A meta-analytic approach to quantifying scientific uncertainty in stock assessments

Quantifying scientific uncertainty when setting total allowable catch limits for fish stocks is a major challenge, but it is a requirement in the United States since changes to national fisheries legislation. Multiple sources of error are readily identifiable, including estimation error, model specification error, forecast error, and errors associated with the definition and estimation of reference points. Our focus here, however, is to quantify the influence of estimation error and model specification error on assessment outcomes. These are fundamental sources of uncertainty in developing scientific advice concerning appropriate catch levels and although a study of these two factors may not be inclusive, it is feasible with available information. For data-rich stock assessments conducted on the U.S. west coast we report approximate coefficients of variation in terminal biomass estimates from assessments based on inversion of the assessment of the model’s Hessian matrix (i.e., the asymptotic standard error). To summarize variation “among” stock assessments, as a proxy for model specification error, we characterize variation among multiple historical assessments of the same stock. Results indicate that for 17 groundfish and coastal pelagic species, the mean coefficient of variation of terminal biomass is 18%. In contrast, the coefficient of variation ascribable to model specification error (i.e., pooled among-assessment variation) is 37%. We show that if a precautionary probability of overfishing equal to 0.40 is adopted by managers, and only model specification error is considered, a 9% reduction in the overfishing catch level is indicated.

Using experiments and expert judgment to model catchability of Pacific rockfishes in trawl surveys, with application to bocaccio (Sebastes paucispinis) off British Columbia

The time series of abundance indices for many groundfish populations, as determined from trawl surveys, are often imprecise and short, causing stock assessment estimates of abundance to be imprecise. To improve precision, prior probability distributions (priors) have been developed for parameters in stock assessment models by using meta-analysis, expert judgment on catchability, and empirically based modeling. This article presents a synthetic approach for formulating priors for rockfish trawl survey catchability (qgross). A multivariate prior for qgross for different surveys is formulated by using 1) a correction factor for bias in estimating fish density between trawlable and untrawlable areas, 2) expert judgment on trawl net catchability, 3) observations from trawl survey experiments, and 4) data on the fraction of population biomass in each of the areas surveyed. The method is illustrated by using bocaccio (Sebastes paucipinis) in British Columbia. Results indicate that expert judgment can be updated markedly by observing the catch-rate ratio from different trawl gears in the same areas. The marginal priors for qgross are consistent with empirical estimates obtained by fitting a stock assessment model to the survey data under a noninformative prior for qgross. Despite high prior uncertainty (prior coefficients of variation ≥0.8) and high prior correlation between qgross, the prior for qgross still enhances the precision of key stock assessment quantities.

Length correction for larval and early-juvenile Atlantic menhaden (Brevoortia tyrannus) after preservation in alcohol

Body length measurement is an important part of growth, condition, and mortality analyses of larval and juvenile fish. If the measurements are not accurate (i.e., do not reflect real fish length), results of subsequent analyses may be affected considerably (McGurk, 1985; Fey, 1999; Porter et al., 2001). The primary cause of error in fish length measurement is shrinkage related to collection and preservation (Theilacker, 1980; Hay, 1981; Butler, 1992; Fey, 1999). The magnitude of shrinkage depends on many factors, namely the duration and speed of the collection tow, abundance of other planktonic organisms in the sample (Theilacker, 1980; Hay, 1981; Jennings, 1991), the type and strength of the preservative (Hay, 1982), and the species of fish (Jennings, 1991; Fey, 1999). Further, fish size affects shrinkage (Fowler and Smith, 1983; Fey, 1999, 2001), indicating that live length should be modeled as a function of preserved length (Pepin et al., 1998; Fey, 1999).

A stochastic model of temporal variations in monthly temperature, precipitation, snowfall, and resulting snowpack

We report a Monte Carlo representation of the long-term inter-annual variability of monthly snowfall on a detailed (1 km) grid of points throughout the southwest. An extension of the local climate model of the southwestern United States (Stamm and Craig 1992) provides spatially based estimates of mean and variance of monthly temperature and precipitation. The mean is the expected value from a canonical regression using independent variables that represent controls on climate in this area, including orography. Variance is computed as the standard error of the prediction and provides site-specific measures of (1) natural sources of variation and (2) errors due to limitations of the data and poor distribution of climate stations. Simulation of monthly temperature and precipitation over a sequence of years is achieved by drawing from a bivariate normal distribution. The conditional expectation of precipitation. given temperature in each month, is the basis of a numerical integration of the normal probability distribution of log precipitation below a threshold temperature (3°C) to determine snowfall as a percent of total precipitation. Snowfall predictions are tested at stations for which long-term records are available. At Donner Memorial State Park (elevation 1811 meters) a 34-year simulation - matching the length of instrumental record - is within 15 percent of observed for mean annual snowfall. We also compute resulting snowpack using a variation of the model of Martinec et al. (1983). This allows additional tests by examining spatial patterns of predicted snowfall and snowpack and their hydrologic implications.

A general framework for integrating environmental time series into stock assessment models: model description, simulation testing, and example

We present a method to integrate environmental time series into stock assessment models and to test the significance of correlations between population processes and the environmental time series. Parameters that relate the environmental time series to population processes are included in the stock assessment model, and likelihood ratio tests are used to determine if the parameters improve the fit to the data significantly. Two approaches are considered to integrate the environmental relationship. In the environmental model, the population dynamics process (e.g. recruitment) is proportional to the environmental variable, whereas in the environmental model with process error it is proportional to the environmental variable, but the model allows an additional temporal variation (process error) constrained by a log-normal distribution. The methods are tested by using simulation analysis and compared to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. In the traditional method, the estimates of recruitment were provided by a model that allowed the recruitment only to have a temporal variation constrained by a log-normal distribution. We illustrate the methods by applying them to test the statistical significance of the correlation between sea-surface temperature (SST) and recruitment to the snapper (Pagrus auratus) stock in the Hauraki Gulf–Bay of Plenty, New Zealand. Simulation analyses indicated that the integrated approach with additional process error is superior to the traditional method of correlating model estimates with environmental variables outside the estimation procedure. The results suggest that, for the snapper stock, recruitment is positively correlated with SST at the time of spawning.

The measurement error in marine survey catches: the bottom trawl case

We have formulated a model for analyzing the measurement error in marine survey abundance estimates by using data from parallel surveys (trawl haul or acoustic measurement). The measurement error is defined as the component of the variability that cannot be explained by covariates such as temperature, depth, bottom type, etc. The method presented is general, but we concentrate on bottom trawl catches of cod (Gadus morhua). Catches of cod from 10 parallel trawling experiments in the Barents Sea with a total of 130 paired hauls were used to estimate the measurement error in trawl hauls. Based on the experimental data, the measurement error is fairly constant in size on the logarithmic scale and is independent of location, time, and fish density. Compared with the total variability of the winter and autumn surveys in the Barents Sea, the measurement error is small (approximately 2–5%, on the log scale, in terms of variance of catch per towed distance). Thus, the cod catch rate is a fairly precise measure of fish density at a given site at a given time.