Taylor's law applies to spatial variation in a human population

Abstract

Taylor's law (TL), which originated in ecology, states that, in many nonhuman populations, the logarithm of the variance of the population density in a set of populations is linearly related to the logarithm of the mean population density of those populations. TL has not been carefully tested by demographers of human populations. We found that TL described well the time course of spatial variation in the population density of the counties, municipalities, and regions of Norway. Plots of the logarithm of the variance of population density by county as a function of the logarithm of the mean of population density by county, with one point per year from 1978 through 2010, were remarkably close to straight lines. Because of the exceptional situation of Oslo, we conducted two analyses, including and omitting Oslo as a county. When Oslo was included, the relationship of log variance to log mean was non-linear for roughly a decade beginning in 1978, and linear regressions yielded different slopes for TL up to 1984 and after 1985, corresponding to the decline and growth of population in Oslo. When Oslo was excluded from the analysis, the curvature disappeared and the linear relationship of log variance to log mean was remarkably precise throughout 1978-2010 ( R 2 >0.99). This example suggests that non-demographic factors may influence the relationship between the spatial log variance and log mean of population density, but also that, in a stable environment (since the early 1980s), changes in the spatial distribution of population density can follow TL with remarkable precision. Joel E. COHEN, Professor of Populations, The Rockefeller University and Columbia University, 1230 York Avenue, Box 20, New York, New York 10065 USA. E-mail: cohen@rockefeller.edu . Meng XU, Laboratory of Populations, The Rockefeller University, 1230 York Avenue, Box 20, New York, 10065 USA. E-mail: mxu@rockefeller.edu . Helge BRUNBORG, Statistics Norway, Pb 8131 Dep, 0033 Oslo, Norway. E-mail: hbr@ssb.no . Joel E. COHEN, Professor of Populations, The Rockefeller University and Columbia University, 1230 York Avenue, Box 20, New York, New York 10065 USA. E-mail: cohen@rockefeller.edu . Meng XU, Laboratory of Populations, The Rockefeller University, 1230 York Avenue, Box 20, New York, 10065 USA. E-mail: mxu@rockefeller.edu . Helge BRUNBORG, Statistics Norway, Pb 8131 Dep, 0033 Oslo, Norway. E-mail: hbr@ssb.no .