Taylor's law (TL) describes a relationship between the variance and mean of population density: log10(variance) ≈ log10(a) + b × log10(mean). Many empirical estimates of b fall in 1 < b < 2, although varied models lead to b ≥ 2 and b ≤ 1. We hypothesized that another factor beside log10(mean) worked in the variance-mean relationship and focused on possible density-independent effects. We analyzed the temporal TL, based on the mean and variance over time for 70 populations of the gray-sided vole in Hokkaido, Japan. The dynamics of vole population were described by a second-order autoregressive model, assuming that Xt, a centered natural logarithm of empirically estimated density of year t, came from a normal distribution with mean = (1 + a1) × Xt-1 + a2 × Xt-2 and standard deviation SD = σ, where a1 and a2 were density-dependent coefficients and σ was the density-independent parameter. TL, log10(variance) ≈ 0.141 + 1.731 × log10(mean), explained approximately 60% of the variation in log10(variance). An extended model including σ^2 improved the model performance, explaining approximately 85% of the log10(variance) variation; log10(variance) ≈ –0.475 + 2.068 × log10(mean) + 0.273 × σ^2. To explore the origin of σ^2, we analyzed meteorological data (temperature and precipitation) observed near each vole population. The 43% of variation in σ^2 was explained by the variance of temperature and precipitation. A modified model, replacing σ^2 with the variances in temperature or precipitation from March to June, performed better than the original TL model. Our simulations of hypothetical time series with possible density-dependent coefficients (a1 and a2) reproduced the empirically observed pattern (demonstrated here) that the deviation of the slope b from b = 2 was higher in time series with lower model performance. In addition, a negative correlation between log10(mean) and σ^2 was found to be critical in forming b < 2. These results reveal new aspects of the relationship between variance in population density and environmental variability.