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.

Larval abundance of summer flounder (Paralichthys dentatus) as a measure of recruitment and stock status

Summer flounder (Paralichthys dentatus) is one of the most economically and ecologically important estuarine-dependent species in the northeastern United States. The status of the population is currently a topic of controversy. Our goal was to assess the potential of using larval abundance at ingress as another fishery independent measure of spawning stock biomass or recruitment. Weekly long-term ichthyoplankton time series were analyzed from Little Egg Inlet, New Jersey (1989–2006) and Beaufort Inlet, North Carolina (1986–2004). Mean size-at-ingress and stage were similar between sites, whereas timing of ingress and abundance at ingress were not similar. Ingress primarily occurred during the fall at Little Egg Inlet and the winter at Beaufort Inlet. These findings agree with those from earlier studies in which at least two stocks (one north and one south of Cape Hatteras) were identified with different spawning periods. Larval abundance at Little Egg Inlet has increased since the late 1990s and most individuals now enter the estuary earlier during the season of ingress. Abundance at Little Egg Inlet was correlated with an increase in spawning stock biomass, presumably because spawning by larger, more abundant fish during the late 1990s and early 2000s provided increased larval supply, at least in some years. Larval abundance at ingress at Beaufort Inlet was not correlated with spawning stock biomass or with larval abundance at ingress at Little Egg Inlet, further supporting the hypothesis of at least two stocks. Larval abundance at Little Egg Inlet could be used as a fishery-independent index of spawning stock size north of Cape Hatteras in future stock assessments. Larval occurrence at Beaufort Inlet may provide information on the abundance of the stock south of Cape Hatteras, but additional stock assessment work is required.

Measurement errors in body size of sea scallops (Placopecten magellanicus) and their effect on stock assessment models

Body-size measurement errors are usually ignored in stock assessments, but may be important when body-size data (e.g., from visual sur veys) are imprecise. We used experiments and models to quantify measurement errors and their effects on assessment models for sea scallops (Placopecten magellanicus). Errors in size data obscured modes from strong year classes and increased frequency and size of the largest and smallest sizes, potentially biasing growth, mortality, and biomass estimates. Modeling techniques for errors in age data proved useful for errors in size data. In terms of a goodness of model fit to the assessment data, it was more important to accommodate variance than bias. Models that accommodated size errors fitted size data substantially better. We recommend experimental quantification of errors along with a modeling approach that accommodates measurement errors because a direct algebraic approach was not robust and because error parameters were diff icult to estimate in our assessment model. The importance of measurement errors depends on many factors and should be evaluated on a case by case basis.

All their eggs in one basket: a rocky reef nursery for the longnose skate (Raja rhina Jordan & Gilbert, 1880) in the southern California Bight

Skates (family Rajidae) are oviparous and lay tough, thick-walled eggs. At least some skate species lay their eggs in spatially restricted nursery grounds where embryos develop and hatch (Hitz, 1964; Hoff, 2007). After hatching, neonates may quickly leave the nursery grounds (Hoff, 2007). Egg densities in these small areas may be quite high. As an example, in the eastern Bering Sea, a site <2 km2 harbored eggs of Alaska skate (Bathyraja parmifera) exceeding 500,000/km2. All skate nursery grounds have been identified over soft sea floors (Lucifora and García, 2004; Hoff, 2007).

A nursery site of the Alaska skate (Bathyraja parmifera) in the eastern Bering Sea

