roy troll border art
nefsc banner
Technical Memoranda Reference Documents Classic Publications Contract/Grant Reports
CMER Publications Series Information Links and Contacts Annual/Biennial Lists
Web Manager Email Search Publications Publications Home Site Map
CONTENTS
Introduction
Stock Structure & Distribution
The Fishery
Stock Abundance and Biomass Indices
Life History Parameters
Estimation of Fishing Mortality Rates and Stock Size
Biological Reference Points and Harvest Control Rule
Conclusions
Acknowledgments
Literatured Cited
Northeast Fisheries Science Center Reference Document 01-03

A Report of the 32nd Northeast Regional Stock Assessment Workshop
Assessment of the Silver Hake Resource in the Northwest Atlantic in 2000

by Jon K.T. Brodziak, Elizabeth M. Holmes, Katherine A. Sosebee, and Ralph K. Mayo

National Marine Fisheries Serv., 166 Water Street, Woods Hole, MA 02543

Print publication date March 2001; web version posted December 16, 2002

Citation: Brodziak, J.K.T.; Holmes, E.M.; Sosebee, K.A.; Mayo, R.K. 2001. Assessment of the silver hake resource in the Northwest Atlantic in 2000. Northeast Fish. Sci. Cent. Ref. Doc. 01-03; 134 p.

get acrobat reader Download complete PDF/print version

Abstract

Silver hake (Merluccius bilinearis) is a short-lived gadid that ranges from Newfoundland to South Carolina. This species is an important component of the food web in the northeast continental shelf ecosystem. In the U.S. EEZ, the silver hake population was intensively harvested by distant water fleets during the 1960s and 1970s with peak annual landings of over 300,000 mt. Since 1980, annual landings have remained stable at roughly 20,000 mt in what is now an entirely domestic fishery.

Two subpopulations of silver hake are assumed to exist within the US EEZ.  For the purpose of assessment, the northern stock is assigned to areas of northern Georges Bank and the Gulf of Maine and the southern stock is assigned to areas of southern Georges Bank, southern New England, and the Mid-Atlantic Bight. While it is recognized that the northern and southern   stocks mix on Georges Bank, the amount of mixing and movement among northern and southern areas are unknown.

Proxies for determining whether northern and southern silver hake are overfished were put forward in 1998 by a panel that reviewed overfishing definitions for northeast groundfish stocks. In 1999, the survey index for the northern stock was above its biomass target while the survey index for the southern stock was below its biomass threshold for SFA determination using the best available survey data. Therefore, the northern stock is considered not overfished while the southern stock is considered to be overfished.

An age-structured sequential population analysis was conducted for the entire silver hake population from Cape Hatteras to the Gulf of Maine using NEFSC autumn and spring numbers-at-age indices and time-varying survey catchability. Another set of population analyses were conducted for the northern stock, the southern stock, and the entire silver hake population using NEFSC autumn and spring biomass indices in a Bayesian surplus production model. In addition, analyses of research vessel survey indices were used to quantify biomass and exploitation rate.

The population dynamics of silver hake in the US EEZ have changed through time. In particular, patterns of growth and spatial distribution have changed substantially over the past 40 years. Age structure of the silver hake population appears to be truncated at about age-6  in recent years whereas historically, silver hake of age-6 and older were much more frequently observed. Older silver hake may be less vulnerable to the fishery and survey in recent years because their spatial distribution has changed. Alternatively, continued high fishing mortality rates may have  precluded the rebuilding of age structure following the cessation of the foreign distant water fleet fishery. Survey data indicate that biomass in the northern stock area is high and that biomass in the southern stock area is low. For the combined stock area, biomass is likely near carrying capacity and harvest rates appear to be low.

INTRODUCTION

Silver hake (Merluccius bilinearis) is a short-lived gadid that ranges from Newfoundland to  South Carolina. This species is an important component of the food web in the northeast continental shelf ecosystem (Sissenwine and Cohen 1991), and according to Bigelow and Schroeder (1953), “Silver hake are strong swift swimmers, well armed and extremely voracious”. In the U.S. EEZ, the silver hake population was intensively harvested by distant water fleets during the 1960s and 1970s with peak annual landings of over 300,000 mt. Since 1980, annual landings have remained stable at roughly 20,000 mt in what is now an entirely domestic fishery. Silver hake was last assessed in 1993 at SAW 17. In that assessment, an age-structured analysis  of the population in two stock areas was attempted, but results were not considered to be reliable. As a result, the previous assessment was index-based and current overfishing thresholds for   silver hake are based on research survey information. The current assessment was undertaken for SAW 32 (2001), where stock assessments for sea scallops, American plaice, Gulf of Maine haddock, and silver hake were reviewed. An Advisory Report on Stock Status and a Consensus Summary of Assessments have been published in draft form as a result of that meeting (NEFSC 2001a, 2001b). This report is intended to serve as a detailed description of the assessment accepted and reviewed by the SAW.

STOCK STRUCTURE AND DISTRIBUTION

Two subpopulations of silver hake are assumed to exist within the US EEZ (Almeida 1987a). Analyses of morphometric characters (Conover et al. 1961, Almeida 1987a) are the primary basis for this delineation. Recent analyses of otolith microconstituent data are also consistent with the existence of two or more stocks (Bolles and Begg 2000). However, genetic analyses of population structure have been inconclusive (Schenk 1981). For the purpose of assessment, the northern stock is assigned to areas of northern Georges Bank and the Gulf of Maine and the southern stock is assigned to areas of southern Georges Bank, southern New England, and the Mid-Atlantic Bight (Figure 1 and Figure 2). These boundaries were established at SAW 11.

While it is likely that the northern and southern stocks mix on Georges Bank, the amount of mixing and movement among northern and southern areas are unknown (Almeida 1987a, Helser et al. 1995, Helser 1996). Silver hake spawn in the Gulf of Maine, southern New England, and  on the southern flank of Georges Bank. Silver hake larvae entrained in the clockwise gyre of Georges Bank may settle in either the southern or northern stock areas (see Distribution of Eggs and Larvae below). As a result, reproductive isolation of the two stocks is unlikely. However, it is unknown to what extent the northern and southern stocks have independent demographic and genetic trajectories. If gene flow is high between northern and southern stocks, on the order of a few migrants per generation, genetic analyses may be of limited utility to separate the subpopulations in areas of mixing (Waples 1998).

Analyses of silver hake size-at-age data show that growth has varied in time and among areas. In particular, recent growth analyses (Helser 1996) indicate that there are consistent differences between silver hake growth in the Gulf of Maine and southern New England/Mid-Atlantic Bight areas. Helser also shows that growth patterns on Georges Bank and the Gulf of Maine were indistinguishable during 1988-1992 and that growth rate changes dynamically on Georges Bank. Growth analyses conducted for this assessment show that there are very minor differences in growth between northern and southern stock areas during the 1990s (see Growth below). In general, differences in silver hake growth between northerly and southerly areas can be expected if there is limited movement between areas based on differences in primary productivity and water temperature between the Gulf of Maine and the continental shelf areas of southern New England and Georges Bank.

The spatial distribution of silver hake has changed through time. Population density, as measured by the NEFSC fall bottom trawl survey has been increasing in northern stock areas (Gulf of Maine: offshore strata 24, 26-30, and 36-40, northern Georges Bank: offshore strata 20-23 and  25) since the late 1960s (Figure 3A). Density in southern stock areas has decreased (Figure 3B) since the 1960s in southern New England (offshore strata 1-12) and Mid-Atlantic Bight waters (offshore strata 61-76, note that 1963-1966 indices are based on average proportion during 1967-1999, see STOCK ABUNDANCE AND BIOMASS INDICES below) while density in southern Georges Bank waters (offshore strata 13-19)  increased in the 1980s and subsequently decreased in the 1990s. In contrast, spring survey information on density is highly variable (Figure 4) and likely provides less information on trend in comparison to the fall survey.

