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Interdecadal change in growth of sablefish (Anoplopoma fimbria) in the northeast Pacific Ocean.

Errors in growth estimates can affect drastically the spawner-per-recruit threshold used to recommend quotas for commercial fish catches. Growth parameters for sablefish sa·ble·fish  
n. pl. sablefish or sa·ble·fish·es
A dark-colored marine food fish (Anoplopoma fimbria) of North American Pacific waters. Also called black cod.
 (Anoplopoma fimbria) in Alaska have not been updated for stock assessment purposes for more than 20 years, although aging of sablefish has continued. In this study, length-stratified data (1981-93 data from the annual longline long·line  
n.
A heavy fishing line usually several miles long and having a series of baited hooks.



long
 survey conducted cooperatively by the Fisheries Agency of Japan and the Alaska Fisheries Science Center of the National Marine Fisheries Service) were updated and corrected for discovered sampling bias. In addition, more recent, randomly collected samples (1996-2004 data from the annual longline survey conducted by the Alaska Fisheries Science Center) were analyzed and new length-at-age and weight-at-age parameters were estimated. Results were similar between this analysis with length-at-age data from 1981 to 2004 and analysis with updated longline survey data through 2010; therefore, we used our initial results from analysis done with data through 2004. We found that, because of a stratified sampling Noun 1. stratified sampling - the population is divided into subpopulations (strata) and random samples are taken of each stratum
proportional sampling, representative sampling

sampling - (statistics) the selection of a suitable sample for study
 scheme, growth estimates of sablefish were overestimated with the older data (1981-93), and growth parameters used in the Alaskan sablefish assessment model were, thus, too large. In addition, a comparison of the bias-corrected 1981-93 data and the 1996-2004 data showed that, in more recent years, sablefish grew larger and growth differed among regions. The updated growth information improves the fit of the data to the sablefish stock assessment model with biologically reasonable results. These findings indicate that when the updated growth data (1996-2004) are used in the existing sablefish assessment model, estimates of fishing mortality increase slightly and estimates of female spawning biomass decrease slightly. This study provides evidence of the importance of periodically revisiting biological parameter estimates, especially as data accumulate, because the addition of more recent data often will be more biologically realistic. In addition, it exemplifies the importance of correcting biases from sampling that may contribute to erroneous parameter estimates.

**********

The views and opinions expressed or implied in this article are those of the author (or authors) and do not necessarily reflect the position of the National Marine Fisheries Service, NOAA NOAA
abbr.
National Oceanic and Atmospheric Administration

Noun 1. NOAA - an agency in the Department of Commerce that maps the oceans and conserves their living resources; predicts changes to the earth's environment;
.

Sablefish (Anoplopoma fimbria) are a long lived, commercially important finfish finfish

fish with fins, that is teleosts, elasmobranches, holocephalids, agnathids and cephalochordates; also a fish marketer's term used to include that section of marketable fish which is neither shellfish nor molluscs.
 abundant along the upper continental slope in the North Pacific, with catches ranging from 10,000 to 35,000 metric tons (t) in Alaskan waters during the last 2 decades (Hanselman et al., 2010). Using data provided by the NOAA National Marine Fisheries Service (NMFS NMFS National Marine Fisheries Service
NMFS National Mortality Followback Survey
NMFS Network Multimedia File System
NMFS Nested Mount File System
) annual domestic longline survey, we modeled the sablefish population with statistical catch-at-age split by sex (Hanselman et al., 2006). To estimate fish abundance accurately, age-structured models require several biological parameters, such as growth, maturity, natural and fishing mortality, and annual age or length data, as well as annual abundance estimates and catches (Quinn and Deriso, 1999). Errors in growth estimates can drastically affect the spawner-per-recruit threshold used to recommend quotas for commercial fish catches. Overestimation o·ver·es·ti·mate  
tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates
1. To estimate too highly.

2. To esteem too greatly.
 of growth rates Growth Rates

The compounded annualized rate of growth of a company's revenues, earnings, dividends, or other figures.

Notes:
Remember, historically high growth rates don't always mean a high rate of growth looking into the future.
 may result in overestimation of biomass and, therefore, recommendation of harvest rates that are too high (Quinn and Deriso, 1999). Conversely con·verse 1  
intr.v. con·versed, con·vers·ing, con·vers·es
1. To engage in a spoken exchange of thoughts, ideas, or feelings; talk. See Synonyms at speak.

2.
, underestimation of fish growth can lead to underutilization of a resource and lost economic yield. Growth parameters for Alaskan sablefish have not been updated for stock assessment purposes since Sasaki's published research (1985). When age-length conversion matrices were first added to the Alaskan sable-fish stock assessment in 1995, they were constructed from data (1981-93) that were collected under a length-stratified sampling scheme. These data were randomized ran·dom·ize  
tr.v. ran·dom·ized, ran·dom·iz·ing, ran·dom·iz·es
To make random in arrangement, especially in order to control the variables in an experiment.
 according to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 the method of Kimura and Chikuni (1987), but they were collected in limited areas and over just a few years and were aggregated in a way that put too much weight on large fish (>66 cm FL). For these reasons, we speculated that size estimates used in the assessment of the sablefish population of Alaska have been too large. Meanwhile, many more sablefish have been aged over a larger geographic area. Additionally, since the last update on sablefish growth rates, significant changes in length-at-age have been discovered for other demersal de·mer·sal  
adj.
1. Dwelling at or near the bottom of a body of water: a demersal fish.

2.
 species, such as Pacific halibut Noun 1. Pacific halibut - a righteye flounder found in the Pacific
Hippoglossus stenolepsis

righteye flounder, righteyed flounder - flounders with both eyes on the right side of the head
 (Hippoglossus stenolepis) and other flatfish species in the northeast Pacific Ocean. These changes have caused substantial changes in stock assessment results (Walters and Wilderbuer, 2000; Clark and Hare hare, name for certain herbivorous mammals of the family Leporidae, which also includes the rabbit and pika. The name is applied especially to species of the genus Lepus, sometimes called the true hares. , 2002). Because both sablefish and Pacific halibut have similar fisheries and are such commercially valuable fishes, a change in the assessment of one of these fishes suggests that an update of the assessment of the other fish is needed.

[FIGURE 1 OMITTED]

A growth analysis of sablefish in the Gulf of Alaska Noun 1. Gulf of Alaska - a gulf of the Pacific Ocean between the Alaska Peninsula and the Alexander Archipelago
Pacific, Pacific Ocean - the largest ocean in the world
 (Sigler et al., 1997) revealed values similar to results from the earlier analysis by Sasaki (1985); therefore, the earlier growth estimates for sablefish in Alaska have continued to be used in models for sablefish stock assessment. In the last 20 or more years, however, more sablefish from a wide geographic area have been aged and another evaluation of growth is warranted.

The overall goal for this study was to evaluate whether changes in growth of sablefish in Alaska have occurred since 1985. Specifically, our objectives were 1) to reevaluate estimates of length at age and weight at age, 2) to compare these new estimates among regions and over time for each sex, 3) to evaluate the sensitivity of the current stock-assessment model using this new growth information and evaluate the implications for management of sablefish in Alaska, and 4) to search for biological or environmental reasons for any discovered changes.

