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NOAA Technical Memorandum NMFS-NE-171

Length-Weight Relationships for 74 Fish Species Collected during NEFSC Research Vessel Bottom Trawl Surveys, 1992-99

Susan E. Wigley, Holly M. McBride, and Nancy J. McHugh
National Marine Fisheries Serv., 166 Water St., Woods Hole, MA 02543

Web version posted June 23, 2003

Citation: Wigley SE, McBride HM, McHugh NJ. 2003. Length-weight relationships for 74 fish species collected during NEFSC research vessel bottom trawl surveys, 1992-9. NOAA Tech Memo NMFS NE 171; 26 p.

Information Quality Act Compliance: In accordance with section 515 of Public Law 106-554, the Northeast Fisheries Science Center completed both technical and policy reviews for this report. These predissemination reviews are on file at the NEFSC Editorial Office.

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This study is the first comprehensive examination of spatially and temporally synoptic length-weight observations collected along the Northeast coast of the United States during the Northeast Fisheries Science Center's (NEFSC's) research vessel winter, spring, and autumn bottom trawl surveys from 1992 to 1999. Linear regression using natural logarithmic transformation data was performed to calculate a and b coefficients. Analysis of covariance was used to test for seasonal and gender differences. Length-weight parameters were calculated for 74 fish species: 39 species showed seasonal differences, and 28 species showed gender differences. Minimum and maximum length observations for the first 37 years of the time series (i.e., 1963-99) of NEFSC research vessel bottom trawl surveys are also presented. Results from this study can be used within the "real-time" auditing of length-weight data collected by the Fisheries Scientific Computer System, the NEFSC's at-sea electronic data acquisition system.

Keywords: length-weight relationship, groundfish, demersal fish


At the Northeast Fisheries Science Center (NEFSC), length-weight parameters are routinely used in the estimation of numbers of fish landed in order to estimate fishery removals for stock assessments (e.g., see Wigley and Serchuk 1992). Additionally, length-weight relationships have been used in the auditing of NEFSC research vessel survey catch and biological data. However, many of the length-weight parameter values currently being used in the audit applications were derived from studies with limited sample sizes, combined genders, incomplete length ranges, restricted seasonal and/or geographical coverage, or, in many cases, from studies of unknown origin. Since the advent of recording individual fish weight during NEFSC bottom trawl surveys in 1992, numerous spatially and temporally synoptic length-weight observations have been obtained. This study is the first comprehensive examination of these data to update the length-weight parameters.

A consideration for updating these length-weight parameters is their use in the NEFSC's survey auditing procedures. Those procedures use length-weight equations at two levels: the species catch level and the individual fish level. At the species catch level, the audit calculates a derived weight for the catch based upon the length frequency of the catch, and compares that derived weight with the observed weight of the catch. At the individual fish level, the audit compares the derived weight of the individual fish with the observed weight of that individual. Updated parameters, especially those sensitive to gender and seasonal differences, could improve the effectiveness of the auditing procedures.

Another consideration for updating the length-weight parameters is the recent implementation of the Fisheries Scientific Computer System (FSCS), an at-sea electronic data acquisition system on board NEFSC research vessels. Within this system, data (i.e., lengths and weights) are digitally recorded, thus enabling real-time auditing of these data using a length-weight equation during the data collection phase. When observed weights deviate from predicted weights, the FSCS produces an error message requiring a manual override which, in turn, slows down data collection. Updated parameters could minimize error messages within the FSCS for those species for which current length-weight relationships are problematic.



The NEFSC has conducted research vessel bottom trawl surveys to assess the distribution and relative abundance of groundfish along the east coast of the United States during the past three decades (Grosslein 1969; Azarovitz 1981). The survey employs a stratified random sampling design with tows at depths ranging from 5 to 366 meters. Geographic coverage of the spring and autumn surveys is from Cape Hatteras to Nova Scotia, and the winter survey from Cape Hatteras to the southern flank of Georges Bank (Figure 1).

Beginning in 1992, biological sampling procedures were expanded to include recording individual fish weight, in addition to recording the fish's length, gender, and maturity stage. Aboard ship, the fish are measured live or freshly killed to the nearest centimeter (total length or fork length, depending on the species, except for rays, where disk width is measured from wing tip to wing tip), and weighed (whole fish) to the nearest 0.001 kg. Gender and maturity stage of the fish are examined macroscopically and recorded into the following categories: 1) unsexed, male, or female; and 2) immature, developing, ripe, ripe & running, spent, or resting (Burnett et al. 1989).

Although many species exhibit dimorphoric growth by sex, the survey procedures for measuring and enumerating fish is, for the most part, conducted at an unsexed species level. However, a few exceptions occur for those species for which gender can be determined from external physical characteristics. Length data by species and gender are collected for spiny dogfish, smooth dogfish, American lobsters, and various crab species. Common and scientific names used throughout this study are in accordance with those endorsed by the American Fisheries Society (Williams et al. 1989; Robins et al. 1991; Turgeon et al. 1998), with the exception of some flounders (Cooper and Chapleau 1998) and rays (McEachran and Dunn 1998) which have undergone subsequent systematic revision.