In terms of the spatial distribution of total population biomass, there has been an increasing trend in the population biomass index in northern stock areas and a decrease in southern stock areas (Figure 5A). The total population biomass index has increased since the historic lows of the late 1960s, while the proportion of total biomass in the Gulf of Maine has increased from about 50% in the late 1960s to over 80% in the late 1990s (Figure 5B). In contrast, the proportion of total biomass in southern New England has decreased from about 40% in the late 1960s to about 10% in the late 1990s. As with the density data, the spring survey total biomass information is highly variable by stock area (Figure 6) and likely provides less information on trend in comparison to the fall survey. Overall, the Gulf of Maine has consistently had the highest density and  proportion of biomass through time and this suggests that the Gulf of Maine is the best habitat  for silver hake among northern and southern stock areas.

Changes in oceanographic conditions of shelf waters have likely affected silver hake  distribution. Near-bottom water temperatures, as indexed during the NEFSC fall and spring bottom trawl surveys,  in the northern and southern stock areas (Figure 7) show that the 1960s was a relatively cool time period and also show that temperatures have increased in recent years. In particular, water temperatures on northern and southern Georges Bank have slowly increased through time, relative to the Gulf of Maine. The ratio of population density of silver hake to temperature has also changed in both northern and southern stock areas (Figure 8). Density per degree has increased in northern areas (Figure 8A,C) and decreased in southern areas (Figure 8B,D). Overall, changes in temperature may have altered the spatial distribution of the two stock components.

Changes in broad-scale oceanographic conditions may also have affected silver hake   distribution. NEFSC bottom trawl survey data collected during fall, winter, and spring (Figure 9) show that a portion of the population is consistently present in deeper waters of the upper continental slope at depths of 100-300 m. This depth range represents the boundary of the NEFSC bottom trawl surveys ,which are primarily designed to sample continental shelf waters. Near the shelf/slope break, warm slope waters impinge upon the upper continental slope and provide year-round habitat for silver hake. In fact, the USSR fishery for silver hake documented this feature of silver hake distribution in the 1960s  (Figure 10). The association of a fraction of the silver hake population with slope waters suggests that changes in the slope water mass between the Gulf Stream and the continental shelf water probably affects the offshore  distribution of silver hake. In particular, changes in the position of the shelf/slope front (Drinkwater et al. 2000) and Gulf Stream position alter slope water characteristics and may influence silver hake distribution in deeper water at the shelf/slope break. One broad-scale  feature that has been correlated with changes in Gulf Stream position is the North Atlantic Oscillation (NAO) index (Jones et al. 1997, Taylor and Stephens 1998). The NAO index has trended up sharply since the 1960s (Figure 11) and this trend may have affected the amount of habitat available to silver hake in offshore waters of the upper continental slope.

In summary, four additional pieces of information on silver hake stock structure have been examined for this assessment. First, the density and proportion of population biomass has decreased in the southern area and increased in the northern area. Second, growth patterns have changed through time and have been similar in northern and southern areas during the 1990s. Third, ichthyoplankton data show that silver hake eggs are continuously distributed over Georges Bank. Fourth, changes in oceanographic conditions over the past 40 years may have influenced the spatial distribution of stock components.

THE FISHERY

The silver hake fishery has changed through time from an inshore fishery prosecuted with pound and trap nets to an otter trawl fishery (Fritz 1960). During the 1960s, landings of silver hake increased substantially (Table 1 and Figure 12). Most of the increase in harvest was due to directed fishing for silver hake by the distant water fleet of the former USSR. During the 1980s and 1990s, total silver hake landings have remained low in comparison to historic yields.

Recreational Fishery

Silver hake once supported a recreational fishery in the Mid-Atlantic Bight (Fritz 1960) with annual landings of around 1,000 mt (2.2 million pounds) in the southern stock area. Recreational fishery landings decreased substantially in the 1970s and 1980s and are currently very low. Recreational landings of silver hake collected by MRFSS have averaged only 18,000 fish per year during 1995-1999.

Commercial Fishery

Directed commercial fishing for silver hake began in the 1920s. The domestic commercial fishery has been relatively stable since the late 1970s. Market demand for silver hake does not appear to have changed much over the past two decades, and landings have remained at roughly 15,000 to 20,000 mt per year.

Commercial Landings

Commercial landings of silver hake during 1993-1999 were collected from the NEFSC weigh- out database. During 1994-1999, the area where silver hake were captured was not recorded for many trips in the weigh-out database due to changes in the reporting system for fishery statistics. As a result,  the unknown-area landings were prorated to the northern and southern stock areas based on fishing location information stored in the vessel-trip reporting database (e.g., fishery logbook data). These prorated landings by stock area for 1994-1999 are considered to be provisional until a final evaluation of the fishery logbook data has been completed.

Silver hake are landed in three commercial market categories: small, large, and unclassified. The vast majority of landings are reported as unclassified (Table 2).

Sampling Intensity

The adequacy of length frequency sampling of commercial silver hake landings has varied  during 1993-1999 (Table 3). Sampling has generally been adequate for the unclassified market category but has been poor for the large and small market categories in several years. Sampling  in the northern stock area has generally been lower than in the southern area (Figure 13). Most commercial fishery length samples collected in port during 1994-1996 had an unknown stock area in the commercial fishery length database (Figure 13). These unknown-area samples were assigned to northern and southern stock areas by identifying each sample with the corresponding vessel trip in the fishery logbook database, wherever possible.

The length samples by market category were evaluated for use in constructing commercial fishery catch at age during 1993-1999. Mean lengths of commercial fishery length samples from the 1st and 2nd half of the year were generally similar for the southern stock (Table 3). Few comparisons between 1st and 2nd half samples were possible in the north but the available data suggested that mean lengths were similar within a market category during the year. As a result, length frequency data from the 1st and 2nd half of each year were combined by market category. Similarly, comparisons of mean lengths of unclassified samples from northern and southern  stock areas suggested that there was no practical difference between unclassified silver hake  from the two areas. For the small and large market categories, there were few data for comparison and it was inconclusive whether differences existed for these minor categories. Because northern and southern samples were similar for the predominant unclassified category, commercial length frequency samples from the two stock areas were combined by market category to derive the length frequency of the landings.

Sampling intensities (1 sample consists of 100 fish lengths) for annual landings combined by half-year and stock area for small, unclassified, and large categories were: 623, 487, and 275 mt per sample in 1993; 377, 234, and 352 mt per sample in 1994; 371, 376, and 146 mt per sample in 1995; 306, 709, and 453 mt per sample in 1996; 215, 277, and 57 mt per sample in 1997; 238, 177, and 90 mt per sample in 1998; 163, 224, and 79 mt per sample in 1999 (Table 2 and Table 3). Overall, sampling intensities for the silver hake fishery have improved in the last couple of  years.

Length distributions of commercial fishery landings were computed as a catch-weighted average of the length distributions by market category (Figure 14). Mean length of commercial landings ranged from a high of 31 cm in 1995 to a low of 28 cm in 1999 and averaged 29 cm during 1993- 1999.

