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.
En conservacion biologica, las consecuencias de aceptar hipotesis nulas falsas pueden ser muy severas puesto que las poblaciones en peligro de extincion dejan poco margen para revertir el efecto de decisiones incorrectas de manejo. El concepto de poder estadistico provee un metodo para estimar la probabilidad de aceptar hipotesis nulas falsas. Nosotros ilustramos como calcular e interpretar el poder estadistico en un contexto de conservacion con dos ejemplos basados en la vaquita (Phocoena sinus), una marsopa en peligro de extincion, y el buho moteado del Norte (Strix occidentalis caurina). El ejemplo de la vaquita muestra como estimar el poder para detectar tendencias negativas en abundancia. El poder para detectar una disminucion en la abundancia decrece a medida que las poblaciones se hacen mas pequenas, y en el caso de la vaquita, es inaceptablemente bajo para el rango de tamanos poblacionales estimados. Por consiguiente, la deteccion de una declinacion en el tamano poblacional no debe ser un criterio necesario para decretar medidas de conservacion en especies raras. En el caso del buho moteado del Norte, la estimacion del poder permite la reinterpretacion de resultados de analisis demograficos previos que concluyeron que la poblacion era estable. Nosotros encontramos que aun si la poblacion del buho moteado a estado declinando un 4% por ano, la probabilidad de detectar esta declinacion fue de a lo sumo 0.64%, y probablemente mas cercana al 0.13%. Por consiguiente, no se justificaba concluir que la poblacion era estable. Finalmente, demostramos como los calculos de poder pueden ser usados para comparar distintos metodos de monitoreo de cambios en el tamano de poblaciones pequenas. El metodo optimo de monitoreo de las poblaciones del buho moteado del Norte depende quizas tanto del tamano del area de estudio en relacion con el esfuerzo realizado como de la densidad de los aminales. A bajas densidades, la aproximacion demografica puede ser mas poderosa que la estimacion directa del tamano poblacional a partir de evaluaciones. A mayores densidades la aproximacion demografica puede ser mas poderosa para poblaciones pequenas, pero las evaluaciones son mas poderosas para poblaciones de mas de 100 buhos. El punto de relacion (tradeoff) depende de la densidad pero aparantemente no depende de la tasa de declinacion. Para tamanos poblacionales bajos, el poder decrece para ambos metodos debido a la estocasticidad demografica.
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