Assessing the effect of poisoning programs on the density of non-target fauna: Design and interpretation

To establish whether poisoning programs affect non-target density, the null hypothesis that density does not decline on poisoned sites needs to be tested. However, where no statistically significant reduction in density is found, there is some probability that a biologically significant reduction has been overlooked. The probability that such an error has occurred (a Type 2 error) depends on the effect poisoning has on non-target density, the precision with which the reduction is assessed, and the number of poisoning operations sampled. Prospective power analysis can identify minimum sample sizes that reduce the probability of a Type 2 error to acceptable levels. Equivalence tests require a priori identification of the minimum change in non-target density that can be safely overlooked and the acceptable probability of doing so. As such, they explicitly link the statistical and biological significance of non-target poisoning assessments. We illustrate these principles using an experimental assessment of the effect rabbit poisoning has on the density of large kangaroo populations in Australia. A rule-of-thumb guide was used to estimate appropriate levels of power (0.85) and reductions in kangaroo density (r = -0.12) for the assessment, and a pilot study conducted to estimate the between-sample standard deviation for estimates of change in kangaroo density(s = 0.089). Prospective power analysis based on these estimates indicated that 6 poisoning programs would provide a robust assessment of the effect of poisoning on kangaroos. However, because the between-sample standard deviation was underestimated, a subsequent assessment based on 6 samples had insufficient power to usefully estimate the effect poisoning had on kangaroos. Retrospective power analysis indicated that at 0.85 power, reductions in kangaroo density as high as r=—2.2 may have been overlooked. Using the between-sample standard deviation from this assessment, changes in kangaroo density would have to be estimated for 17-19 poisoning programs if a subsequent experiment was to achieve a biologically as well as statistically robust result.