Materials and methods

Data collection

We used data available from the annual longline survey conducted cooperatively by the Fisheries Agency of Japan (1981-94) and the NMFS Alaska Fisheries (AFSC AFSC American Friends Service Committee
AFSC Alaska Fisheries Science Center
AFSC Air Force Systems Command
AFSC Air Force Specialty Code
AFSC Air Force Space Command
AFSC Armed Forces Services Corporation
AFSC Army Field Support Command
) (1988-present). The Fisheries Agency of Japan conducted the survey solely from 1981 to 1987. Starting in 1988, the NMFS conducted the survey cooperatively with Japan between 1988 and 1994, creating survey overlap between the efforts of the 2 countries. NMFS took over conducting the survey solely in 1995. Samples were collected from June through September, 1981 to 2004, in all 6 management regions defined by the North Pacific Fishery Management Council The Pacific Fishery Management Council (PFMC) is an advisory body; it is charged with regulating most fisheries in U.S. federal waters off Washington, Oregon, and California.  (NPFMC NPFMC North Pacific Fisheries Management Council ). Four of these regions are in the Gulf of Alaska (GOA): Southeast, Kodiak, Chirikof, and Shumagin. The other 2 management regions are in the eastern Bering Sea Bering Sea, c.878,000 sq mi (2,274,020 sq km), northward extension of the Pacific Ocean between Siberia and Alaska. It is screened from the Pacific proper by the Aleutian Islands. The Bering Strait connects it with the Arctic Ocean.  (EBS See Swiss Electronic Bourse.

EBS

See electronic blue sheet (EBS).
) and Aleutian Islands Aleutian Islands (əl`shən), chain of rugged, volcanic islands curving c.1,200 mi (1,900 km) west from the tip of the Alaska Peninsula and approaching Russia's Komandorski Islands.  (AI) (Hanselman et al., 2010; Fig. 1). Predefined stations have been sampled along the upper continental slope at depths of 200-1000 m in the GOA annually from 1981 to the present and in the BSAI BSAI Bering Sea and Aleutian Islands
BSAI British School of Archaeology in Iraq
BSAI Blois Specialités Auto Industrie (Blois, France) 
 at 2 different schedules annually from 1981 to 1994 and in alternating years from 1996 to the present (EBS in odd years and AI in even years). At each station, 7200 hooks baited with cut squid (Illex spp.) and spaced 2 m apart are set (Sigler and Fujioka, 1988).

Length measurements and otoliths of sablefish have been collected since the inception of the Japan-U.S. cooperative longline survey in 1981, and data collection has continued as part of the current NMFS domestic longline survey that started in 1988. However, these data were collected under 2 different sampling designs.

In the first sampling design, fish samples from the Japan-U.S. cooperative survey (1981-93) were stratified stratified /strat·i·fied/ (strat´i-fid) formed or arranged in layers.

strat·i·fied
adj.
Arranged in the form of layers or strata.
 by length (5 fish were aged per centimeter centimeter (sĕn`tĭmē'tər), abbr. cm, unit of length equal to 0.01 meter, the basic unit of length in the metric system. The centimeter is the unit of length in the cgs system. It is approximately equal to 0.  length per sex per area). The sex and fork length (FL) of all collected fish were recorded. No assessment of weight was performed.

A change of sampling method took place in 1996 in the NMFS domestic longline survey. A random subsample sub·sam·ple  
n.
A sample drawn from a larger sample.

tr.v. sub·sam·pled, sub·sam·pling, sub·sam·ples
To take a subsample from (a larger sample).
 of fish was collected (if the first hook of a skate skate, fish: see ray.
skate

Any of nine genera (suborder Rajoidea) of rounded to diamond-shaped rays. These bottom-dwellers are found from tropical to near-Arctic waters and from the shallows to depths of more than 9,000 ft (2,700 m).
 contained a sablefish, it was sampled) to acquire age and weight data (Hanselman et al., 2010). A "skate" is a unit of gear that is 100 m long and contains 45 hooks. As before, fork-length measurements and sex of all fish brought aboard were recorded. Age was determined from otoliths stored in 50% ethanol by using the break and burn technique (Beamish and Chilton, 1982; Nielsen and Johnson, 1983).

Length-at-age analysis

Mean length-at-age was calculated from the age-length data in 3 ways by 3 different strata: 1) by sex, region, and survey period, 2) by sex and survey period, and 3) by sex and region. Data were split between the 2 sexes because it was already known that male and female sablefish have different growth rates (Sasaki, 1985) and because the current sablefish assessment model is split by sex. Data were split into 2 periods by using the shift in sampling design: 1981-93 and 1996-2004 (no otoliths were collected in 1994 and 1995). Fish aged 31 years and older were pooled into a 31+ age category (Hanselman et al., 2010). Only the 6 regions sampled consistently across the entire time series (Southeast, Kodiak, Chirikof, Shumagin, EBS, AI; Fig. 1) were used in regional comparisons.

Estimates of mean length-at-age produced by simple averaging with length-stratified data are biased. This bias is caused by aging smaller and larger specimens more often than would be aged under a random sampling design. The mean size-at-age for early age groups is too small, and the mean size-at-age for the oldest age groups is too large (Goodyear, 1995; Sigler et al., 1997; Bettoli and Miranda, 2001). As a result, we determined that size estimates used in the assessment of the sablefish population in Alaska have been too large. To account for stratification stratification (Lat.,=made in layers), layered structure formed by the deposition of sedimentary rocks. Changes between strata are interpreted as the result of fluctuations in the intensity and persistence of the depositional agent, e.g. , the length-frequency distribution from the survey catch data was used in combination with the length-stratified age samples to create bias-corrected age-length estimates for 1981-93 (Goodyear, 1995; Sigler et al., 1997). The following equation was used (Bettoli and Miranda, 2001):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. .] (1)

Here, [L.sub.a] = the estimated mean length at age a;

[l.sub.j] = the median of the length group j;

[N.sub.j] = the number of fish in the jth length group;

[n.sub.j] = the number of fish subsampled for age determination in the jth length group; and

[n.sub.a,j] = the number of fish in age group a in the subsample from the jth length group.

Sablefish growth was modeled with the von Bertalanffy (VB) age-length model, which was fitted by nonlinear A system in which the output is not a uniform relationship to the input.

nonlinear - (Scientific computation) A property of a system whose output is not proportional to its input.
 least squares weighted by sample size,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

Here, [L.sub.[infinity]] = the average maximum length;

[kappa Kappa

Used in regression analysis, Kappa represents the ratio of the dollar price change in the price of an option to a 1% change in the expected price volatility.

Notes:
Remember, the price of the option increases simultaneously with the volatility.
] = the mean growth coefficient;

[t.sub.0] = the mean theoretical age a fish would have been at zero length; and

[[epsilon].sub.a] = an additive normally distributed error term.

Standard errors, correlation estimates, and 95% confidence intervals for growth curve parameters were estimated by the Hessian method of second partial derivatives (Quinn and Deriso, 1999).

Individual parameters of growth models were compared using the univariate Fisher-Behrens test. Likelihood ratio tests (LRTs) were carried out to determine whether growth curves differed between the 2 survey periods, among regions, or both survey period and region (Kimura, 1980; McDevitt, 1990; Sigler et al., 1997). The LRT LRT Light-Rail Transit
LRT Likelihood Ratio Test
LRT Light Rapid Transit
LRT Lower Respiratory Tract
LRT Lehrstuhl für Raumfahrttechnik
LRT Long Range Transportation
LRT Light Railway Transit
LRT London Regional Transport
LRT Loving Relationships Training
 for comparing nested models was logtransformed and calculated as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

Here, N = the total number of observations (of length-at-age); and

[RSS (Really Simple Syndication) A syndication format that was developed by Netscape in 1999 and became very popular for aggregating updates to blogs and the news sites. RSS has also stood for "Rich Site Summary" and "RDF Site Summary. .sub.F] and [RSS.sub.R] = the estimated residual sum of squares In statistics, the residual sum of squares (RSS) is the sum of squares of residuals,



In a standard regression model , where a and b
 (RSS) of the full (F) and reduced (R) models, respectively (Kimura, 1980; Quinn and Deriso, 1999).