Species for which five or more length-weight observations existed were analyzed in this study. For most species, data from two or three seasons were available; however, for a few species, a limited number of observations were available for a single season. Due to the limited geographic coverage of the winter survey, data from the winter surveys were excluded from analyses for several species, such as Acadian redfish, whose primary distribution occurs within the Gulf of Maine.


Length and weight observations were transformed using natural logarithms, and were plotted for visual inspection of outliers. Only extreme outliers attributed to data error were omitted from the analyses.

Where sufficient data were available, analysis of covariance (i.e., test for homogeneity of slopes) was performed using PROC GLM (SAS Institute1985) to detect significant differences (P <0.05) between season and gender. Since the NEFSC species audit compares observed catch weight with predicted catch weight based on the length frequency of observed fish, the first task was to test for seasonal differences in length-weight parameters for each species (with genders combined). Further exploration of the data was then conducted to determine if gender differences existed within seasonal group. Length-weight parameters were estimated by gender within a seasonal group as appropriate, according to the following linear regression using PROC REG (SAS Institute 1985):

ln W = ln a + b ln L

where W = weight (kg), L = length (cm), a = y-intercept, and b = slope.

Residuals from the linear regressions were plotted and visually inspected for trends. Since raw data for existing length-weight relationships were not available for more rigorous statistical analysis, comparisons with length-weight relationships derived in this study were performed as follows: 1) 95% confidence intervals were derived for each length-weight relationship; 2) significant differences occurred if the predicted weights from the existing relationship fell outside the 95% confidence interval of the new length-weight relationship.


To evaluate whether the 1992-99 data used in this study to derive length-weight relationships were representative of the length ranges available to the survey for each species, historical observations of minimum and maximum lengths collected during NEFSC spring, autumn, and winter research vessel bottom trawl surveys from 1963 to 1999 were updated and compared to minimum and maximum lengths in this study. Additionally, range ratios were calculated by dividing the study length range by the historical length range.

The update of these length ranges was expanded beyond the 74 species in this study to include all species sampled during the surveys. This updated information can be utilized as part of the real-time audit of length measurements within the FSCS.



Between 1992 and 1999, a total of 24 NEFSC research vessel bottom trawl surveys were conducted, during which 242,693 individual fish length and weight observations were recorded for the 74 fish species (comprising 2 classes, 9 orders, and 35 families) analyzed in this study. Sample sizes ranged from six for greater amberjack, northern kingfish, and smooth butterfly ray, to 26,590 for spiny dogfish (Table 1). In Table 1 and all subsequent tables, species are ordered according to the National Oceanographic Data Center (NODC) taxonomic code.

For 19 species, data were not available for multiple seasons, precluding seasonal analyses for those species. Of the remaining 55 species, 16 did not exhibit significantly different (P <0.05) length-weight relationships by season; 39 did. For four species (i.e., round herring, Atlantic thread herring, Atlantic spadefish and buckler dory), data were not available on gender, precluding gender analyses for these species. Of the remaining 70 species, 28 had significantly different length-weight relationships by gender; 42 did not. Sample sizes, length ranges, length-weight parameter estimates and the standard deviations (standard errors) of those estimates, standard errors of the weight estimates, and regression correlation coefficients are presented in Table 1 by species for appropriate season or seasonal groups and for gender.

Although residual patterns generally showed no trend, a few exceptions should be noted. For some species, residual patterns (either positive or negative) existed for smaller fish, and may relate to the sensitivity of the Marel weighing scales in open-deck environments and/or recorder bias in determining a true weight during scale fluctuations in heavy seas. Small sea ravens exhibited negative residuals, which might be attributed to some size specificity in the characteristic behavior of this species to "gulp" water when captured. The analysis of bluefish in the spring revealed a pattern in which residuals were negative at smaller sizes and became positive at larger sizes; although this pattern would normally result in rejection of the regression, the analysis was retained due to the possibility that fish greater than 40 cm (the length around which the residuals pivoted) collected in the southern portion of the survey might be reproductively active and therefore include the weight of the maturing gonad. Scup exhibited a funnel-shaped residual pattern, with decreasing deviation as fish length increased; this pattern may be related to the log-log transformation model used in the study (Pienaar and Thomson 1969).