A nursery site for the Alaska skate (Bathyraja parmifera) was sampled seasonally from June 2004 to July 2005. At the small nursery site (~2 km2), located in a highly productive area near the shelf-slope interface at the head of Bering Canyon in the eastern Bering Sea, reproductive males and females dominated the catch and neonate and juvenile skates were rare. Seasonal samples showed summertime (June and July) as the peak reproductive time in the nursery although some reproduction occurred throughout the year. Timeseries analysis of embryo length frequencies revealed that three cohorts were developing simultaneously and the period of embryonic development was estimated at 3.5 years and average embryo growth rate at 0.2 mm/day. Estimated egg case deposition occurred mainly during summertime and hatching occurred during winter months. Protracted hatching times may be common for oviparous elasmobranch species and may be directly correlated with ambient temperatures as evident from a meta-data analysis. Evidence indicates that the Alaska skate uses the eastern Bering Sea outer continental shelf region for reproduction and the middle and inner shelf regions as habitat for immature and subadults. Skate nurseries may be vulnerable to disturbances because they are located in highly productive areas and because embryos develop slowly.

Determination of population structure and stock composition of chum salmon (Oncorhynchus keta) in Russia determined with microsatellites

Variation at 14 microsatellite loci was examined in 34 chum salmon (Oncorhynchus keta) populations from Russia and evaluated for its use in the determination of population structure and stock composition in simulated mixed-stock fishery samples. The genetic differentiation index (Fst) over all populations and loci was 0.017, and individual locus values ranged from 0.003 to 0.054. Regional population structure was observed, and populations from Primorye, Sakhalin Island, and northeast Russia were the most distinct. Microsatellite variation provided evidence of a more fine-scale population structure than those that had previously been demonstrated with other genetic-based markers. Analysis of simulated mixed-stock samples indicated that accurate and precise regional estimates of stock composition were produced when the microsatellites were used to estimate stock compositions. Microsatellites can be used to determine stock composition in geographically separate Russian coastal chum salmon fisheries and provide a greater resolution of stock composition and population structure than that previously provided with other techniques.

Use of genetic data to assess the uncertainty in stock assessments due to the assumed stock structure: the case of albacore (Thunnus alalunga) from the Atlantic Ocean

Stock assessments can be problematic because of uncertainties associated with the data or because of simplified assumptions made when modeling biological processes (Rosenberg and Restrepo, 1995). For example, the common assumption in stock assessments that stocks are homogeneous and discrete (i.e., there is no migration between the stocks) is not necessarily true (Kell et al., 2004a, 2004b).

The use of otolith morphology to indicate the stock structure of common coral trout (Plectropomus leopardus) on the Great Barrier Reef, Australia

We investigated the use of otolith morphology to indicate the stock structure of an exploited serranid coral reef fish, Plectropomus leopardus, on the Great Barrier Reef (GBR), Australia. Otoliths were measured by traditional one-and two-dimensional measures (otolith length, width, area, perimeter, circularity, and rectangularity), as well as by Fourier analysis to capture the finer details of otolith shape. Variables were compared among four regions of the GBR separated by hundreds of kilometers, as well as among three reefs within each region, hundreds of meters to tens of kilometers apart. The temporal stability in otolith structure was examined by comparing two cohorts of fully recruited four-year-old P. leopardus collected two years before and two years after a signif icant disturbance in the southern parts of the GBR caused by a large tropical cyclone in March 1997. Results indicated the presence of at least two stocks of P. leopardus, although the structure of each stock varied depending on the cohort considered. The results highlight the importance of incorporating data from several years in studies using otolith morphology to discriminate temporary and possibly misleading signals from those that indicate persistent spatial structure in stocks. We conclude that otolith morphology can be used as an initial step to direct further research on groups of P. leopardus that have lived at least a part of their life in different environments.

A Bayesian method for identification of stock mixtures from molecular marker data

Molecular markers have been demonstrated to be useful for the estimation of stock mixture proportions where the origin of individuals is determined from baseline samples. Bayesian statistical methods are widely recognized as providing a preferable strategy for such analyses. In general, Bayesian estimation is based on standard latent class models using data augmentation through Markov chain Monte Carlo techniques. In this study, we introduce a novel approach based on recent developments in the estimation of genetic population structure. Our strategy combines analytical integration with stochastic optimization to identify stock mixtures. An important enhancement over previous methods is the possibility of appropriately handling data where only partial baseline sample information is available. We address the potential use of nonmolecular, auxiliary biological information in our Bayesian model.

