Sequential testing of complementary hypotheses about population density

Abstract Making inferences about population density is paramount in ecology and pest management for decision‐makers who often seek to determine how a population compares to a pre‐established static or dynamic threshold through sampling or monitoring. Sequential data analysis is appealing for monitoring and decision making as it is more cost‐efficient than fixed‐sample‐size approaches. However, a limitation of existing sequential testing procedures is that they require specification of two non‐complementary competing hypotheses to allow for sequential calculation of probability ratios as sampling proceeds. We overcame this limitation by using Bayes' theorem to sequentially update the posterior probability of a tested hypothesis against its complementary as data is collected. The new test can explicitly consider simple or composite hypotheses about static or dynamic population densities and process either purely sequential (one‐at‐a‐time) or group sequential data to produce a trajectory of posterior probabilities related to the tested hypothesis. The efficiency of our new test is demonstrated with three case studies that involve inferences about static or dynamic pest populations and the detection of rare species through monitoring. Our new test, the sequential test of Bayesian posterior probabilities, offers a more efficient and accurate approach to assess if a sampled population exceeds or is below a threshold than probability ratios or fixed‐sample‐size approaches. Although the test requires fewer samples, more incorrect decisions may be produced for purely sequential designs when densities are below the thresholds (type I error), compared with probability ratios. We show the new test is a powerful, easily implementable framework with applications in natural resource and pest management, whose outputs are easily interpretable for decision making.