The Uses of Statistical Power in Conservation Biology: The Vaquita and Northern Spotted Owl

The consequences of accepting a false null hypothesis can be acute in conservation biology because endangered populations leave little margin for recovery from incorrect management decisions. The concept of statistical power provides a method of estimating the probability of accepting a false null hypothesis. We illustrate how to calculate and interpret statistical power in a conservation context with two examples based on the vaquita ( Phocoena sinus ), an endangered porpoise, and the Northern Spotted Owl ( Strix occidentalis caurina ). The vaquita example shows how to estimate power to detect negative trends in abundance. Power to detect a decline in abundance decreases as populations become smaller, and, for the vaquita, is unacceptably low witin the range of estimated population sizes. Consequently, detection of a decline should not be a necessary criterion for enacting conservation measures for rare species. For the Northern Spotted Owl, estimates of power allow a reinterpretation of results of a previous demographic analysis that concluded the population was stable. We find that even if the owl population had been declining at 4% per year, the probability of detecting the decline was at most 0.64, and probably closer to 0.13; hence, concluding that the population was stable was not justified. Finally, we show how calculations of power can be used to compare different methods of monitoring changes in the size of small populations. The optimal method of monitoring Northern Spotted Owl populations may depend both on the size of the study area in relation to the effort expended and on the density of animals. At low densities, a demographic approach can be more powerful than direct estimation of population size through surveys. At higher densities the demographic approach may be more powerful for small populations, but surveys are more powerful for populations larger than about 100 owls. The tradeoff point depends on density but apparently not on rate of decline. Power decreases at low population sizes for both methods because of demographic stochasticity.