The degrees of freedom for the test are the difference in the number of parameters between the full and reduced models. The increase in the RSS between each of the reduced models and the full model was used to test for temporal and spatial effects. This increase also was used to further test for differences among pairs of regions and between survey periods within each region if a regional or temporal effect was discovered.

Weight-at-age analysis

Weight-at-age curves were fitted to data by sex and region strata. Sasaki (1985) reported sablefish weight estimates; however, no weight data were collected before 1996 in the domestic longline survey; therefore, no temporal changes were investigated. Because weight data were collected only from random samples, no correction for stratification was needed. Fish of ages >31 were pooled into a 31+ age category (Hanselman et al., 2010). To determine weight-at-age for the stock assessment model, first the length-weight relationship was determined by using the typical nonlinear allometric al·lom·e·try  
n.
The study of the change in proportion of various parts of an organism as a consequence of growth.



al
 relationship:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

Here, length l, [alpha], and [beta] are parameters estimated by procedures for nonlinear least squares. This equation was combined with the length-at-age model to construct the weight-at-age model. The weight-at-age model was log-transformed to the following equation because the data had a multiplicative error structure:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

where [epsilon] = a normally distributed error term.

Because of high parameter correlation with only one dependent variable, the allometric parameter [beta] was fixed, determined from the length-weight relationship. The 3 remaining parameters, [W.sub.[infinity]], [kappa], and [t.sub.0] were estimated by a nonlinear procedure (Quinn and Deriso, 1999).

Two age-weight models were fitted to each sex to test whether sablefish weight-at-age differed by region. The full model used separate growth curves fitted to each of the 6 regions, and the reduced model relied on one growth curve fitted to pooled data. Equation 3 was used to compare the full model against the reduced model at a significance level of [alpha]=0.05 (Sigler et al., 1997; Quinn and Deriso, 1999).

Biological and oceanographic explanations for observed changes

Several hypotheses have been formulated to explain the possible change in growth of sablefish in Alaska: interspecific competition Interspecific competition, in ecology, is a form of competition in which individuals of different species vie for the same resource in an ecosystem (e.g. food or living space).  with healthy arrowtooth flounder The arrowtooth flounder, Atheresthes stomias, is a species of righteye flounder. It can be caught from the Bering Sea to Santa Rosa Island, California. Spawning occurs from December through February. This species of flounder can live up to 25 years.  (Atheresthes stomias) populations, intraspecific in·tra·spe·cif·ic   also in·tra·spe·cies
adj.
Arising or occurring within a species: intraspecific competition.
 density-dependent processes, and changing environmental conditions (Hanselman et al., 2006; Maloney and Sigler, 2008). We explored the possibility that temporal growth changes can be attributed to density-dependent effects or to environmental factors, including winter sea-surface temperature (SST SST: see airplane. ), summer SST, and the Pacific Decadal Oscillation The Pacific Decadal Oscillation (PDO) is a pattern of Pacific climate variability that shifts phases on at least inter-decadal time scale, usually about 20 to 30 years. The PDO is detected as warm or cool surface waters in the Pacific Ocean, north of 20° N.  (PDO PDO Php Data Objects (PHP extension)
PDO Protected Designation of Origin (EC)
PDO Pacific Decadal Oscillation (weather)
PDO Property Damage Only
) index.

To test for intra- and interspecific in·ter·spe·cif·ic  
adj.
Arising or occurring between species.



interspecific also interspecies  

Arising or occurring between species.

Adj. 1.
 density-dependence, linear regressions were performed between each of the response variables (the growth parameter k, mean length at age 4, and mean length at age 6), and each of the explanatory variables (biomass values for age-2 sablefish, age-4+ sablefish, and age-4+ arrow-tooth flounder flounder: see flatfish.
flounder

Any of about 300 species of flatfishes (order Pleuronectiformes). When born, the flounder is bilaterally symmetrical, with an eye on each side, and it swims near the sea's surface.
). Biomass estimates were obtained from the 2008 Alaskan sablefish stock assessment (Hanselman et al., 2007) and 2008 Alaska arrowtooth flounder stock assessment (Turnock and Wilderbuer, 2007). Growth estimates were taken from data pooled across the entire series, 1981-2004, for all regions, fitted to the von Bertalanffy growth curve. Significance was determined using a level of [alpha]=0.05, and then the coefficients of determination ([r.sup.2]) were used to assess the explanatory power of the model.

To discern the effect of density-dependence while sablefish were in the juvenile stage, abundance estimates for sablefish and arrowtooth flounder were lagged by 2, 3, and 4 years. This calculation was made to compare the growth rate and size of sablefish at age 4 and age 6 with the abundance of sablefish and arrowtooth flounder exposed to while young of the year (YOY YOY Year Over Year
YOY Year On Year
YOY Young of the Year
YOY Yield on Year
), and at age 1, age 2, and age 3.

To examine the influence of environment on growth, linear regressions were performed between each of the response variables (mean length at age 4 and mean length at age 6), and each of the explanatory variables (winter SST, summer SST, and an index used to quantify the PDO). Because YOY and juvenile sablefish are more susceptible to surface temperatures and are considered to be more susceptible to oceanographic variability than are adults, we lagged the SST by 2, 3, and 4 years to compare the size of an age 4 sablefish with the SST exposed to while as a YOY, and at age 1, and age 2, and we lagged the SST by 4, 5, and 6 years to compare the size of an age 6 sablefish with the SST exposed to as a YOY, and at age 1 and age 2.

Monthly values of the PDO index were obtained from the Joint Institute for the Study of Atmosphere and Oceans (Mantua Mantua (măn`chə, –tə), Ital. Mantova, city (1991 pop. 53,065), capital of Mantova prov.  et al., 1997; http://jisao.washington. edu/pdo/PDO.latest, accessed January 2008; http://www.beringclimate.noaa.gov/data/index.php, accessed January 2008), which incorporated data from the United Kingdom's Meteorological me·te·or·ol·o·gy  
n.
The science that deals with the phenomena of the atmosphere, especially weather and weather conditions.



[French météorologie, from Greek
 Office's (UKMO UKMO United Kingdom Meteorological Office ) Historical SST Dataset and Reynolds' Optimally Interpolated SST. SST values for the Bering Sea (http://www.beringclimate.noaa.gov/data/BCresult.php, accessed January 2008) and the GOA (Kaplan et al., 1998; http://www. esrl.noaa.gov/psd/data/timeseries/, accessed January 2008) were taken from a data set of SST anomalies, Kaplan Extended SST V2, provided by the Physical Sciences Division of NOAA's Earth System Research Laboratory, Boulder, Colorado The City of Boulder (, Mountain Time Zone) is a home rule municipality located in Boulder County, Colorado, United States. Boulder is the 11th most populous city in the State of Colorado, as well as the most populous city and the county .

Management implications

We examined the sensitivity of the current stock assessment model to the use of the new growth information from our study. The AFSC models the Alaskan sablefish population with statistical catch-at-age methods. It uses a penalized pe·nal·ize  
tr.v. pe·nal·ized, pe·nal·iz·ing, pe·nal·iz·es
1. To subject to a penalty, especially for infringement of a law or official regulation. See Synonyms at punish.

