Using Multistage Design‐Based Methods to Construct Abundance Indices and Uncertainty Measures for Delta Smelt

Abstract

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 the capture or detection probabilities. We develop and demonstrate consistent methodology for multiple monitoring programs that sample different life stages of Delta Smelt Hypomesus transpacificus, a critically endangered fish species endemic to the San Francisco Estuary, whose abundance indices have been at the center of much controversy 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 by means of a single methodological approach. These new indices are highly correlated with existing ones, but the approach taken here illuminates different sources of bias and quantifies between‐year variation using probabilistic statements where the previous indices cannot. Decomposition of uncertainty into its 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 a lognormal distribution is preferable to 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.

Resistance and resilience of pelagic and littoral fishes to drought in the San Francisco Estuary

“…It seems unlikely that the level of population declines and recoveries observed in the SFE would be predominantly driven by gear avoidance (Tobias 2020). The overall patterns seen in this study are generally consistent with those observed in larval fish surveys where swimming capabilities of fishes would be of less concern (Dege and Brown 2004), other sampling methods that we expect to be unaffected by turbidity (Grimaldo et al 2009), and with studies that have adjusted for fish catchability (Mahardja et al 2017b, Peterson and Barajas 2018, Polansky et al 2019).…”

“…In addition, spawning for some species (e.g., Sacramento sucker, striped bass, American shad) occur in upstream tributaries not sampled in our study area and a portion of their young‐of‐year may continue to rear in these upstream areas (Moyle 2002). The imperfect spatial coverage of our data may bias our resistance and resiliency estimates to some extent; however, most of the juvenile fishes we analyzed either migrate through or occur largely within our study area, and the patterns described in our study are consistent with large‐scale changes in the populations of these fish species documented by other monitoring programs (Brown and Michniuk 2007, Feyrer et al 2015, Polansky et al 2019). Last, our analysis did not account for catchability or detection probability, which can often vary considerably over time and space (MacKenzie et al 2002).…”

Improving inference for nonlinear state‐space models of animal population dynamics given biased sequential life stage data

“…Different choices of the conditional distribution for can be made, which in turn can affect inference (Knape et al ., 2011). We chose a lognormal distribution because it ensures strictly positive abundance indices (especially useful when abundance indices are near zero), it is perhaps the most common assumption (although more often in terms of a normal distribution when working with log abundances), and because earlier work (Polansky et al ., 2019) suggests it is to be preferred over a normal distribution for the case study model described in Section 5.…”

Did a Shifting Ecological Baseline Mask the Predatory Effect of Striped Bass on Delta Smelt?

“…Delta Smelt were considered to have been abundant until the early 1980s, when relatively large and prolonged declines in available abundance indices were first observed (Moyle et al 1992;2016). Delta Smelt abundance indices declined abruptly again in the early 2000s; the latter resulting in a nearly continual decline to its contemporary nearly extirpated status (Thomson et al 2010;Polansky et al 2019).…”