SCRS/2018/168 Collect. Vol. Sci. Pap. ICCAT, 75(4): 700-718 (2018)

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A COMPARATIVE REVIEW OF SIZE-WEIGHT RELATIONSHIPS IN NORTH

ATLANTIC SWORDFISH (XIPHIAS GLADIUS) BASED ON RECORDS OBTAINED

IN THE SPANISH SURFACE LONGLINE FLEET

1A. Ramos-Cartelle, B. García-Cortés, I. González-González,

A. Carroceda, J. Fernández-Costa, J. Mejuto

SUMMARY

Linear and non-linear fits were performed for 38,660 LJFL cm-RW kg data pairs from the

North Atlantic stock. The equations obtained from both fits (RW= 3.71811E-06 * LJFL3.245243 and

RW= 7.8485161E-06 * LJFL3.09943) were compared with other previously obtained in this fleet.

The equations obtained using linear fit were almost identical to those previously reported.

Minor differences in predicting individual weight at size were observed for most size classes,

but all equations tested seem to show a less satisfactory fit for some of the largest fishes.

Despite differences in constants among the equations tested, less impact was observed for both

the predictive individual mean weight in most size ranges regularly caught as well as for

predicted whole weight from size distributions representative of the fish caught by longline

fleets. A review of the literature on size-weight relationships was carried out, suggesting a

diversity of results probably due to various factors which are discussed.

RÉSUMÉ

Des ajustements linéaires et non linéaires ont été effectués pour 38.660 paires de données LJFL

cm-RW kg du stock de l'Atlantique Nord. Les équations obtenues à partir des deux ajustements

(RW = 3,71811E-06 * LJFL3,245243 et RW = 7,8485161E-06 * LJFL3,09943) ont été

comparées aux autres obtenues précédemment pour cette flottille. Les équations obtenues par

ajustement linéaire étaient presque identiques à celles déclarées précédemment. Des

différences mineures dans la prédiction du poids individuel par taille ont été observées pour la

plupart des classes de taille, mais toutes les équations testées semblent montrer un ajustement

moins satisfaisant pour quelques poissons plus gros. Malgré les différences de constantes entre

les équations testées, un impact moins fort a été observé pour le poids moyen individuel prédit

dans la plupart des gammes de tailles capturées régulièrement ainsi que pour le poids total

prédit à partir de distributions de tailles représentatives des poissons capturés par les flottilles

palangrières. Un examen des publications sur la relation taille-poids a été réalisé et suggère

une diversité des résultats s'expliquant probablement par divers facteurs qui sont discutés.

RESUMEN

Se realizaron ajustes lineales y no lineales a partir de 38.660 pares de datos LJFL cm-RW kg

del stock de pez espada del Atlántico Norte. Las ecuaciones obtenidas de los ambos ajustes

(RW= 3,71811E-06 * LJFL3,245243 and RW= 7,8485161E-06 * LJFL3,09943) fueron

comparadas con otras relaciones previamente obtenidas en esta misma flota. Las ecuaciones

obtenidas usando un ajuste lineal fueron casi idénticas a otras previamente descritas. En las

predicciones del peso medio por talla se detectaron diferencias menores para la mayoría de

clases de talla, pero todas las ecuaciones testadas parecen mostrar un ajuste menos

satisfactorio para algunos de los peces más grandes. Pese a la diferencia de constantes entre

ecuaciones testadas, se obtuvo un impacto menor tanto en la predicción del peso medio para la

mayoría de rangos de tallas capturados así como sobre el peso total predicho a partir de una

distribución de tallas representativa de la selectividad de la flota palangrera. Una revisión de

la literatura sobre relaciones talla-peso sugirió diversidad de resultados probablemente

debidos a diversos factores que son discutidos.

KEYWORDS

Swordfish, Length-weight relationship, Biology, North Atlantic

1 Instituto Español de Oceanografía, P.O. Box 130, 15080 A Coruña. Spain. Email: tunidos.corunha@ieo.es

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Introduction

The size-weight relationship is an important biological parameter of fish species, as it is involved in descriptive

and predictive average weight at size calculations, providing constants for defining individual growth in weight

from individual growth in length. Size-weight relationships are also used in assessment models and in the Task1-

Task2 raising procedures. In some fleets individual standard-size data can be estimated from commercial

individual weight records (e.g. from dressed weight records) or from carcass length. Therefore, size-weight and

other relationships as well as the conversion factors used could have an impact on the resulting CAS-CAA

matrices for the purposes of assessment and exert an influence on estimates of the demographic/biomass

distribution of the stocks. Reducing any possible uncertainty regarding this parameter will thus contribute to

reducing uncertainty in assessments.