Commercial Landings at Age

Commercial landings at age data for 1955-1992 were based on the previous silver hake assessment (NEFSC 1994). Commercial landings at age during 1993-1999 were derived from commercial length frequency data, research survey age-length keys, and length-weight relationships derived from research survey data. Commercial length frequency distributions were derived from market category samples as described above. The silver hake age-length key for each year was calculated as the average of the age-length keys from the spring and fall NEFSC bottom trawl surveys during each year because no commercial fishery age data are available for silver hake. The length-weight relationship for each year was calculated as the average of the length-weight relationships from the spring and fall NEFSC bottom trawl surveys. The spring survey age-length keys were not available for 1998-1999 and the age-length keys in 1998 and 1999 were derived from the spring 1997 age-length key and the fall age-length key for that year.

Commercial landings at age have varied substantially through time (Table 4 and Figure 15). During 1955-1959, roughly 300 million silver hake were landed each year. Landings peaked at  an average over 1 billion silver hake per year in the late 1960s. Landings of silver hake have decreased since then and now average roughly 85 million fish per year, less than one-tenth of the peak value. The age composition of silver hake landings has also changed substantially through time. In the late 1950s to 1960s, age-4 and older silver hake comprised almost half of the landed catch. In contrast, during the 1990s, age-4 and older silver hake account for less than 20% of the landed catch. Similarly, age-6 and older silver hake accounted for 5% or more of the landed  catch during 1955-1974, but these age classes were very rare in the sampled catch during the 1990s. 

Bycatch and Discards

Bycatch and discard of silver hake occurs in directed and non-directed fisheries. Several sources of information were used to examine patterns of discarding. These were weigh-out interview  data for 1983-1993, sea sampling data for 1989-1999, and fishing vessel logbook data for 1994-1999. Data on discarding patterns prior to 1983 were very limited and no estimates of the magnitude of discarding were attempted for this assessment.

Weigh-out interview data were screened to include only trips that were also recorded in the commercial weigh-out database. This was done to ensure that ratios of discarded catch weight to kept catch were accurate. The weigh-out interview data for otter trawl fishing operations indicated that discard to kept ratios ranged from 10% to 80% during 1983-1993. Based on the interview data, the average discard to kept ratio was roughly 30%.

Sea sampling data collected during 1989-1999 showed that discarding of silver hake captured by otter trawls occurred throughout the northern and southern stock areas (Figure 16). Discarding of silver hake by scallop dredges also occurred in both northern and southern stock areas (Figure  17) while discarding by sink gill nets occurred primarily in the northern stock area (Figure 18). Discard to kept ratios by weight, summarized by year, quarter, gear-type, and stock area (Table 5), varied through time and ranged from 0% to over 100%  for the directed silver hake fishery (small mesh otter trawl, codend mesh 3" or less) and for the non-directed fisheries (large mesh otter trawl, shrimp trawl, sink gill net, and scallop dredge). Overall, it is unknown whether the variability in the discard ratios was due to non-random coverage of the fleet, small sample sizes, or inherent variation in discard rates and practices.

Fishery logbook data collected during 1994-1999 also show that silver hake discarding practices varied through time and differed between directed and non-directed fisheries. Discard to kept ratios in the logbook data, summarized by year, quarter, gear-type, and stock area (Table 6) represent a fraction of all fishing operations and range from 0% to over 100%. For scallop dredges, there were no records of discarding although some silver hake are discarded in the sea scallop fishery.

STOCK ABUNDANCE AND BIOMASS INDICES

Research Survey Indices

Research survey indices for relative biomass and population numbers at age were recomputed for the combined stock area using NEFSC spring and fall survey data. This was done for three reasons: (i) to improve the precision of the southern area indices, (ii) to ensure that the southern area was consistently sampled through time, and (iii) to correct a minor error in the value of the 1992 autumn biomass index for the southern stock. First, to improve precision of the southern  area indices, the delta-distribution was used to compute southern area abundance indices (stratified mean kg or numbers/tow). In general, use of the delta-distribution gives higher precision than use of the arithmetic mean (see Pennington 1986). In the previous assessment, stratified means were based on the delta-distribution for the northern stock and were based on   the arithmetic mean for the southern stock. Second, to ensure that the southern area was consistently sampled through time (1963-1999), inshore survey strata were excluded from the southern survey index calculations. This was done because inshore survey strata were not sampled until 1972. As a result, southern silver hake indices from the 1963-1971 period were not directly comparable to indices from 1973-present because different geographic areas were surveyed. In addition, the inshore survey strata were sampled using a different vessel (R/V Atlantic Twin) with different survey gear during 1972-1974 compared to the 1975-1999 period when the R/V Albatross IV and R/V Delaware II were used. These inconsistencies were resolved by excluding inshore survey strata for the southern area in the current assessment.  It should be noted that inshore survey strata contain a very small proportion of silver hake biomass in the southern area (<0.01% in all years). Third, the 1992 autumn survey biomass index was reported as 0.72 in the previous assessment while the correct value, using the arithmetic average, was  0.85.  Overall, these improvements altered the survey time series for the southern area but did   not affect the northern area time series.

The recomputation of the autumn survey indices also altered the values of the survey biomass threshold and survey biomass target for the southern stock. According to the overfishing definition for the southern stock,  the survey biomass target for the southern stock is computed as one-half of the arithmetic average of the NEFSC autumn survey biomass indices (kg/tow) during 1973-1982. Under this definition, the survey biomass threshold for the southern stock changed from 0.78 kg/tow, using data from the previous assessment (see Table B5 in NEFSC 1994  [SARC 17]), to 0.89 kg/tow using data from the current assessment (see Table 7).   Coincidentally, the 1999 biomass index for overfishing status determination in the southern   stock (computed as three-year average of the 1997-1999 biomass indices in Table 7), as recomputed in this assessment, was 0.78 kg/tow (see Table 14). It is important to note that the 1999 biomass index (0.78) must be compared to the revised survey biomass threshold (0.89) to  be logically consistent. Similarly, the survey biomass target for the southern stock changed from 1.56 kg/tow based on data from the previous assessment to 1.78 kg/tow using the current data.

No attempt was made to adjust survey data for possible day-night variation in silver hake distribution in the water column. Although day-night differences in catchability might be expected for this species (Bowman and Bowman 1980), the NEFSC surveys operate  continuously through day and night and no systematic bias would be expected since allocation of a tow location to day or night is random. On the other hand, use of survey catch information   from day and night time periods can be expected to increase the variability of calculated indices.

During 1963-1966, survey strata in the Mid-Atlantic Bight (offshore strata 61-76) were not sampled. To calculate the survey biomass time series of the southern stock for 1963-1966, it was assumed that the proportion of total silver hake biomass in the Mid-Atlantic Bight during these years was equal to the long-term average of 1.8%. Given this assumption, the fall biomass index for the southern area was extended to 1963-1966. This was important for population modeling because the largest silver hake catches occurred during the 1963-1966 period.

Biomass indices for northern and southern stock areas show differing trends (Table 7). Biomass indices for the northern stock area show an increasing trend while biomass indices for the southern stock area show a decreasing trend (Figure 19). Biomass indices for the combined stock area show an increasing trend in the fall (Figure 20) and vary without trend in the spring.

Numbers-at-age indices from the NEFSC spring and fall bottom trawl surveys were computed  for the combined stock area using all available age-length data (Tables 8 and 9, Figures 21, 22, and 23). For the spring survey, there were no ageing data collected prior to 1973. It was assumed that the average of the spring age-length keys during 1973-1975 was an adequate representation of silver hake size-at-age during 1968-1972. In addition, there were no age-length data available for spring during 1998-1999 and here it was assumed that the 1997 spring age-length key was an adequate representation of silver hake size-at-age during 1998-1999. Similarly, for the fall survey, there were no age data collected prior to 1973 and no age data collected in 1974. The average of the 1973 and 1975 age-length keys was used to represent silver hake size at age  during 1963-1972 and 1974, when no age data were collected.

