Efficacy of depletion models for estimating abundance of endangered fishes in streams

Conservation programs for imperiled fish require a sampling method for quantifying their habitat relationships and their progress toward recovery, via abundance estimation and subsequent monitoring. Depletion sampling is a commonly used method, although the assumptions of homogeneous capture probabilities are tenuous. Recently, Bayesian hierarchical models have been used to describe the conditional relationships between abundance of animals and detection probability, but their performance remains untested when detection varies across successive passes. We tested such approaches within a depletion-sampling framework for estimating abundance of three endemic and imperiled fish species in southeastern Arizona, USA. Our procedure uses depletion sampling, via simulation and field trials, and removes the untenable assumption of constant detectability across sampling passes. Specifically, we evaluated how population size, the number of depletion passes, the probability of fish detection, the amount of decline in this probability across removal passes, and the effects of variable detection probability affect bias and precision when using models with constant and variable detection probability. Abundance estimates were negatively biased when detection probability declined by 20% or more across successive passes, with detection probability <0.30 on the first pass. When detection probability declined by <10% across successive passes, unbiased estimates could be attained with detection probabilities of 0.20. Increasing depletion passes improved precision but not bias. Field trials underscored the importance of incorporating changes in detection probability among species and successive depletion passes. Our work demonstrates the efficacy of depletion experiments to estimate abundance, and highlights the importance of sampling a known abundance to accompany simulation analyses. Monitoring programs ignoring variability in detection probability using a depletion framework can produce biased abundance estimates.