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Spatial distribution, sampling efficiency and Taylor's power law. 2. Interpreting density‐dependent sampling efficiency

The intimate relationship between sampling efficiency and Taylor's power law (TPL) was investigated with gypsy moth sample data. The data were used to compute sampling efficiency directly and indirectly by TPL. Comparison of TPLs and efficiency plots of male and female pupae confirmed the identities linking TPL with sampling efficiency. Divergence of sex‐specific TPL plots indicated local scale density‐dependent sex ratio. Egg mass sample data confirmed the sampling efficiency and TPL identities provided the same variance and mean vectors were used to compute TPLs. Small differences in sample numbers destroy the identities but approximate efficiency estimates are still obtainable from the TPLs. Sampling efficiency of timed walks, fixed area and variable area surveys were estimated and ranked. Rescaling moth catches per trap to number per unit volume changes slope, intercept and correlation coefficient while stretching the pattern of data points. Comparison of absolute density estimates over two different time intervals showed density‐dependent variation declining with increasing sample interval. Fitting power laws by ordinary dependent regression is less efficient than fitting by geometric mean regression and produces biased regression parameters. The significance of this for the analysis and interpretation of ecological sample data generally is discussed.