2.
 maximum likelihood function to estimate parameters simultaneously to obtain the best fit between predicted and observed data. Data in the sablefish stock assessment model include catch, several abundance indices, and age and length data from the longline survey and from the fishery. For details of the assessment model, see Hanselman et al. (2010).

This assessment model in its current form uses age-length conversion matrices, not empirical age-length keys, to describe the probability that a fish of a given age is of a certain length. This model uses these age-length conversion matrices to predict lengths. The weight-at-age is input as a fixed vector for the whole time series. If the conversion matrices and the weight-at-age vector are developed with growth data that do not correspond with the true underlying growth, they can bias the stock assessment (Hanselman et al., 2007). Using the updated growth curves from the 2 survey periods reported in this study, we created new length-age conversion matrices and a new weight-at-age vector and applied them to the current stock assessment model (Hanselman et al., 2007).

Results

Length-at-age analysis

Our results indicate that previously used growth estimates in the stock assessments of sablefish in Alaska (assessments before 2007) obtained from length-stratified sampling were erroneously too large. A comparison of growth estimates from 1981-93 data updated to correct for this bias with estimates from more recent data (1996-2004) indicates that sablefish are growing to a larger maximum size in more recent years. The estimates of average maximum length ([L.sub.[infinity]]) used in the stock assessment of Alaskan sablefish in 2007 (Sasaki's [1985] estimate from length-stratified data) were 69 cm FL for males and 83 cm FL for females (Hanselman et al., 2006). Maximum lengths were smaller in our bias-corrected estimates for the same time period (1981-93; Tables 1, 2) than in the 2007 stock assessment model: males=64.6 cm FL, females=75 cm FL. Our estimates for the more recent period (1996-2004; Tables 1, 2) are significantly larger (males=67.7 cm FL, females=80.1 cm FL) than the bias-corrected estimates from the earlier period, but these estimates for the recent period are still smaller than the estimated lengths incorrectly used in earlier stock assessments.

The growth rates of male and female sablefish in Alaska differed significantly across areas and survey periods (P<0.05; Tables 3, 4). In the data from the earlier period, both male and female sablefish display smaller asymptotic lengths ([L.sub.[infinity]]) and younger ages to than do sablefish in data from the more recent time period (Fig. 2). Significant differences were detected between the 2 male growth curves (P<0.001; Table 1). Test results on the female data showed that the [L.sub.[infinity]] estimates (P<0.001) and the growth curves were significantly different (P<0.001; Table 2) between the 2 periods.

A comparison of male growth curves between the 2 survey periods, stratified by region, showed a consistent pattern of slower growth and smaller asymptotic lengths during the earlier survey period. There were significant differences between growth curves fitted to the 2 periods in 5 of the 6 management regions (Fig. 3, Table 1). Fish from most regions had a smaller asymptotic length and slower growth during the earlier survey period than during the more recent period. In contrast, during the earlier survey period versus the more recent one, males in the Shumagin region reached a smaller maximum length but grew faster and males in the Chirikof region displayed a larger asymptotic length and grew more slowly.

Age-length relationships for females between the 2 survey periods differed significantly in 5 of the 6 management regions (Fig. 4, Table 2). Female asymptotic lengths ranged from 68.3 to 78.3 cm FL during the earlier survey period, with the lowest maximum lengths occurring in the EBS region and highest lengths in the Southeast. In the more recent period, asymptotic lengths were much larger, ranging from 76.4 cm (EBS) to 81.6 cm FL (Shumagin region). During the earlier time period, compared to the more recent one, AI, Kodiak, and Southeast females grew slower and Shumagin, Chirikof, and EBS females displayed the opposite pattern.

Several tests for differences in growth between pairs of regions were significant (P<0.05) for both sexes. Male sablefish showed fewer differences in growth between regions, with Chirikof males differing significantly from Shumagin (P=0.02), AI (P=0.01) and EBS (P=0.01) males, and EBS males differing significantly from males in the Southeast (P=0.04). For female sablefish, most regional comparisons were highly significant, with the exception of the difference between AI and Shumagin (P=0.55), Chirikof and Kodiak (P=0.12) and Southeast (P=0.12), and Kodiak and Southeast (P=0.37).

A consistent pattern of smaller estimates of to, the theoretical age at zero length, was seen for both male and female sablefish in the earlier survey period, than estimates for the more recent survey period. These smaller values could be a result of small sample sizes of fish <4 years old in the older data sets (Sigler et al., 1997).

Weight-at-age

The age-weight relationship differed significantly among regions in both males (P<0.001, Table 5) and females (P<0.001, Table 6). Maximum weights for male (Table 7) and female (Table 8) sablefish in all regions combined were smaller than the values used in the current stock assessment model, likely because of differences in age at length. Female sablefish in pooled regions reached a higher average maximum weight-at-age than did male sablefish, 5.5 kg versus 3.2 kg, respectively.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Maximum average weights among male sablefish varied slightly, but still significantly (P<0.05), by region (Table 7). The lightest males, with maximum weight of 3.0 kg, were found in the Kodiak region, and the heaviest males, with maximum weight of 3.4 kg, were observed in the EBS region. Females showed a larger range of average maximum weights, from 4.7 kg in the EBS region to 5.8 kg in the Shumagin region (Table 8). Several maximum weights differed significantly between regions for both sexes; similar age-weight relationships were seen only for females in the AI and Shumagin regions and the Kodiak and Southeast regions. Male sablefish in all of the 6 regions displayed highly significant differences in weight-at-age, although their growth curves appeared similar. These minor growth differences may not be of biological importance and may not need to be considered for assessment purposes.

[FIGURE 4 OMITTED]

Biological and oceanographic explanations for observed changes

There was no evidence of a common climatic forcing factor among the management regions in relation to changes in sablefish growth. Arrowtooth flounder biomass likewise was unrelated to sablefish growth. Intraspecific, density-dependent effects appeared to be a more plausible explanation for changes in growth of Alaskan sablefish because measures of age-4+ biomass at some lags (in years) were correlated with reduced growth. Significant relationships included mean length at age 6 regressed on the total age-4+ biomass (coefficient of determination Coefficient of determination

A measure of the goodness of fit of the relationship between the dependent and independent variables in a regression analysis; for instance, the percentage of variation in the return of an asset explained by the market portfolio return. Also known as R-square.
 [[r.sup.2]]=0.28, P=0.02), and mean length at age 4 regressed on the age-4+ biomass from 3 years prior, when the sablefish were age 1 ([r.sup.2]=0.5, P=0.04). Both of these analyses revealed a decrease in average length with an increase in biomass. Although not significant, a negative correlation Noun 1. negative correlation - a correlation in which large values of one variable are associated with small values of the other; the correlation coefficient is between 0 and -1
indirect correlation
 between the growth coefficient k and both age-2 and age-4+ biomass also was evident.