Age composition and distribution of red drum (Sciaenops ocellatus) in offshore waters of the north central Gulf of Mexico: an evaluation of a stock under a federal harvest moratorium

Because of a lack of fishery-dependent data, assessment of the recovery of fish stocks that undergo the most aggressive form of management, namely harvest moratoriums, remains a challenge. Large schools of red drum (Sciaenops ocellatus) were common along the northern Gulf of Mexico until the late 1980s when increased fishing effort quickly depleted the stock. After 24 years of harvest moratorium on red drum in federal waters, the stock is in need of reassessment; however, fisherydependent data are not available in federal waters and fishery-independent data are limited. We document the distribution, age composition, growth, and condition of red drum in coastal waters of the north central Gulf of Mexico, using data collected from a nearshore, randomized, bottom longline survey. Age composition of the fishery-independent catch indicates low mortality of fish age 6 and above and confirms the effectiveness of the federal fishing moratorium. Bottom longline surveys may be a cost-effective method for developing fishery-independent indices for red drum provided additional effort can be added to nearshore waters (<20 m depth). As with most stocks under harvest bans, effective monitoring of the recovery of red drum will require the development of fishery-independent indices. With limited economic incentive to evaluate non-exploited stocks, the most cost-effective approach to developing such monitoring is expansion of existing fishery independent surveys. We examine this possibility for red drum in the Gulf of Mexico and recommend the bottom longline survey conducted by the National Marine Fisheries Service expand effort in nearshore areas to allow for the development of long-term abundance indices for red drum.

Potential use of offshore marine structures in rebuilding an overfished rockfish species, bocaccio (Sebastes paucispinis)

Although bocaccio (Sebastes paucispinis) was an economically important rockfish species along the west coast of North America, overfishing has reduced the stock to about 7.4% of its former unfished population. In 2003, using a manned research submersible, we conducted fish surveys around eight oil and gas platforms off southern California as part of an assessment of the potential value of these structures as fish habitat. From these surveys, we estimated that there was a minimum of 430,000 juvenile bocaccio at these eight structures. We determined this number to be about 20% of the average number of juvenile bocaccio that survive annually for the geographic range of the species. When these juveniles become adults, they will contribute about one percent (0.8%) of the additional amount of fish needed to rebuild the Pacific Coast population. By comparison, juvenile bocaccio recruitment to nearshore natural nursery grounds, as determined through regional scuba surveys, was low in the same year. This research demonstrates that a relatively small amount of artificial nursery habitat may be quite valuable in rebuilding an overfished species.

A prior for steepness in stock-recruitment relationships, based on an evolutionary persistence principle

Priors are existing information or beliefs that are needed in Bayesian analysis. Informative priors are important in obtaining the Bayesian posterior distributions for estimated parameters in stock assessment. In the case of the steepness parameter (h), the need for an informative prior is particularly important because it determines the stock-recruitment relationships in the model. However, specifications of the priors for the h parameter are often subjective. We used a simple population model to derive h priors based on life history considerations. The model was based on the evolutionary principle that persistence of any species, given its life history (i.e., natural mortality rate) and its exposure to recruitment variability, requires a minimum recruitment compensation that enables the species to rebound consistently from low critical abundances (Nc). Using the model, we derived the prior probability distributions of the h parameter for fish species that have a range of natural mortality, recruitment variabilities, and Nt values.