LIFE HISTORY PARAMETERS

Recent research on silver hake life history parameters includes studies of larval settlement and growth (Steves and Cowen 2000), variation in otolith morphometrics (Bolles and Begg 2000), growth variation of larvae in relation to water masses (Jeffrey and Taggart 2000), acoustic measurements of the distribution of silver hake and euphausiid prey (Cochrane et al. 2000), spatial and temporal patterns of growth (Helser 1996), and potential effects of density-dependent growth and maturation on population dynamics (Helser and Brodziak 1998). Together, these studies have expanded the information base on silver hake population dynamics.

Distribution of Eggs and Larvae

Silver hake have a protracted spawning period that lasts from late-spring through autumn. Spawning occurs during May-October on Southern Georges Bank, during June-October in the Gulf of Maine and northern Georges Bank, and during June-December in the Mid-Atlantic Bight (Colton et al. 1979). Silver hake larvae are widely distributed in continental shelf waters during summer and early autumn. Silver hake has been classified as a ubiquitous, extended spawner by Sherman et al. (1984) based on the broad distribution of its larvae and its protracted spawning period. Ichthyoplankton surveys conducted from 1977-1987 show the extensive distribution of silver hake eggs during May to October (Figures 24 and 25). This broad distribution may be in part due to multiple spawnings by individual fish; Fahay (1974) reported that silver hake can spawn up to three times per year. In addition, Fahay (1974) observed that larger females tend to mature and spawn earlier in the season compared to smaller mature females. More recently, Steves and Cowen (2000) investigated settlement patterns and habitat use of juvenile silver hake and reported that the outer continental shelf was an important nursery habitat for silver hake in the Southern New England/Mid-Atlantic Bight region. Because most of these observations are based on data that were collected over a decade ago, it is unclear whether these distributional patterns have persisted in recent years.

Growth

Helser (1996) investigated dynamic changes in growth rates of silver hake from Cape Hatteras to the Gulf of Maine during 1975-1992. He found that there were spatial and temporal patterns in growth among four areas: the Mid-Atlantic Bight/Southern New England area (MAB, offshore strata 1-12, 61-76), Southern Georges Bank (SGB, offshore strata 13-19), Northern Georges  Bank (NGB, offshore strata 20-23, 25), and the Gulf of Maine (GM, offshore strata 24, 26-30, 36-40). In particular, there were three distinct area growth patterns during 1975-1980:

MAB, SGB/NGB, and GM. During 1982-1987, there were four distinct growth patterns: MAB, SGB, NGB, and GM. More recently, there were only two distinct area growth patterns: MAB  and SGB/NGB/GM. This shows that silver hake growth changes in space and time and suggests that growth on Georges Bank is influenced by stock mixing. In addition, the study by Helser and Brodziak (1998) shows that density-dependent changes in growth rates can have a substantial impact on management advice for silver hake.

Growth analyses conducted for this assessment were based on NEFSC survey size-at-age data from the spring and fall surveys. Growth curves were computed for the early 1970s (1973-1974) and the 1990s (1993-1999) to investigate time periods not covered in Helser’s study. Schnute’s (1981) growth model was fit to mean size-at-age data for these analyses. As in Helser (1996), growth curves were computed for size at age on January 1st, where spring survey data were assigned ages of observed year plus 3 months and fall survey data were assigned ages of observed year plus 8 months. Results showed a substantial change in growth between the early 1970s and the 1990s for the northern and southern stock areas and the combined stock area (Figure 26). During the early 1970s the average silver hake growth pattern conformed to a von Bertalanffy model while during the 1990s the average growth pattern has been nearly linear with age. The recent change in growth pattern was not expected to be a result of errors in age determinations because quality control measures are in place to ensure consistent age readings. For example, paired comparisons of otolith readings from the fall 1998 survey show 92% agreement between age readers. One implication of recent increases in growth rate is that the mean weights at capture of some age classes have increased during the 1990s (Table 10).

Natural Mortality

Silver hake are assumed to have a relatively high natural mortality rate consistent with their lifespan. The assumed natural mortality rate of 0.4 is generally consistent with estimates derived from life history parameters (Table 11, for details of estimation methods, see Hoeing (1983) and Quinn and Deriso (1999)). Regardless, there is probably age-specific, geographic, and temporal variation in the natural mortality rate of silver hake in the northwest Atlantic.

The maximum age of silver hake in NEFSC surveys has changed dramatically through time (Figure 27). Maximum ages averaged 9.5 y during 1963-1988 and subsequently decreased to an average of 5.6 y during 1989-1999 based on spring and fall survey data. The important question raised by this truncation of age structure is, what has happened to the older fish? One possibility  is that natural mortality on older ages changed substantially in the late 1980s due to  environmental changes. Another possibility is that the availability of older silver hake to the NEFSC surveys has changed due to a shift in their spatial distribution. Another possibility is that fishing mortality from directed and non-directed fisheries has been too high to allow the age structure to rebuild. Unfortunately, this important question is unlikely to be answered through age-structured modeling because estimation of natural mortality and survey selectivity  parameters determining capture probabilities at older ages are probably confounded (Thompson 1994). As a result, further field investigation will be needed to determine the most likely cause of the truncation of age structure.

Silver hake are an important component of the northeast continental shelf food web. Silver hake diet primarily consists of euphausiids, shrimp, fish, and other hakes (Garrison and Link 2000a,2000b). Smaller silver hake feed intensively on euphausiids. Silver hake undergo an ontogenetic shift to increased piscivory (Garrison and Link 2000b,2000c). Fish has been a consistent component of silver hake diet through time, although fish consumption by silver hake was relatively lower in the 1980s. There has been a shift in diet in recent years from sand lance to herring (Pers. comm. Jason Link, NEFSC, unpublished data).  Silver hake exhibit a higher frequency of cannibalism than other gadids in the northwest Atlantic, with medium-sized adults (age-2 and age-3) preying heavily upon age-0 and age-1 juveniles (Pers. comm., Jason Link, NEFSC). Predation by silver hake on groundfish is also substantial and may be on the order of 100,000 mt per year (Overholtz et al. 1999, Overholtz et al. 2000).

Length-Weight Relationship

Length-weight relationships of silver hake for northern, southern, and combined stock areas during 1992-1999 were estimated using methods described in Hayes et al. (1995). For each year, to determine the number of fish landed at age the estimated curves for the spring and fall were averaged to predict the mean weight at length at the midpoint of the year. In addition, possible changes in condition factor, as indexed by predicted mean weight at 25 cm, were investigated to see whether there had been declines in weight at length similar to those observed in the Scotian Shelf silver hake population (Hunt 1997, Showell and Fanning 1998).  Results showed that there has been no apparent decline in silver hake condition factor in either northern or southern stock areas during the 1990s (Figure 28). Thus, the Scotian Shelf silver hake population appears to have a different trend in condition factor compared to the population in the US EEZ.

Maturity and Fecundity

Density-dependence in fraction of silver hake mature at age has been suggested for the northern and southern stock areas (see Helser and Brodziak 1998, and references therein). These density- dependent maturity models were not used in this assessment because of their dependence upon absolute estimates of stock sizes. Instead, maturity ogives from the most recent assessment reported in Helser and Mayo (1994) were used to characterize population percent mature at age. In particular, percent mature at ages 1 through 6 and older were: 10%, 75%, 100%, 100%, 100%, and 100%, where the age-1 and age-2 values were the average of northern and southern stock values to the nearest 5%. These values of fraction mature at age were used in age-structured population modeling to provide an index of spawning biomass through time.