Management implications

The use of updated growth data (length-at-age fitted to 2 survey periods and weight-at-age from the more recent survey period) improved the fit of the current AFSC assessment model of sablefish to the data and slightly increased the recommended fishing-induced mortality. The updated growth also had an effect on the estimated time series of female spawning biomass (Fig. 5). Three prominent changes in the estimates of female spawning biomass were observed when the assessment model that used the estimates of Sasaki (1985) was run with our updated growth estimates: 1) the initial estimated spawning biomass in 1960 was substantially higher, 2) the minima in female spawning biomass are lower, and 3) the estimated spawning biomass was slightly lower for recent years (2000 to present). The increase, between the use of Sasaki estimates and our bias-corrected data, in estimated spawning biomass in 1960 is biologically reasonable because fishing mortality before 1960 was low (Hanselman et al., 2007). The lower spawning biomass minima in the updated series imply that the resource was not managed as conservatively as expected during the periods of lowest biomass. Results from our study show that recent estimates of female spawning biomass from our updated growth data are slightly lower but appear to be rising at a steeper trajectory Trajectory

The curve described by a body moving through space, as of a meteor through the atmosphere, a planet around the Sun, a projectile fired from a gun, or a rocket in flight.
 than recent estimates determined with Sasaki's growth data in the current model.

Discussion

Although a specific cause (changes in sampling method, environmental factors, or differences in fish abundance) and time of the changes observed in sablefish growth were not identified, these changes have occurred. The division of the sablefish age-and-length data set into 2 growth regimes was not based on any detectable shift in growth but on a change in the sampling design of the longline survey. Separating the data into 2 time intervals might not completely capture the temporal pattern of changes in growth. Sablefish growth, for example, might have changed slowly, instead of in a stepwise stepwise

incremental; additional information is added at each step.


stepwise multiple regression
used when a large number of possible explanatory variables are available and there is difficulty interpreting the partial regression
 fashion. However, we also analyzed growth data by individual years, and no obvious temporal patterns were noted. It is unlikely that other changes in the survey could explain apparent differences in growth over the time series because of the standardization in most other aspects of the survey design between the 2 periods (Hanselman et al., 2007). In addition, both the ages and the abundance indices for the sablefish stock assessment are treated as separate surveys (Japan-U.S. cooperative and domestic NMFS longline surveys) with different catchability values and sensitivities, and therefore updated growth estimates fitted to these 2 survey periods (which theoretically represent the 2 surveys) follow accordingly.

[FIGURE 5 OMITTED]

Aging error could be a very plausible cause for seeing changes in growth when in fact growth has not changed. Although Heifetz et al. (1999), among others, have validated the currently accepted aging practices (Beamish and Chilton, 1982) and have examined sources of error in the aging of sablefish, there is still much disagreement on the possibility of obtaining reliable ages from sablefish otoliths (Pearson and Shaw, 2004). We feel aging error is an unlikely cause for the growth changes seen in this study. The NMFS stock assessment of sablefish in Alaska uses an aging error matrix, one with known ages that make it particularly realistic. Aging error should not have a major effect on growth estimation if the aging error is imprecise im·pre·cise  
adj.
Not precise.



impre·cisely adv.
 but not biased, and Heifetz et al. (1999) found bias to be at a minimum for younger ages when most growth is occurring. In addition, otoliths for Alaskan sablefish have been read consistently by the same age-reader using the same protocol during the timeline of this study and age-reader agreement tests have been in place throughout that entire time thus, removing the possibility of an age-reader effect.

The best documented causes for change in growth of various fish species (juvenile sablefish; Pacific halibut; yellowtail flounder Noun 1. yellowtail flounder - flesh of American flounder having a yellowish tail
Limanda ferruginea, yellowtail flounder - American flounder having a yellowish tail

flounder - flesh of any of various American and European flatfish

2.
 [Limanda ferruginea Noun 1. Limanda ferruginea - American flounder having a yellowish tail
yellowtail flounder

righteye flounder, righteyed flounder - flounders with both eyes on the right side of the head
]; haddock haddock: see cod.
haddock

Valuable North American food fish (Melanogrammus aeglefinus, family Gadidae). A bottom-dweller that feeds on invertebrates and fishes, it resembles the cod, with its chin barbel (fleshy feeler) and two anal and three dorsal
 [Melanogrammus aeglefinus]; and Pacific chub Chub, in the Bible
Chub (kŭb), in the Bible, an African people. This may be a textual error for Lub (i.e., Lubim).
chub, in zoology
chub: see minnow.
 mackerel mackerel, common name for members of the family Scombridae, 60 species of open-sea fishes, including the albacore, bonito, and tuna. They are characterized by deeply forked tails that narrow greatly where they join the body; small finlets behind both the dorsal and  [Scomberjaponicas] have been density dependence and environmental conditions (Ross and Nelson, 1992; Clark et al., 1999; Wilson, 2000; Sogard and Olla, 2001; Watanabe and Yatsu, 2004). In our study, we did find evidence that changes in growth may be the result of intraspecific density-dependent mechanisms. It appears that sablefish growth is most influenced by fish density that fish are exposed to while in the larval larval

1. pertaining to larvae.

2. larvate.


larval migrans
see cutaneous and visceral larva migrans.
 and juvenile stages. This response in turn is linked highly to favorable fa·vor·a·ble  
adj.
1. Advantageous; helpful: favorable winds.

2. Encouraging; propitious: a favorable diagnosis.

3.
 environmental conditions for recruitment and YOY survival (McFarlane and Beamish, 1992; Sigler and Lunsford, 2001; Sogard and Olla, 2001). Results of our growth analysis show that sablefish from the more recent time period of our study (1996-2004), when compared to sablefish from earlier time period of our study (1981-93), exhibited faster growth rates and reached larger sizes-at-age as biomass steadily declined (Hanselman et al., 2007). Although the Alaskan sablefish population is considered to be at a sustainable, healthy level and is neither overfished nor approaching an overfished level, it is by no means close to its peak abundances of the late 1980s and early 1990s (Hanselman et al., 2010). Across the time series, abundance of Alaskan sablefish was characterized by relatively consistent high values (e.g., age-4+ abundance of 489 kt in 1986) during the early period of this study and consistently lower values (e.g., age-4+ abundance of 223 kt in 2000) during the more recent period (Hanselman et al., 2010). Since 1988, abundance has decreased substantially, whereas growth has increased significantly (Hanselman et al., 2007).

Although no direct relationships were observed between sablefish growth and any of the tested environmental factors, it is important to note that evaluating which environmental variables are appropriate proxies for the ambient conditions that influence growth may be done best with data from smaller time and space scales than with the data available for the purposes of this study and that environmental data at fine temporal or spatial scales are likely to be difficult to interpret for fish species that move long distances (Heifetz and Fujioka, 1991; Kimura et al., 1998). The use of broad geographic and time-averaged representations of environmental effects misses short-term changes in temperature regimes brought on by weather events, such as wind-driven mixing and upwelling up·well·ing  
n.
1. The act or an instance of rising up from or as if from a lower source: an upwelling of emotion.

2.
. In the future, to determine an appropriate scale, results from the extensive tagging studies with sablefish should be examined (the Fisheries Agency of Japan and NMFS have been tagging sablefish throughout the entire geographic range of the annual longline survey since 1972). Further, analysis should be done with the El Nino-Southern Oscillation Oscillation

Any effect that varies in a back-and-forth or reciprocating manner. Examples of oscillation include the variations of pressure in a sound wave and the fluctuations in a mathematical function whose value repeatedly alternates above and below some
 as an environmental variable in a similar manner to work done by Kimura et al. (1998) who found growth of groundfish species to be significantly enhanced by events of the El Nino-Southern Oscillation.

