Bayesian Methods in Conservation Biology

: Bayesian statistical inference provides an alternate way to analyze data that is likely to be more appropriate to conservation biology problems than traditional statistical methods. I contrast Bayesian techniques with traditional hypothesis-testing techniques using examples applicable to conservation. I use a trend analysis of two hypothetical populations to illustrate how easy it is to understand Bayesian results, which are given in terms of probability. Bayesian trend analysis indicated that the two populations had very different chances of declining at biologically important rates. For example, the probability that the first population was declining faster than 5% per year was 0.00, compared to a probability of 0.86 for the second population. The Bayesian results appropriately identified which population was of greater conservation concern. The Bayesian results contrast with those obtained with traditional hypothesis testing. Hypothesis testing indicated that the first population, which the Bayesian analysis indicated had no chance of declining at >5% per year, was declining significantly because it was declining at a slow rate and the abundance estimates were precise. Despite the high probability that the second population was experiencing a serious decline, hypothesis testing failed to reject the null hypothesis of no decline because the abundance estimates were imprecise. Finally, I extended the trend analysis to illustrate Bayesian decision theory, which allows for choice between more than two decisions and allows explicit specification of the consequences of various errors. The Bayesian results again differed from the traditional results: the decision analysis led to the conclusion that the first population was declining slowly and the second population was declining rapidly. Resumen: Las inferencias de la estadistica Bayesiana proveen una forma alternativa de analizar datos que probablemente sea mas apropiada para la conservacion biologica que los metodos estadisticos tradicionales. Compare tecnicas Bayesianas con tecnicas tradicionales de prueba de hipotesis, mediante el uso de ejemplos aplicables a la conservacion. Utilice un analisis de tendencias de dos poblaciones hipoteticas para ilustrar lo facil que es entender los resultados Bayesianos, los cuales se obtienen en forma de probabilidades. El analisis Bayesiano de tendencias indico que las dos poblaciones tenian probabilidades muy diferentes de disminuir a tasas biologicamente importantes. Por ejemplo, la probabilidad de que la primera poblacion disminuyera mas de un 5% por ano fue de 0.0, comparada con una probabilidad de un 0.86 para la segunda poblacion. Los resultados Bayesianos identifican adecuadamente cual poblacion era la de mayor interes para conservar. Los resultados Bayesianos se contrastan con aquellos obtenidos mediante pruebas de hipotesis tradicionales. Las pruebas de hipotesis indicaron que la primera poblacion ( la cual fue indicada por las pruebas Bayesianas como teniendo una probabilidad de disminucion mayor al 5% por ano) disminuia significativamente debido a que la disminucion ocurria a una tasa muy baja y las estimaciones de abundancia eran precisas. A pesar de la alta probabilidad de que la segunda poblacion experimente una disminucion seria, la prueba de hipotesis fallo al rechazar la hipotesis nula de no-disminucion, debido a que las estimaciones de abundancia eran poco precisas. Extendi el analisis de tendencias para ilustrar la teoria de decision Bayesiana, la cual permite decidir entre mas de dos posibilidades y permite una especificacion explicita de las consecuencias de varios errores. Los resultados Bayesianos difirieron una vez mas de los resultados tradicionales: el analisis de decisiones condujo a la conclusion de que la primera poblacion disminuia despacio y la segunda disminuia rapidamente.