 locations in Hokkaido, Japan, Cohen and Saitoh (20) verified that spatial and temporal TL held for the data as well as simulations of a previously validated Gompertz model of the dynamics of these populations. However, simulated time series had spatial and temporal TL slopes substantially steeper than those from data.…”

“…Although Eisler, et al (7) focus on temporal TL, they state without proof or details that many of their results also apply to TL more generally. Relationships between spatial and temporal TL have recently been examined (20) and may help connect the TL in the above example to the spatial TL of our study. Perhaps all of these versions of TL could be formally related to each other and synchrony.…”

“…However, simulated time series had spatial and temporal TL slopes substantially steeper than those from data. Cohen and Saitoh (20) observed that most pairs of vole populations were significantly temporally correlated and modified the Gompertz model accordingly. When densityindependent perturbations in model dynamics were synchronized, inducing synchrony in simulated population time series, and when simulated populations with higher mean density had a reduced variance of density-independent perturbations, the modeled slopes of spatial and temporal TL were reduced to values similar to those of the data.…”

“…It is the tendency for time series of population densities of the same species measured in geographically separated locations to be correlated through time. It has been observed in organisms as diverse as protists (17), insects (18), mammals (19,20), and birds (21; ref. 22 has many other examples).…”

“…Although some empirical and theoretical connections have been made between synchrony and TL (7,14,20,25), the connections are far from completely understood and do not encompass all versions of TL. Synchrony, like TL, may reflect aggregation, because the spatial extent of correlations among population time series indicates the geographic size of outbreaks (26).…”