There appear to be significant differences in growth patterns among management regions; the GOA regions consistently displayed the largest (in asymptotic length and average size) sablefish for both sexes in this study and in past research (McDevitt, 1990; Sigler et al., 1997). Sasaki (1985) reported regional differences in mean sizes between young sablefish from the EBS, AI, and GOA and a temporal increase in weight-at-age in the EBS from the 1960s to the late 1970s similar to the temporal increase in growth (length-at-age) reported here. Sasaki's reported differences were minor and not significant. McDevitt (1990) reported significant growth differences between the EBS and GOA but did not find significant differences in growth between the AI and EBS and the AI and GOA. She speculated that her findings were the result of high variability of the data from the AI. Consequently, differences between the AI and EBS regions were not detected because of the low power of the tests. In accord with our results, Sigler et al. (1997) found that female sablefish in the Shumagin and Southeast regions of the GOA differed significantly in growth, but no regional differences were detected for males.

In both the AI and EBS regions, poor model fits and atypical atypical /atyp·i·cal/ (-i-k'l) irregular; not conformable to the type; in microbiology, applied specifically to strains of unusual type.

a·typ·i·cal
adj.
 rates of growth and average maximum sizes were noted in this and past studies (McDevitt, 1990). Both of these regions displayed notably high estimates of the growth parameter k, likely because samples from these two regions consisted mostly of larger (>66 cm FL) fish, and smaller (<57 cm FL) fish are required for an accurate estimate of k. Data from both of these regions exhibit the highest variability (large residual population variances) and the poorest fit to the growth curves, compared with data from other regions in this study. The most notable differences among observed sablefish were consistently found in the EBS region, where smaller asymptotic lengths were reported than those for sablefish found in all other regions.

Alaskan sablefish are assessed by the AFSC as one stock, and therefore sablefish found throughout Alaskan waters are assumed to display similar growth rates; however, this stock is highly mobile (Heifetz and Fujioka, 1991; Maloney and Sigler, 2008). Younger fish move into deeper waters onto the slope, moving from the Eastern Gulf of Alaska (EGOA) in a counter clockwise clock·wise  
adv. & adj. Abbr. cw.
In the same direction as the rotating hands of a clock.


clockwise
Adverb, adj

in the direction in which the hands of a clock rotate
 direction through the Central Gulf of Alaska (CGOA) to the Western Gulf of Alaska (WGOA WGOA Wearing Glasses on Arrival ), returning to the EGOA as larger, older fish (Heifetz and Fujioka, 1991; Maloney and Sigler, 2008). In theory, one would not expect there to be many regional differences in sablefish growth and average size-at-age because a large part of the sablefish population moves each year, maintaining a well-mixed population (Heifetz and Fujioka, 1991). Several competing hypotheses are available to explain these observed regional differences: geographic differences in food abundance, oceanographic condition, or sablefish abundance. Any explanation for these regional differences, however, has to be consistent with this observed movement pattern. As with observed geographical variation any variation of a species which is dependent on climate or other geographical conditions.

See also: Geographic
 for the northern anchovy anchovy: see herring.
anchovy

Any of more than 100 species of schooling saltwater fishes (family Engraulidae) related to the herring. Anchovies are distinguished by a large mouth, almost always extending behind the eye, and by a pointed snout.
 (Engraulis mordax) along the west coast of North America North America, third largest continent (1990 est. pop. 365,000,000), c.9,400,000 sq mi (24,346,000 sq km), the northern of the two continents of the Western Hemisphere. , geographical variation in age composition could have influenced the observed variation in mean size of sablefish in the 6 management regions (Parrish et al., 1985; Saunders et al., 1997). Sablefish in the GOA may have displayed apparently faster growth and larger asymptotic lengths and weights than have sablefish in the AI and EBS regions because size-dependent migration results in a mixture of faster-growing young fish with older spawning fish (Heifetz and Fujioka, 1991). In contrast, in the EBS region, which primarily comprises fish >4 years of age, sablefish might have displayed slower growth because of the absence of the youngest, fastest-growing fish (Quinn and Deriso, 1999; Sogard and Olla, 2001).

Alternatively, varying growth rates might be explained in part by regional differences in abiotic factors, such as oceanographic conditions (Sasaki, 1985; McDevitt, 1990; Saunders et al., 1997; Kuznetsova, 2003). If fish are grouped within a highly migratory migratory /mi·gra·to·ry/ (mi´grah-tor?e)
1. roving or wandering.

2. of, pertaining to, or characterized by migration; undergoing periodic migration.


migratory

emanating from or pertaining to migration.
 population, environmental effects would appear as growth differences between the 6 management regions. Temperature differences may explain the divergence divergence

In mathematics, a differential operator applied to a three-dimensional vector-valued function. The result is a function that describes a rate of change. The divergence of a vector v is given by
 in growth rates between fish in the EBS region and fish in regions in the GOA, such as the Southeast region. Several marine species (e.g., northern anchovy; Atlantic cod [Gadus morhua L.]; walleye walleye, in medicine
walleye: see strabismus.
walleye, in zoology
walleye or walleyed pike: see perch.
 pollock [Theragra chalcogrammna]; turbot turbot: see flatfish.
turbot

Species (Scophthalmus maximus, family Scophthalmidae or Bothidae) of broad-bodied European flatfish, a highly valued food fish. It lives along sand and gravel shores.
 [Scophthalmus maximus]; and blacknose shark The blacknose shark, Carcharhinus acronotus, is a requiem shark of the family Carcharhinidae, found in subtropical waters of the western Atlantic Ocean between latitudes 40° N and 37° S, from the surface to about 10 m. Its length is up to about 2 m.  [Carcharhinus acronotus]) are of larger sizes and are faster growing in the southern extent of their ranges than in other areas of their distributions (Parrish et al., 1985; Imsland et al., 2001; Kuznetsova, 2003; Armstong et al., 2004; Driggers et al., 2004; Stark et al., 2007).

For the purposes of the management of Alaskan sablefish, updated and corrected growth estimates divided into the 2 survey periods, 1981-93 and 1996-2004, have been incorporated into the Alaskan sablefish stock assessment conducted by the AFSC. We ran the model used in our study with the data updated through 2010 and found results that were not significantly different from the results of our analysis with data collected through 2004. Therefore, our initial results were used: VB parameter estimates for females from 1996-2010, [L.sub.[infinity]] =79.9, k=0.22, [t.sub.0]=-2.23; VB parameter estimates for males from 1996-2010, [L.sub.inifity]] =68, k=0.273, [t.sub.0]=-3.01. The updated growth estimates provide a better fit to the data, and they are the result of decades more age and growth collections with previous size biases corrected. We view these updated growth estimates as a needed and substantial increase in biological realism for the Alaskan sablefish stock assessment model. In the future, growth will be revisited periodically, but as data accumulate, the addition of the newest data should have only nominal effects on recommendations for harvest rates (Hanselman et al., 2007).

Conclusions

In moving closer to estimating true underlying sablefish growth, we have revealed that, historically, the sizes of sablefish modeled in the Alaskan sablefish stock assessment were slightly too large. This study aids in describing the population of sablefish in Alaska more realistically as having a smaller maximum size. The use of these improved estimates will result in more conservative management in the short term but more harvest stability in the future. Although a specific cause and time for the changes in sablefish growth was not identified, these changes have occurred. To properly manage this important economic resource, the updated estimates for growth should continue to be used for the NMFS assessment of the Alaskan sablefish stock.

This study provides an example of the importance of identifying and correcting for biases that may be produced from different data collection strategies and of scientists periodically revisiting life history parameter estimates used in assessment of various stocks. The result of such efforts could mean the difference in overestimation or underestimation of abundance and, in turn, could have an effect on allotted al·lot  
tr.v. al·lot·ted, al·lot·ting, al·lots
1. To parcel out; distribute or apportion: allotting land to homesteaders; allot blame.