Comparisons of length-weight relationships established by this study with those currently used in the NEFSC auditing process indicated no significant differences at the catch level (genders combined) for 42 of 74 species. However, there were nine instances in which the weights predicted by the current length-weight relationships fell entirely outside of the 95% confidence intervals of the weights predicted by this study. These species were: chain dogfish, rosette skate, southern stingray, bluntnose stingray, cownose ray, Atlantic thread herring, fawn cusk-eel, Atlantic spadefish, and spot. For Atlantic angel shark, predicted weights from the current relationship for intermediate-sized fish occurred within the confidence interval, but those for smaller- and larger-sized fish did not. There were five species for which predicted weights from the current relationship were significantly different for larger fish (i.e., Atlantic sturgeon, round herring, Atlantic herring, greater amberjack, and cunner), and 17 species for which smaller fish were problematic (i.e., spiny butterfly ray, Atlantic sharpnose shark, smooth dogfish, spiny dogfish, clearnose skate, Spanish sardine, red hake, alewife, cusk, silver hake, Acadian redfish, bluefish, black sea bass, scup, southern kingfish, fourspot flounder, and witch flounder).

There were seven species for which gender-specific predicted weights from the current length-weight relationship were significantly different from gender-specific predicted weights in this study (i.e., rosette skate, red hake, white hake, Acadian redfish, striped bass, weakfish, and yellowtail flounder). No comparisons were possible for the seven species for which no current gender-specific relationship existed (i.e., clearnose skate, little skate, winter skate, spiny butterfly ray, longhorn sculpin, ocean pout, and sea raven).


Generally, the length ranges used to derive length-weight relationships in this study represented a significant proportion of the ranges which have been historically observed, as evidenced by an all-species average range ratio of 72% (Table 2). For 14 species, range ratios were below 0.50, suggesting that the length ranges utilized in this study may not have represented the historically observed length range. However, for 10 of those 14 species, sample sizes were quite small (i.e., Atlantic torpedo ray, smooth butterfly ray, Atlantic sturgeon, alewife, northern searobin, greater amberjack, vermilion snapper, northern kingfish, Atlantic spadefish, and tautog). There appeared to be adequate sample sizes for the remaining four species with range ratios below 0.50, but larger-sized specimens of those species were noticeably absent from the study data set (i.e., Atlantic sharpnose shark, Spanish sardine, fawn cusk-eel, and Spanish mackerel; Table 2).

The observed minimum and maximum lengths (cm) for all species measured during NEFSC bottom trawl surveys since 1963 are summarized in Table 3. Approximately 2.83 million lengths have been obtained from species comprising 9 phyla, 25 classes, 89 orders, and 171 families. For species which are sorted by gender during the survey (e.g., spiny dogfish, American lobster), length values for males, females, and unknown genders are reported in Table 3.


Zar (1968), Glass (1969), and more recently Hayes et al. (1995) presented information supporting the use of nonlinear least-squares regression techniques for allometric modeling; however, Xiao and Ramm (1994) concluded that the use of log-transformed data was appropriate for describing length-weight relationships in fishes. In this study, the small sample sizes associated with several species were potentially problematic with respect to asymptotic variance properties of nonlinear regression. Our choice of an allometric model was practical; linear regression using log-log transformed data facilitated statistical comparisons of gender and seasonal relationships, and allowed a single method to be applied to all species within the study, regardless of sample size.

Length-weight relationships derived in this study generally compare favorably with those of other published studies. For 35 of 78 species analyzed by Wilk et al. (1978) which were also examined in this study, only the relationship for fawn cusk-eel was significantly different. While this might be attributed to the larger sample size and greater size range available to Wilk et al. (1978), the use of the Wilk et al. (1978) relationship within the FSCS during the NEFSC spring 2001 bottom trawl survey resulted in numerous real-time audit messages indicating an erroneous weight for a given length. When the parameters derived in this study were substituted into FSCS, these error conditions were eliminated for subsequent fawn cusk-eel samples.

There were also no apparent differences between length-weight relationships for four of the six flatfish species derived by Lux (1969) and the relationships derived by this study; differences for witch and fourspot flounders may be related to the restricted geographical range of Lux's (1969) samples. This similarity in relationships is somewhat remarkable given the difficulties in obtaining accurate fish weights at sea prior to the development of modern electronic motion-compensated scales. Wilk et al. (1978) froze fish at sea and obtained thawed weights back at the laboratory, while Lux (1969) weighed his samples at sea with hand-held spring scales. This similarity in findings suggests both the diligence of these investigators as well as the underlying robustness of fish length-weight relationships to measurement error.

In summary, this study updates length-weight parameters for many species routinely encountered during NEFSC bottom trawl surveys, utilizing uniform methods and modern scale technology. The availability of whole live body weight from sexed fish collected across seasonal surveys takes into account annual cycles of fish feeding and reproduction, allowing derivation of length-weight relationships at the gender and/or season level. Analysis of these data provided insights into areas, such as length range or sample size for some species, in which additional sampling can be targeted in future surveys. The length-weight relationships derived in this study also support the improved processing of survey data within the recently-implemented FSCS environment, providing critical fishery independent data in a more timely fashion.


We wish to express our appreciation to the sea-going scientific staff of the NEFSC who diligently collected the biological observations used in this study. We thank the anonymous reviewers for their helpful comments and review of this manuscript.


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FSCS = Fisheries Scientific Computer System
NEFSC = Northeast Fisheries Science Center
NODC = National Oceanographic Data Center
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