ESTIMATION OF FISHING MORTALITY RATES AND STOCK SIZE

Brief History of Assessments

The first preliminary assessment of silver hake in Subarea 5 (Georges Bank and the Gulf of Maine) is given in Gulland (1968) in the form of a series of interpretations of the likely sustainability of catches from the early 1960s.  The foundation for the present VPA assessment framework was laid down in a series of papers by Anderson (1975a, 1975b, 1977), and a description of changes in ageing techniques is provided in (Anderson and Nichy 1975).  Since the late 1970s, the assessment has been performed by several individuals in the form of multi- year updates (Anderson 1977, Anderson and Almeida 1979, Anderson and Almeida 1981, Almeida 1987b, NEFC 1990a, NEFC 1990b).

There are 4 major events in the evolution of the catch at age data which has formed the basis of the assessment of the silver hake stocks:

1)    Pooled age-length keys from USA and USSR ageing based on whole otoliths were used to derive the 1955-1972 catch at age.

2)    Thin sectioned otoliths were used for ageing beginning in 1973 and this practice continues to present.

3)    Discard estimates were included in the initial catch at age matrix for Division 5Y and Subdivision 5Ze silver hake assessments in the 1975 assessments.  Discards primarily

consisted of age 0 and 1 fish.  Discards were excised from the catch at age data in all subsequent assessments.

4)    A change in the assumed stock structure from 3 stocks to 2 stocks was implemented in the 1987 assessment.

VPAs were tuned using age-aggregated ad hoc techniques prior to 1990.  In 1990 (SAW 11) both Laurec-Shepherd and ADAPT tuning methods were attempted.  VPAs for both silver hake stocks were accepted with reservation at SAW 11, but the subsequent VPA assessments were rejected at SAW 17, due to a high degree of uncertainty and instability in parameter estimates.

Exploitation Rate Indices

Indices of relative exploitation rate were computed for northern and southern stock areas based  on the ratio of landings to fall survey biomass index (Figure 29). The exploitation rate index for the northern stock area shows high values for 1963-1975 followed by low values since 1976. The index for the southern stock is higher than for the northern stock throughout the time series. The southern exploitation rate index shows high values during 1963-1977 followed by a period of   low values during 1978-1993. Since 1994, the southern exploitation rate index appears to be increasing. Together, the exploitation rate indices suggest that exploitation rates in recent years are much lower than during the 1960s and 1970s when foreign distant water fleets intensively harvested silver hake.

Age-specific exploitation rate indices were calculated for the combined stock area using NEFSC spring and fall survey data. The age-specific indices were examined to see whether the ratio of landings at age to survey numbers at age has changed through time. Substantial changes in age- specific exploitation rate indices were apparent (Figure 30).  Some of the changes in the early 1970s coincide with prohibitions on fishing for silver hake in southern New England waters during January-March in 1970-1972 and during April 1973-1974 (Anderson et al. 1980). The age-specific exploitation rate indices were very high for ages 4, 5, and 6+ during the late 1960s and early 1970s. Between 1974 and 1975 there was a reduction in exploitation rate indices for  the fall survey to low values that have persisted to the present. For the spring survey, there was a gradual reduction in the exploitation rates from 1975 to 1980 after which the indices were low and stable. Thus, the age-specific exploitation rate indices show that exploitation rates were higher in the 1960s through early 1970s, especially for older ages, and have remained low since around 1980.

Total Mortality Indices from Research Surveys

Estimates of instantaneous total mortality were computed for the combined stock area using NEFSC spring and fall numbers-at-age data and Heincke’s method as used in the most recent assessment (NEFSC 1994). Results indicated that total mortality was high during the 1960s and that there has been an increasing trend in total mortality since the early 1980s (Table 12 and Figure 31). If natural mortality has been constant and equal to 0.4, then the increasing trend in total mortality implies that fishing mortality has increased and is currently very high (F>1). This increase in F appears to contradict the trend in exploitation rate indices.

Sequential Age-Structured Population Analyses

An age-structured population analysis was conducted to estimate stock size and fishing mortality for silver hake in the combined stock area. This approach contrasts the approach taken in the  most recent assessment where separate analyses were attempted for northern and southern stock areas. There were six reasons why separate age-structured analyses were not conducted for the northern and southern stock areas. First, catch-at-age data from the stock mixing area of Georges Bank likely contain errors in allocation to northern and southern components due to stock mixing and also due to errors in reporting catch amount and location, especially during the 1960s when distant water fleets intensively harvested silver hake on Georges Bank. Second, the commercial length frequency sampling of the northern stock area has been poor in the 1990s and was considered to be inadequate to characterize this component in isolation. Third, there has been a south to north shift in distribution of population biomass in recent years with the possible implication that silver hake stock components do not have the same spatial distribution through time. Fourth, there have been spatial changes in silver hake growth through time (see Helser 1996) and these changes in growth are not consistent with two distinct subpopulations separated by a boundary across Georges Bank. Fifth, analyses of silver hake growth data from the 1990s show that growth rates in northern and southern stock areas are very similar and therefore, silver hake from the two stock areas are currently exhibiting similar growth dynamics. Sixth, the most recent age-structured assessment based on two stocks was rejected because the models did not fit the data. Thus, it was expected that similar two-stock analyses would reproduce this lack of fit and provide no technical improvement over an index-based assessment of population status.

The ADAPT tuned-VPA model was applied to conduct age-structured analyses of the combined silver hake population using derived input data for catch at age (Table 4), survey numbers at age (Tables 8 and 9), catch weight at age (Table 10), and assumed natural mortality of 0.4. There were multiple model formulations examined. Of these, output for two model formulations that represent the baseline model with a very poor fit to the data and the best fit model were  examined in detail at SAW32 whereas key features of other model formulations were summarized (Table 13).

Residual patterns for model predictions of age-specific survey indices were very poor in the baseline model. There was a clear non-random trend in residuals across all age indices that went from low to high values (Figure 32). As a result, the baseline model was not considered to be reliable.

The best fit model was a model with 3 time periods of constant catchability for the spring and   fall survey indices. These time periods were 1963-1974, 1975-1980, and 1981-1999. These periods were chosen based on observed residual patterns, changes in age-specific exploitation  rate indices in 1974/75 for the fall survey and 1980/81 for the spring survey, possible changes in silver hake distribution associated with changes in the position of the shelf/slope front and the northern edge of the Gulf Stream (see Drinkwater et al. 2000), as well as reduced landings by the foreign fishery. The residuals for the 3-period catchability model were satisfactory (Figure 33), although some indications of low or high residuals were apparent. Estimated catchabilities for   the 3-period catchability model showed an increasing trend through time for both spring and fall surveys (Figure 34), with the exception of the age-1 index during 1975-1980. This implied that the spatial distribution of the population had changed and was more available to both spring and fall surveys since 1980. Overall, recent outputs of the best fit ADAPT model (Figure 35) appeared to be inconsistent with the long-term trend in exploitation rate indices and for this reason, the model was discounted by both the Northern Demersal Working Group and the SARC in their reviews of the silver hake assessment.

Biomass Dynamics Population Analyses

A Bayesian state-space formulation of the Schaefer surplus production model was developed by Meyer and Millar (1999) and an extension of their model forms the basis for biomass dynamics analyses of silver hake in the northern, southern, and combined stock areas. We briefly describe the model, the Northern Demersal Groups’ consensus on the most appropriate model structure and priors, and then show the surplus production results for the northern, southern, and combined silver hake stock areas.

The Bayesian surplus production (BSP) model uses a reparameterized form of the Schaefer surplus production model. The standard form of the Schaefer model relates stock biomass in year t (Bt) to biomass the previous year, intrinsic growth rate (r), carrying capacity (K) and catch the previous year (Ct-1) as

The reparameterized form relates the fraction of carrying capacity (Pt=Bt/K) to intrinsic growth rate, carrying capacity, and the catch time series as

This relationship is the basis of the state equations for the state-space model.