2.
 harvest recommendations.

Acknowledgments

We thank N. Hillgruber for reviewing this manuscript and for providing much guidance and C. Lunsford for his contributions and suggestions.

Manuscript submitted 4 January 2012.

Manuscript accepted 31 May 2012.

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Katy B. Echave (contact author) [1]

Dana H. Hanselman [1]

Milo Milo, athlete of ancient Greece
Milo (mī`lō) or Milon (mī`lŏn), fl. 500 B.C., athlete of ancient Greece, b. Crotona.
 D. Adkison [2]

Michael F. Sigler [1]

Email address See Internet address.  for contact author: katy.echave@noaa.gov

[1] Auke Bay Laboratories Alaska Fisheries Science Center, National Marine Fisheries Service, NOAA Ted Stevens Marine Research Institute 17109 Pt Lena Lena (lē`nə, Rus. lyĕ`nə), river, easternmost of the great rivers of Siberia, c.2,670 mi (4,300 km) long, rising near Lake Baykal, SE Siberian Russia.  Loop Rd. Juneau, Alaska 99801

[2] University of Alaska Fairbanks UAF is home to seven major research units: the Agricultural and Forestry Experiment Station; the Geophysical Institute, which operates the Poker Flat Research Range; the International Arctic Research Center; the Arctic Region Supercomputing Center; the Institute of Arctic Biology; the  School of Fisheries and Ocean Sciences 23S O'Neill Fairbanks, Alaska 99445
Table 1

Growth parameters ([L.sub.[infinity]] =average maximum length, is=mean
growth coefficient, [t.sub.0]=mean theoretical age a fish would have
been at zero length) for male sablefish (Anoplopoma fimbria) in
Alaska estimated with data from the annual longline survey conducted
cooperatively by the Fisheries Agency ofJapan and the Alaska Fisheries
Science Center of the National Marine Fisheries Service in 1981-93
and by the Alaska Fisheries Science Center during 1996-2004. Estimates
were made for 6 management regions with the von Bertalanffy model
fitted to age-length data stratified by region and survey period,
where n is the number of age-length observations and an asterisk (*)
indicates a significant difference between the 2 periods, 1981-93 and
1996-2004, in that particular region. The 6 regions are the Chirikof,
Kodiak, Shumagin, and Southeast, all in the Gulf of Alaska, and the
eastern Bering Sea and Aleutian Islands. Standard errors of the mean
(SE) are provided in parentheses. RSS=residual sum of squares.

Region        Survey period   [L.sub.[infinity]]   k

All regions   1981-93         64.6 (0.38)          0.287 (0.03)
combined      1996-2004 *     67.7 (0.16)          0.292 (0.01)
              1981-2004       66.2 (0.28)          0.30 (0.03)
Chirikof      1981-93         70.2(l.02)           0.239 (0.03)
              1996-2004 *     67.3 * (0.48)        0.335 (0.06)
              1981-2004       67.8 (0.45)          0.327 (0.03)
Aleutian      1981-93         67.0 (0.55)          0.195 (0.03)
              1996-2004       68.1 (0.48)          0.243 (0.02)
              1981-2004       67.0 (0.55)          0.195 (0.03)
Kodiak        1981-93         65.1 (0.66)          0.352 (0.06)
              1996-2004 *     66.6 (0.34)          0.357 (0.07)
              1981-2004       66.0 (0.39)          0.365 (0.04)
Shumagin      1981-1993       64.3 (0.50)          0.440 (0.07)
              1996-2004 *     70.1 (0.98)          0.193 (0.03)
              1981-004        65.3 (0.49)          0.352 (0.05)
Bering        1981-1993       64.9 (0.64)          0.197 (0.04)
              1996-2004 *     69.3 * (0.50)        0.237 (0.03)
              1981-2004       66.7 (0.71)          0.186 (0.03)
Southeast     1981-1993       67.0 (0.79)          0.219 (0.04)
              1996-2004 *     68.3 (0.37)          0.307 (0.04)
              1981-2004       67.7 (0.45)          0.271 (0.03)

Region        Survey period   [t.sub.0]         RSS      n

All regions   1981-93         -2.07 (0.60)      3644   3429
combined      1996-2004 *     -2.25 (0.21)       904   2614
              1981-2004       -2.19 (0.51)    18,954   6043
Chirikof      1981-93         -2.288 (0.70)      448    128
              1996-2004 *     -1.617 (1.02)      487    294
              1981-2004       -1.287 (0.48)     1230    422
Aleutian      1981-93         1329               726
              1996-2004       -2.898 (0.59)      478    543
              1981-2004       -5.101 (1.23)     2235   1269
Kodiak        1981-93         -1.685 (0.79)     1737    598
              1996-2004 *     -2.052 (1.21)      606    542
              1981-2004       -1.423 (0.55)     3239   1140
Shumagin      1981-1993       -0.793 (0.60)     1625    684
              1996-2004 *     -4.501 (1.08)      438    267
              1981-004        -1.669 (0.63)     2914    951
Bering        1981-1993       -6.264 (1.67)     1154    757
              1996-2004 *     -3.48 (0.86)       600    363
              1981-2004       -6.250 (1.69)     4695   1120
Southeast     1981-1993       -3.827 (1.19)     1998    536
              1996-2004 *     -1.714 (0.73)      829    605
              1981-2004       -2.384 (0.65)     4136   1141

Table 2

Growth parameters ([L.sub.[infinity]]=average maximum length,
[kappa]=mean growth coefficient, [t.sub.0]=mean theoretical age a fish
would have been  at zero length) for female sablefish (Anoplopoma
fimbria) in Alaska estimated with the von Bertalanffy model fitted to
age-length  data stratified by region and time period, where n is the
number of age-length observations and an asterisk (*) indicates a
signifi-cant difference between the 2 survey periods, 1981-93 and
1996-2004, for that particular region. Standard errors of the mean
(SE) are presented in parentheses. RSS=residual sum of squares.

Region        Survey period   [L.sub.[infinity]]        k

All regions   1981-93         75.0 (0.35)          0.263 (0.01)
combined      1996-2004 *     80.1 * (0.26)        0.223 (0.01)
              1981-2004       77.1 (0.77)          0.25 (0.02)
Chirikof      1981-93         75.3 (1.29)          0.298 (0.04)
              1996-2004       77.5 (0.51)          0.294 (0.02)
              1981-2004       76.8 (0.56)          0.302 (0.02)
Aleutian      1981-93         73.8 (0.84)          0.197 (0.04)
              1996-2004 *     77.9 * (1.31)        0.218 (0.03)
              1981-2004       73.8 (0.69)          0.248 (0.03)
Kodiak        1981-93         74.5 (0.84)          0.305 (0.04)
              1996-2004 *     78.6 * (0.50)        0.311 (0.03)
              1981-2004       76.7 (0.63)          0.292 (0.03)
Shumagin      1981-93         73.2 (0.69)          0.295 (0.03)
              1996-2004 *     81.6 * (1.30)        0.177 * (0.02)
              1981-2004       74.7 (0.72)          0.256 (0.02)
Bering        1981-93         68.3 (0.59)          0.351 (0.05)
              1996-2004 *     76.4 * (0.87)        0.223 * (0.02)
              1981-2004       70.2 (0.74)          0.306 (0.05)
Southeast     1981-93         78.3Q.02)            0.189 (0.03)
              1996-2004 *     80.8 * (0.50)        0.273 * (0.02)
              1981-2004       79.3(0.72)           0.217 (0.02)

