Quantifying factors that explain the slopes of the temporal Taylor's law of Hokkaido vole populations

Abstract

AbstractTaylor's law (TL) describes the relationship between the variance and mean of population density: log10(variance) ≈ log10(a) + b × log10(mean), a > 0. This study analyzed the temporal TL, for which mean and variance are calculated over time, separately for each population in a collection of populations, considering the effects of the parameters of the Gompertz model (a second‐order autoregressive time‐series model) and the skewness of the density frequency distribution. Time series of 162 populations of the gray‐sided vole in Hokkaido, Japan, spanning 23–31 years, satisfied the temporal TL: log10(variancej) ≈ 0.199 + 1.687 × log10(meanj). This model explained 62% of the variation of log10(variancej). An extended model with explanatory variables log10(meanj), the density‐dependent coefficient for 1‐year lag (α1,j), that for 2‐year lag (α2,j), the density‐independent variability (σj2), and the skewness (γj), explained 93.9% of the log10(variancej) variation. In the extended model, the coefficient of log10(meanj) was 1.949, close to the null value (b = 2) of the TL slope. The standardized partial regression coefficients indicated that density‐independent effects (σj2 and γj) dominated density‐dependent effects (α1,j and α2,j) apart from log10(meanj). The negative correlations observed between σj2 and log10(meanj), and between γj and log10(meanj), played an essential role in explaining the difference between the estimated slope of TL (b = 1.687) and the null slope (b = 2). The effects of those explanatory variables on log10(variancej) were interpreted based on the theory of a second‐order autoregressive time‐series model.