Stock biomass changes through time due to harvest and biomass production. The state equations determine changes in relative stock biomass through time (t=1,...,N) via:

where the independent lognormal process errors for relative biomass are exp(ut ) with ut ~ N(0,2) and the annual catch error distribution is a uniform distribution with time-varying upper (CU(t)) and lower (CL(t)) bounds.

Relative abundance in year t is measured by the mean weight per tow index (It) from the NEFSC autumn and/or spring bottom trawl surveys. In the simplest form, the survey index is assumed to be proportional to stock biomass with constant survey catchability (q) throughout the assessment time horizon

It = qBt

This relationship is the basis of the observation equations for the state-space model. Stock biomass is measured by the time series of survey indices. The observation equations relate the observed survey indices to model parameters via:

where the independent lognormal observation errors are exp(vt ) with vt ~ N(0,2).

In the simplest form for two surveys with constant catchability, the BSP model has eight parameters (r, K, qFALL, fall_2, fall_2, qSPR,spr_2,spr_2), N unknown relative biomasses (Pt), and N unknown catches (Ct) for a total of 2N+8 unknowns. To describe the Bayesian estimation procedure, let the joint prior of the parameters and unobservables be p(r,K,qFALL,fall_2,fall_2, qSPR,spr_2,spr_2, Pt, Ct) p(). Further, let the joint likelihood of the survey indices given the parameters and unobserved states be p(It | r,K,qFALL,fall_2,fall_2, qSPR,spr_2,spr_2, Pt, Ct) p(Data | ) and the joint posterior distribution of the unobservables  be p(r,K,qFALL,fall_2,fall_2, qSPR,spr_2,spr_2 Pt, Ct | It ) p( | Data).

Bayes’ theorem determines the posterior as a function of the prior and likelihood via

Direct calculation of the posterior distribution is not possible for the BSP model because the integral in the denominator of the right hand side is not tractable. As a result, Markov chain Monte Carlo (MCMC) methods were used to obtain samples from the posterior distribution of a Bayesian model (Gilks et al. 1996, Brooks 1998). Gibbs sampling is one type of MCMC algorithm that can be   readily applied using the BUGS software (Gilks et al. 1994; Meyer and Millar 1999). Computer   code to fit the BSP model was implemented using the WINBUGS1.3 software.

Several candidate versions of the three BSP models (northern, southern, and combined silver hake) were evaluated by the Northern Demersal Working Group during their review of the silver hake assessment. These included models that used the fall survey biomass index alone with constant catchability, as well as models that included both surveys with 2 time periods of catchability and population dynamics. The single index models did not perform well and had moderate to strong residual patterns for the predicted survey indices. The Working Group concluded that the single  index models had less information than the two index model, and as a result, the single index models were not used in further analyses. The 2-period catchability models using both survey indices were  fit for 1963-1974 and 1975-1999 time periods with separate values of catchability, intrinsic growth rate, and carrying capacity for each time period. The 2-period, 2-index models had adequate residual patterns but did not have plausible biological parameters; these models implied marked changes in carrying capacity that were considered to be unrealistic. As a result, the Northern Demersal Working Group chose to use BSP models with a single catchability using both spring and fall survey indices  as the basis for assessing stock status.

Initial choices of prior distributions for parameters and unobservables were refined for northern, southern, and combined silver hake BSP models following discussions of the Northern Demersal Working Group. The prior distribution for carrying capacity was a lognormal distribution with parameters chosen to set the 10th and 90th percentiles of the distribution. These percentiles were: combined area (700,000 mt, 2,000,000 mt), northern area (200,000 mt, 1,000,000 mt), southern area (400,000 mt, 2,000,000 mt).  The prior distribution for intrinsic growth rate was a broad uniform distribution for each model with r~Uniform[0.01, 1.99].

The prior distribution for the inverse of survey catchability was chosen to be a high-variance gamma distribution as described in Meyer and Millar (1999). That is, the inverse of q was assumed to be distributed as Gamma(0.001,0.001). This choice gives a vague prior for q, p(q), that is   approximately proportional to 1/q, that is, p(q) 1/q. In addition, the range of possible values of q was bounded to fall within the interval [0.001, 10]. In effect, the bounding of q ensured that model predictions of survey biomass indices (qKPt) were also bounded. The prior for process error variance parameter (2) was also chosen to be an inverse gamma distribution for both northern and southern monkfish. The inverse of 2 was distributed as Gamma(4.00, 0.01). This choice led to a 10% and   90% quantiles for F of 0.04 and 0.08, respectively. Similarly, the prior for observation error variance parameter (2) was chosen to be an inverse gamma distribution for both northern and southern monkfish. The inverse of 2 was distributed as Gamma(2.00, 0.01). This choice led to a 10% and   90% quantiles for of 0.05 and 0.14, respectively. Also note that the prior distribution for process error variance parameter was stochastically dominated by the prior for observation error variance parameter. That is, observation error was assumed to be somewhat larger than process error.

The prior distributions for the relative biomasses (Pt) were lognormal distributions for each BSP model. The prior distribution for relative biomass in the initial year of the assessment time horizon was P1  ~ Lognormal(0, 2). For subsequent years, the conditional prior distribution of Pt (conditioned on values of  Pt-1, K, r, and 2) was

Thus, the prior distribution for relative biomass in year t was dependent upon the previous year’s relative biomass, intrinsic growth rate, carrying capacity, and the process error parameter.

Uniform error distributions were assumed for total annual catch of northern, southern, and combined silver hake models during two time periods, 1963-1976 and 1977-1999. These time periods were based on the Northern Demersal Working Group discussion of the reliability of the time series of annual catches {Ct} for each stock area. In particular, the accuracy of reported catches of silver hake by distant water fleets was raised. It was pointed out that there was a potential for under-reporting or over-reporting of silver hake catches during the 1960s and 1970s. Thus, catches were initially modeled during 1963-1976 as being Uniform[CL(t) , CU(t)] = [0.5Ct , 1.5Ct], where Ct was the reported landings (Table 1). This implied that the catch error was up to 50% during 1963-1976. After viewing the posterior distribution of total catches, the Working Group concluded that there was no information to estimate the total catch during this time period and chose to set the catch error distribution to be Uniform[CL(t) , CU(t)] = [0.9Ct , 1.1Ct]. This implied that the catches were likely measured with error but were unbiased. For the 1977-1999 period, it was assumed that total catch  was under-reported due to discarding. The Working Group concluded that discard rates were not well-known and decided that a uniform catch error distribution of Uniform[CL(t) , CU(t)] = [Ct , 1.1Ct] for the period 1977-1999 was the most appropriate prior. This implied that the mean discard rate was 5% of reported catch since 1977.

Residual patterns of the three BSP models as well as convergence diagnostics were examined by the Working Group. The distribution of model predictions for the spring and fall survey indices were generally adequate and appeared randomly distributed for the combined (Figure 36), northern  (Figure 37), and southern (Figure 38) BSP models. For each parameter, convergence of the MCMC samples to the stationary posterior distribution was also evaluated using the corrected ratio (RC) of mixture-of-sequences variance (V) to the within-sequence variance (W) as defined by German and Rubin (1992) and generalized by Brooks and German (1998). At convergence, the RC is expected to be near 1. For each of the three models, the convergence diagnostics generally indicated that the model parameters had converged. In contrast, the extremely low intrinsic growth rate (r=3%) for the southern stock led the Northern Demersal Working Group to discount this model. Overall, given the uncertainties about misallocation of catches to northern and southern stocks and the north-south changes in the spatial distribution of the silver hake population, the Working Group recommended that the combined BSP model be used for management advice.