Region        Survey period   [t.sub.0]          RSS      n

All regions   1981-93         -2.00 (0.29)       3945   4788
combined      1996-2004 *     -1.92 (0.14)       1191   3493
              1981-2004       -1.91 (0.32)     23,963   8281
Chirikof      1981-93         -0.798 (0.58)      1275    165
              1996-2004       -0.802 (0.40)       609    485
              1981-2004       -0.697 (0.33)      2201    650
Aleutian      1981-93         -3.888 (1.30)      4839   1037
              1996-2004 *     -2.246 (0.69)      2191    795
              1981-2004       -2.210 (0.70)      9466   1832
Kodiak        1981-93         -1.288 (0.51)      3334    831
              1996-2004 *     -0.49 (0.42)       1081    602
              1981-2004       -1.220 (0.40)      7231   1433
Shumagin      1981-93         -1.724 (0.58)      1993    975
              1996-2004 *     -3.046 (0.49)       877    563
              1981-2004       -2.028 (0.48)      4830   1538
Bering        1981-93         -1.79 (0.76)       1925    993
              1996-2004 *     -2.746 (0.62)       695    533
              1981-2004       -2.163 (0.82)      6979   1526
Southeast     1981-93         -3.579 (0.95)      4488    787
              1996-2004 *     -0.816* (0.42)      964    515
              1981-2004       -2.489(0.61)       8949   1302

Table 3

Comparison of 4 age-length models used for analyses of regional and
temporal effects on growth of male sablefish (Anoplopoma imbria) in
Alaska. The most reasonable model, indicated with an asterisk (*), is
the reduced model with a residual sum of squares  (RSS) not
significantly greater than the RSS for the full model. n =the number
of observations, and [chi square] = the chi-squared value.

Model                RSS      [chi square]   P         No. of
                                                      parameters

Data split by each   11,729                               36
combination of
region and survey
period *

Data split into 2    16,354   114.7          <0.001       6
survey periods
Data split into 6    18,449   156.3          <0.001       18
regions
All data pooled      21,642   211.3          <0.001       3

Model                n

Data split by each
combination of
region and survey
period *

Data split into 2
survey periods
Data split into 6
regions
All data pooled      6043

Table 4
Comparison of 4 age-length models used for analyses of regional and
temporal effects on growth of female sablefish (Anoplo-poma fimbria)
in Alaska. The most reasonable model, indicated with an asterisk (*),
is the reduced model with a residual sum of  squares (RSS) not
significantly greater than the RSS for the full model. n=the number of
observations, and [chi square] = the chi-squared  value.

Model                       RSS      [chi square   P         No. of
                                                            parameters

Data split by each          24,271                              36
combination of region
and survey period *
Data split into 2           48,717   238.9         <0.001        6
survey periods
Data split into 6 regions   39,656   168.4         <0.001       18
All data pooled             68,900   357.9         <0.001        3

Model                       n

Data split by each
combination of region
and survey period *
Data split into 2
survey periods
Data split into 6 regions
All data pooled             8281

Table 5

Comparison of 2 age-weight models used for analyses of regional
effects on growth of male sablefish (Anoplopoma fimbria) in Alaska.
The most reasonable model, indicated with an asterisk (*), is the
reduced model with a residual sum of squares (RSS) not significantly
greater than the RSS for the full model. n = the number of observations,
and [chi square] = the chi-squared value.

Model             RSS     [chi square]   P        No. of parameters

Data split into   144.4                                  24
6 regions *
All data pooled   151.8      174.6       <0.001           4

Model             n

Data split into
6 regions *
All data pooled   2614

Table 6

Comparison of 2 age-weight models used for analyses of regional
effects on growth of female sablefish (Anoplopoma fimbria) in
Alaska. The most reasonable model, indicated with an asterisk (*) is
the reduced model with a residual sum of squares (RSS) not
significantly greater than the RSS for the full model. n=the number
of observations, and [chi square] =the chi-squared value.

Model             RSS   [chi square]   P        No. of parameters

Data split into   262                                  24
6 regions *
All data pooled   277      145.5       <0.001           4

Model             n

Data split into
6 regions *
All data pooled   3493

Table 7

Estimates o- weight-at-age parameters ([W.sub.[infinity]] =average
maximum weight, [kappa]=mean growth coefficient, [t.sub.0]=mean
theoretical age a  fish would have been at zero weight) for male
sablefish (Anoplopoma fimbria) in Alaska determined with the von
Bertalanffy model fitted to age-weight data for the pooled survey
periods of 1996-2004 stratified by region and combined for Alaskan
waters ([W.sub.[infinity]]= average maximum weight, rc=mean growth
coefficient, [t.sub.0]=mean theoretical age a fish would have been at
zero weight). Standard errors of the mean (SE) are presented in
parentheses. [beta] was fixed at 3 and is, therefore, not included in
this table. n=the  number of age-weight observations.

                     [W.sub.[infinity]]   k              [t.sub.0]

All regions pooled   3.2 (0.03)           0.355 (0.01)   -1.113 (0.18)
Aleutian             3.3 (0.09)           0.285 (0.03)   -1.949 (0.50)
Bering               3.4 (0.07)           0.313 (0.03)   -1.630 (0.47)
Chirikof             3.1 (0.06)           0.460 (0.07)   0.019 (0.59)
Kodiak               3.0 (0.03)           0.762 (0.10)   1.106 (0.35)
Shumagin             3.3 (0.15)           0.272 (0.04)   -2.252 (0.73)
Southeast            3.2 (0.04)           0.421 (0.03)   0.019 (0.30)

                     RSS           n

All regions pooled   152           4889
Aleutian             38.1          543
Bering               17.4          363
Chirikof             13.9          294
Kodiak               23.2          542
Shumagin             18.3          267
Southeast            33.5          605

Table 8

Estimates of weight-at-age parameters for female sablefish (Anoplopoma
fimbria) determined with the von Bertalanffy model fitted to age-
weight data for the pooled survey period of 1996-2004 stratified by
region and combined for all Alaskan waters ([W.sub.[infinity]]=
average maximum weight, [kappa] = mean growth coefficient, [t.sub.0] =
mean theoretical age a fish would have been at zero weight). Standard
errors (SE) are presented in parentheses. [beta] was fixed at 3 and
is, therefore, not included in this table. n=the number  of age-
length observations.

              [W.sub.[infinity]]   k                [t.sub.0]

All regions   5.5 (0.06)           0.238 (0.01)   -1.387 (0.13)
pooled
Aleutian      5.5 (0.22)           0.209 (0.02)   -2.092 (0.37)
Bering        4.7 (0.16)           0.267 (0.02)   -1.598 (0.42)
Chirikof      5.0 (0.12)           0.326 (0.03)   -0.206 (0.33)
Kodiak        5.2 (0.10)           0.336 (0.02)   -0.064 (0.27)
Shumagin      5.8 (0.33)           0.197 (0.02)   -2.349 (0.37)
Southeast     5.5 (0.11)           0.300 (0.02)   -0.114 (0.27)

              RSS    n

All regions   277    5767
pooled
Aleutian      71.5    795
Bering        34.2    533
Chirikof      29.5    485
Kodiak        42      602
Shumagin      47.9    563
Southeast     38.2    515
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Author:Echave, Katy B.; Hanselman, Dana H.; Adkinson, Milo D.; Sigler, Michael F.
Publication:Fishery Bulletin
Date:Jul 1, 2012
Words:9543
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