Hatching date, nursery grounds, and early growth of juvenile walleye pollock (Theragra chalcogramma) off northern Japan*

Walleye pollock (Theragra chalcogramma) is widely distributed in the North Pacific Ocean and plays an important role in coastal subarctic ecosystems. The Japanese Pacific population of this species is one of the most important demersal fishes for commercial fisheries in northern Japan. The population is distributed along the Pacific coast of Hokkaido and the Tohoku area (Fig. 1), which is the southern limit of distribution of the species in the western North Pacific. In Funka Bay, the main spawning ground for this population, pollock spawn from December to March (Kendall and Nakatani, 1992). Planktonic eggs and larvae are transported into the bay, where juveniles usually remain until late July when they reach 60−85 mm in total length (Hayashi et al., 1968; Nakatani and Maeda, 1987). These juvenile pollock then migrate from Funka Bay eastward to the Doto area off southeastern Hokkaido (Honda et al., 2004). Many studies on eggs, larvae, and juveniles of the species have been conducted in or near Funka Bay, but little information is available on the ecology of the early life stages in the Tohoku area. Hashimoto and Ishito (1991) suggested that eggs are transported from Funka Bay southward to the Tohoku area by the coastal branch of the Oyashio Current, but there has been no study to verify this hypothesis.

A catch-free stock assessment model with application to goliath grouper (Epinephelus itajara) off southern Florida

Many modern stock assessment methods provide the machinery for determining the status of a stock in relation to certain reference points and for estimating how quickly a stock can be rebuilt. However, these methods typically require catch data, which are not always available. We introduce a model-based framework for estimating reference points, stock status, and recovery times in situations where catch data and other measures of absolute abundance are unavailable. The specif ic estimator developed is essentially an age-structured production model recast in terms relative to pre-exploitation levels. A Bayesian estimation scheme is adopted to allow the incorporation of pertinent auxiliary information such as might be obtained from meta-analyses of similar stocks or anecdotal observations. The approach is applied to the population of goliath grouper (Epinephelus itajara) off southern Florida, for which there are three indices of relative abundance but no reliable catch data. The results confirm anecdotal accounts of a marked decline in abundance during the 1980s followed by a substantial increase after the harvest of goliath grouper was banned in 1990. The ban appears to have reduced fishing pressure to between 10% and 50% of the levels observed during the 1980s. Nevertheless, the predicted fishing mortality rate under the ban appears to remain substantial, perhaps owing to illegal harvest and depth-related release mortality. As a result, the base model predicts that there is less than a 40% chance that the spawning biomass will recover to a level that would produce a 50% spawning potential ratio.

Meso-scale transboundary units for the management of coral reefs in the South China Sea area

Local communities and local government units are recognized as the primary stakeholders and participants in the management of coral reef resources and the primary beneficiaries of small-scale fishing activities in the nearshore areas of the coastal zone. The issues relating to the management of the coastal zone are multi-faceted and some issues are largely intertwined with national policy and development goals. Thus, national governments have jurisdiction over these nearshore coastal resources to harmonize policies, monitor resource use and provide incentives for sustainable use. However, the natural boundaries of these reef resources, the processes that support reef ecosystems, and the local or national affiliation of the people who benefit from them may transcend the boundaries of the local and national management units. Therefore, efforts to arrest the decline in fish catch and loss of biodiversity for reefs require management interventions and assessment activities to be carried out at varying scales. In Southeast Asia, some aspects of reef and reef resources management — particularly in deciding the allocation of catch among competing fisheries, development of sustainable harvest strategies, use of broodstock for restocking or stock enhancement programs, protection of nursery and spawning areas, designation of systems of marine protected areas, and the identification of representative, adequate and comprehensive areas for biodiversity conservation in the region — may require the definition of larger management units. At the regional level, multi-country initiatives will need to define units for the transboundary management of resources. The use of large marine ecosystems (LMEs) to identify and manage fisheries resources may be a starting point; however, given the relatively sedentary nature of coral reef-dwelling and reef-associated organisms compared with other pelagic and demersal species, meso-scale transboundary units within the LMEs have to be defined. This paper provides suggestions for transboundary management units for coral reef and reef-associated resources in Southeast Asia based on information from genetic structures of model organisms in the region. In addition, specific reef areas are identified, which may be important beyond their national boundaries, as potential sources of recruits.