Summary statistics and marginal densities of model parameters of interest (r,K,qFALL,fall_2,fall_2, qSPR,spr_2,spr_2) were computed for each model (Appendix 1). In addition, several derived    parameters were also summarized: stock biomass (thousand mt) at the beginning of the each year;  the annual exploitation rate, the exploitation rate that would produce maximum surplus production (HMSP), the ratio of the exploitation rate in 1999 to HMSP, and the maximum surplus production (thousand mt) from the stock. Time series of stock biomass (Figure 39) and exploitation rate (Figure 40) were also computed.

BIOLOGICAL REFERENCE POINTS AND HARVEST CONTROL RULE

Age-Based Biological Reference Points

Yield- and spawning biomass per recruit analyses were conducted for both areas. Catch weights at age were the 7-year average of observed catch weights at age. The growth curve for 1993-1998 was used to compute stock weights at age, except for ages 5 and 6 where the catch weights were used. The fraction mature at age and natural mortality rate were the same as used in the ADAPT analyses.

Analyses were conducted for two partial recruitment patterns: dome-shaped and flat topped  selectivity at older ages. For the dome-shaped analysis, partial recruitment values were the 7-year average of most recent values taken from the best fit ADAPT model. For spawning biomass per recruit analyses, the value of 40% of unfished spawning potential was chosen as a target based on Clark’s (1993) paper and based on previous values used for northern and southern silver hake stocks. Results show that F40%=0.49 and F0.1= 0.38 for dome-shaped selectivity while F40%=0.40=M and F0.1=0.34 for flat-topped selection.

Index-Based Biological Reference Points

Proxies for determining whether northern and southern silver hake are overfished were put forward in 1998 by a panel that reviewed overfishing definitions for northeast groundfish stocks (NEFMC 1999). In 1999,  the survey index for the northern stock was above its biomass target while the survey index for the southern stock was below its biomass threshold using the best available survey data (Table 14). Therefore, the northern stock is considered to be not overfished while the southern stock is considered to be overfished.

Biomass-Based Biological Reference Points

The biomass dynamics models provide estimates of the biomass that would produce maximum surplus production, BMSP, the harvest rate that would produce maximum surplus production, HMSP, and the amount of maximum surplus production, MSP, for the combined, northern, and southern stock areas (Table 15). As noted in the section on Biomass Dynamics Analyses, the Northern Demersal Working Group recommended that the combined silver hake analyses be used for management advice given the changes in spatial distribution of the resource and the potential misallocation of catches to northern and southern components.

Harvest Control Rule

Hypothetical harvest control rules were developed for northern, southern, or combined silver hake stock areas using information from the surplus production model. The target harvest rate was proposed to be 60% of the median of the distribution of exploitation rate that would produce maximum surplus production for the stock unit. The limit harvest rate was proposed to be the median of the distribution of exploitation rate that would produce maximum surplus production. A value of 60% was chosen for the uncertainty reduction in the target harvest rate to account for the importance of silver hake within the northeast continental shelf food web as well as to account for uncertainties due to misallocation of catch to stock unit and also due to discarding of silver hake.

CONCLUSIONS

The population dynamics of silver hake in the US EEZ have changed through time. In particular, patterns of growth and spatial distribution have changed substantially over the past 40 years. Age structure of the silver hake population appears to be truncated at about age-6  in recent years whereas historically, silver hake of age-6 and older were much more frequently observed. Older silver hake may be less vulnerable to the fishery and survey in recent years because their spatial distribution has changed. Alternatively, continued high fishing mortality rates may have precluded the rebuilding of age structure following the cessation of the foreign distant water fleet fishery. Survey data indicate that biomass in the northern stock area is high and that biomass in the southern stock area is low. For the combined stock area, biomass is likely near carrying capacity and harvest rates appear to be low. Regardless of uncertainties about the status of northern and southern components, the silver hake population constitutes an important link in the food web and increases in exploitation rate should be made with due caution.

ACKNOWLEDGMENTS

We thank Jason Link for sharing his data and thoughts and also thank the Northern Demersal Working Group and the 32nd Stock Assessment Review Committee for their insights and comments.

LITERATURE CITED

Almeida, F. 1987a. Stock definition of silver hake in the New England-Middle Atlantic area. N. Amer. J. Fish. Mgt. 7:169:186.

Almeida, F.P. 1987b.  Status of the silver hake resource off the Northeast coast of the United States - 1987.  NMFS, NEFC, Woods Hole, Laboratory Ref. Doc. 87-03.

Anderson, E.D. 1975a.  Assessment of the ICNAF Subdivision 5Ze and Subdivision 5Zw -  Statistical Area 6 silver hake stocks.  Int. Comm. Northw. Atl. Fish. Res. Doc. 75/94, Ser. No. 3574, 17p.

Anderson, E.D. 1975b.  Assessment of the ICNAF Division 5Y silver hake stock.  Int. Comm. Northw. Atl. Fish. Res. Doc. 75/62 (Revised), Ser. No. 3544, 13p.

Anderson, E.D. and F.E. Nichy. 1975.  A comparison between US and USSR silver hake ageing. Int. Comm. Northw. Atl. Fish. Res. Doc. 75/13, Ser. No. 3457, 5 p.

Anderson, E.D. 1977.  Assessment of the Georges Bank silver hake stock.  NMFS, NEFC, Woods Hole, Laboratory Ref. Doc. 77-21.

Anderson, E.D. and F.P. Almeida. 1979.  Status of the Georges Bank silver hake stock - 1978.  Int. Comm. Northw. Atl. Fish. Res. Doc. 79/VI/84, Ser. No. 5446, 11p.

Anderson, E.D. and F.P. Almeida. 1981.  Status of the silver hake resource off the Northeast coast of the United States - 1981.  NMFS, NEFC, Woods Hole, Laboratory Ref. Doc. 81-36.

Anderson, E., F. Lux, and F. Almeida. 1980. The silver hake stocks and fishery off the northeastern United States. Mar. Fish. Rev. 1:12-20.

Berrien, P., and J. Sibunka. 1999. Distribution patterns of fish eggs in the U.S. northeast continental shelf ecosystem, 1977-1987. NOAA Tech. Rep. NMFS 145.

Bigelow, H., and W. Schroeder. 1953. Fishes of the Gulf of Maine. Fishery Bulletin of the U.S. Fish & Wildlife Service, Fishery Bulletin 74, Washington, DC.

Bolles, K., and G. Begg. 2000. Distinction between silver hake (Merluccius bilinearis) stocks in U.S. waters of the northwest Atlantic based on whole otolith morphometrics. Fish. Bull. 98:451-462.

Bowman, R., and E. Bowman. 1980. Diurnal variation in the feeding intensity and catchability of silver hake. Can. J. Fish. Aquat. Sci. 37:1565-1572.

Brooks, S. 1998. Markov chain Monte Carlo method and its application. Statistician, 47:69-100.

Brooks, S. and A. Gelman. 1998. General methods for monitoring convergence of iterative simulations. J. Computational and Graphical Statistics, 7(4):434-455.

Clark, W. 1993. The effect of recruitment variability on the choice of a target level of spawning biomass per recruit. In: Proceedings of the International Symposium on Management Strategies for Exploited Fish Populations. Alaska Sea Grant College Program, AK-SG-93-02, pp. 233-246.

Cochrane, N, D. Sameoto, and A. Herman. 2000. Scotian shelf euphausiid and silver hake population changes during 1984-1996 measured by multi-frequency acoustics. ICES J. Mar. Sci. 57:122-132.

