Using multistage design-based methods to construct abundance indices and uncertainty measures for Delta Smelt

Population abundance indices and estimates of uncertainty are starting points for many scientific endeavors. However, if the indices are based on data collected by different monitoring programs with possibly different
sampling procedures and efficiencies, applying consistent methodology for calculating them can be complicated. Ideally the methodology will provide indices and associated measures of uncertainty that account for the sample design, the level of sampling effort (e.g., sample size), and capture or detection probabilities. We develop and demonstrate such consistent methodology to multiple monitoring programs that sample different life stages of Delta Smelt, a critically endangered fish species endemic to the San Francisco Estuary whose abundance indices have been at the center of much controversy and debate given the regulatory consequences of their listed status. Current indices use different and incomparable methods, do not account for gear selectivity, and do not provide measures of uncertainty. Using recently available information on gear specific length-based conditional probabilities of capture given availability, we develop new abundance indices along with measures of uncertainty using a single methodological approach. These new indices are highly correlated with existing ones, but the approach applied here illuminates different sources of bias and quantifies between year variation using probabilistic statements where the previous indices cannot. Decomposition of uncertainty into constituent sources reveals that early life-stage uncertainty is dominated by gear inefficiency while later life-stage uncertainty is dominated by sample size, thus providing guidance for improvements to existing surveys. An additional result of general methodological interest is a demonstration, via simulation intended to reflect realistic data properties, that use of a lognormal distribution is to be preferred over the normal distribution for making probabilistic statements about the indices. The work here facilitates the fitting of models attempting to identify factors associated with the dynamics and decline of the species.