TAYLOR POWER-LAW AND THE MEASUREMENT OF VARIATION IN THE SIZE OF POPULATIONS IN-SPACE AND TIME

The problems of the measurement of variation and the selection of appropriate spatial and temporal units of observation are discussed. Besides theoretical considerations, the performance of variability measures in data on annual catches of noctuid moths was assessed. Any measure of variability is potentially biased by its dependence on mean population size. The crucial role of dependence of variance on the mean is indicated. Taylor's power law is not a good model when the population mean is low. The potential bias is large when the population mean is small; in real data, the dependence of SD[log(N+1)], CV and Lloyd's index was weak when the mean annual catch was greater than 5 individuals. Lloyd's index was the least dependent on the mean. There is no single appropriate spatial or temporal scale for the analysis of variability. Specific scales are appropriate to specific questions. Multiple scale pattern analyses of time series and transects or grids are informative.