Colton, J., W. Smith, A. Kendall, Jr., P. Berrien, and M. Fahay. 1979. Principal spawning areas and times of marine fishes, Cape Sable to Cape Hatteras. Fish. Bull. 76:911-915.

Conover, J., R. Fritz, and M. Viera. 1961. A morphometric study of silver hake. US Fish and Wildlife Special Scientific Report. Fisheries 368.

Drinkwater, K., E. Colbourne, and D. Gilbert. 2000. Overview of environmental conditions in the Northwest Atlantic in 1998. Northw. Atl. Fish. Org. Sci. Counc. Stud. 33: 39-88.

Gelman, A. and D. Rubin. 1992. Inference from iterative simulation using multiple sequences. Statistical Science, 7:457-511.

Fahay, M. 1974. Occurrence of silver hake eggs and larvae along the Middle Atlantic continental shelf during 1966. Fish. Bull. 72:813-829.

Fritz, R. 1960. A review of the Atlantic coast whiting fishery. Commer. Fish. Rev. 22(11):1-11.

Garrison, L., and J. Link. 2000a. Diets of five hake species in the northeast United States continental shelf ecosystem. Mar. Ecol. Prog. Ser. 204:243-255.

Garrison, L., and J. Link. 2000b. Fishing effects on spatial distribution and trophic guild structure of the fish community in the Georges Bank region. ICES J. Mar. Sci. 57:723-730.

Garrison, L., and J. Link. 2000c. Dietary guild structure of the fish community in the Northeast United States continental shelf ecosystem. Mar. Ecol. Prog. Ser. 202:231-240.

Gilks, W.R., A. Thomas, and D.J. Spiegelhalter. 1994. A language and program for complex Bayesian modeling. Statistician, 43:169-178.

Gilks, W.R., S. Richardson, and D.J. Spiegelhalter. 1996. Markov chain Monte Carlo in practice. Chapman and Hall, London.

Gulland, J.A.  1968.  A preliminary assessment of silver hake in sub-area 5.  Int. Comm. Northw. Atl. Fish. Res. Doc. 68/76, Ser. No. 2065, 5 p.

Hayes, D. B., J. K. T. Brodziak, and J. B. O'Gorman. 1995. Efficiency of estimators and  sampling designs for determining length-weight relationships. Can J. Fish. Aquat. Sci. 52:84-92.

Helser, T. 1996. Growth of silver hake within the U.S. continental shelf ecosystem of the northwest Atlantic Ocean. J. Fish. Biol. 48: 1059-1073.

Helser, T., and R. Mayo. 1994. Estimation of discards in the silver hake fisheries and a reanalysis of the long-term yield for the stocks. NEFSC Lab. Ref. Doc. 94-01, Woods Hole, MA, 02543.

Helser, T. , F. Almeida, and D. Waldron. 1995. Biology and fisheries of north-west Atlantic hake (silver hake: M. bilinearis). pp. 203-237 in: Alheit, J., and T. Pitcher (eds.). Hake: Fisheries, ecology and markets. Chapman & Hall, New York.

Helser, T., and J. Brodziak. 1998. Impacts of density-dependent growth and maturation on assessment advice to rebuild depleted U.S. silver hake stocks. Can. J. Fish. Aquat. Sci. 55:882-892.

Hoenig, J. 1983. Empirical use of longevity data to estimate mortality rates. Fish. Bull. 82:898-903.

Hunt, J. 1997. Evaluation of changes in weight-at-age for Divisions 4VWX silver hake, 1983-94. NAFO Sci. Counc. Stud. 30:65-73.

Jeffrey, J., and C. Taggart. 2000. Growth variation and water mass associations of larval silver hake on the Scotian Shelf. Can. J. Fish. Aquat. Sci. 57:1728-1738.

Jones, P.D., T. Jonsson, and D. Wheeler. 1997. Extension of the North Atlantic Oscillation using early instrumental pressure observations from Gibralter and southwest Iceland. International Journal of Climatology 17:1433-1450.

Meyer, R. and R.B. Millar. 1999. BUGS in Bayesian stock assessments. Can. J. Fish. Aquat. Sci. 56:1078-1086.

Northeast Fisheries Center [NEFC]. 1990a.  Report of the Spring 1990 NEFC Stock Assessment Workshop (Tenth SAW).  NMFS, NEFC, Woods Hole, Laboratory Ref. Doc. 90-07.

NEFC. 1990b.  Report of the Eleventh NEFC Stock Assessment Workshop, Fall 1990.  NMFS, NEFC, Woods Hole, Laboratory Ref. Doc. 90-09.

New England Fishery Management Council [NEFMC]. 1999. Amendment #12 to the northeast multispecies fishery management plan (Whiting, Red Hake, and Offshore Hake), April 2nd, 1999, Supplement. NEFMC, 50 Water Street, Mill 2 Newburyport, MA 01950.

Northeast Fisheries Science Center [NEFSC]. 1994. Report of the 17th Northeast Regional Stock Assessment Workshop: Consensus Summary of Assessments. NEFSC Lab. Ref. Doc. 94-06, Woods Hole, MA, 02543.

NEFSC. 2001a. Report of the 32nd Northeast Regional Stock Assessment Workshop: Advisory Report on Stock Status. NEFSC Lab. Ref. Doc. 2001-XX, Woods Hole, MA, 02543.

NEFSC. 2001b. Report of the 32nd Northeast Regional Stock Assessment Workshop: Consensus Summary of Assessments. NEFSC Lab. Ref. Doc. 2001-XX, Woods Hole, MA, 02543.

Overholtz, W., J. Link, and L. Suslowicz. 1999. Consumption and harvest of pelagic fishes and squids in the Gulf of Maine-Georges Bank ecosystem. pp. 163-186 in: Ecosystem approaches for fisheries management. Alaska Sea Grant College, AK-SG-99-01.

Overholtz, W., J. Link, and L. Suslowicz. 2000. Consumption of important pelagic fish and squid by predatory fish in the northeastern USA shelf ecosystem with some fishery comparisons. ICES J.  Mar. Sci. 57:1147-1159.

Pennington, M. 1986. Some statistical techniques for estimating abundance indices from trawl surveys. Fishery Bulletin, 84:519-525.

Quinn, T., II, and R. Deriso. 1999. Quantitative fish dynamics. Oxford University Press, New York, 542 pp.

Sarnits, A., and V. Sauskan. 1966, Hydrographic conditions and distribution of silver hake on Georges Bank and off Nova Scotia in 1964. Int. Comm. Northw. Atl. Fish., Res. Doc. 66-51.

Schenk, R. 1981. Population identification of silver hake (Merluccius bilinearis) using isoelectric focusing. Hole Laboratory Reference Document 81-44, NEFSC, Woods Hole, Massachusetts, 31 pp.

Schnute, J. 1981. A versatile growth model with statistically stable parameters. Can. J. Fish. Aquat. Sci. 38:1128-1140.

Sherman, K., W. Smith, W. Morse, M. Berman, J. Green, and L. Ejsymont. 1984. Spawning strategies of fishes in relation to circulation, phytoplankton production, and pulses in zooplankton off the northeastern United States. Mar. Ecol. Prog. Ser. 18(1-2):1-19.

Showell, M., and P. Fanning. 1998. Assessment of the Scotian Shelf silver hake population in 1998. Canadian Stock Assessment Secretariat, Working Paper 99/58.

Sissenwine, M., and E. Cohen. 1991. Resource productivity and fisheries management of the Northeast shelf ecosystem. pp. 107-124 in: Sherman, K., L. Alexander, and D. Gold. (eds.). Food chains, yields, models and management of large marine ecosystems. Westview Press, San Francisco.