The debate regarding the suitability of size-weight equations for tuna and tuna-like species is reopened with

some frequency on the grounds that there could be significant short-term changes in these relationships or that

the new methods could give rise to improved equations for these species/stocks. However, the impact of using

different/similar size-weight relationships within a biologically reasonable margin probably contributes little to

the overall uncertainty of assessments compared with other variables or assumptions that are much more

significant as potential sources of uncertainty. As a result, the debate concerning the size-weight relationships

applicable to a particular stock often ends up being a theoretical or statistical refinement rather than having a

significant impact on estimates of relative stock biomass trends over the years. Nevertheless, the debate can help

to corroborate the reliability of the parameter assumed, or detect errors in the data used, in the size-weight types

assumed, or in the conversion factors applied, etc., which are often the main cause of discrepancies between

studies.

Adult swordfish individuals may migrate vertically hundreds of meters between day and night, but they may

migrate horizontally thousands of miles per year/s from temperate waters for feeding to some warm waters for

spawning. Early studies had already described this migratory behavior (Anon. 1985) indicating that different

age-sex individuals of the stock may migrate differently. This behavior was later confirmed using conventional

and recent pop-up tagging data and other evidences. Under these circumstances of broad horizontal migratory

behavior, it is postulated that there could be statistically significant differences in the size-weight relationships

between years, sexes and/or the different areas and/or seasons, based on changes in the condition factor (so-call

fattening condition) of each individual during their respective biological phases (e.g. feeding, spawning or

transition).

Since the 1970s at least various authors have proposed equations to establish a relationship between the size and

weight of swordfish that could be representative for Atlantic stocks. The earliest descriptions of the relationship

between lower jaw-fork length (LJFL) and round weight (RW) for regions in the NW Atlantic were probably

those included in the synopsis by Palko et al. (1981) [referenced as Guitart-Manday (1964) and Beardsley et al.

(1979)], while other authors later proposed equations for sub-areas of the NW Atlantic and for quarter-year

intervals (e.g. Turner 1986). The first size-weight relationship established for the NE Atlantic was probably that

developed by Rey and Garcés (1979). Equations were later developed for more extensive areas in the North-

eastern and North-central Atlantic (e.g. by Garcés and Rey 1984, Mejuto et al. 1988), while others were

developed based on sex taking advantage of studies of reproduction (García and Mejuto 1988). More recent

studies have also proposed or summarized size-weight relationships for Atlantic and Mediterranean stocks (see

summaries in Abid and Idrissi (2016), Hanke et al. (2018-in press.), and in other sources referred to

subsequently in the present study).

The formulae most frequently used in size-weight studies of swordfish have been of the type W=a*Lb, “W”

being the weight of each individual – according to the criteria for weight used by each author –, “L” the length –

according to the type of measurement and criteria used by each author – and “a” and “b” being constants

generally based on the assumption of a linear relationship between the logarithmic transformation of the

respective size-weight variables (Sparre and Venema 1997), or alternatively using non-linear fits (e.g. Turner

1986, Hanke et al. 2018-in press). Some authors suggest that it may be useful to establish non-linear

relationships between the two variables. However, irrespective of theoretical debates, it is clear that the

differences generally obtained by applying either type of fit is barely perceptible in practice when the size-

weight data set is sufficiently robust in terms of the quality and quantity of observations and adequately

represents the different areas, sexes and ranges of size present in the natural environment and/or those most

frequently caught (e.g. Carroceda and Colmenero 2016).

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The literature on size-weight relationships for swordfish in the Atlantic and other oceans includes a variety of

approaches and constants obtained, for example: North Atlantic: Guitart-Manday (1964), Garcés and Rey

(1984), González et al. (1999), Turner (1986), García and Mejuto (1988). South Atlantic: Amorin (1977),

Forselledo et al. (2017), Hazin et al. (2002), Oliveira et al. (2005). Atlantic and Mediterranean Sea: González-

Garcés and Mejuto (1985), Mejuto et al. (1988), Rey and Garcés (1979). North and South Atlantic: Amorin et al.

(1979), Hanke et al. (2018). Mediterranean Sea: Alicli et al. (2012), De la Serna et al. (1995), Hattour (1996),

Lombardo et al. (2017, 2018-in press), Mejuto and De la Serna (1993), Tserpes et al. (2003, 2017). Indian

Ocean: Varghese et al. (2013). Pacific: Barbieri et al. (1998), Caton et al. (1998), Sun et al. (2002), Uchiyama et

al. (1999), Wang et al. (2006), Williams (1998). North Atlantic and South Pacific: García-Cortés and Mejuto

(2002).

Size can be recorded in different units (centimeters, millimeters, inches, etc.) according to the type of

measurement used by each author (e.g. TL, LJFL, EOFL, or other) and determined using different measuring

equipment and criteria (calipers, straight tape measure, tape measure following curve, etc.), while different

criteria can be applied to define the size groups used to determine fit (e.g. 1 cm or 5 cm intervals, size defined by

the lower limit or the average size of the intervals, etc.). Similarly, different units of weight (e.g. kilos, grams,

pounds) and different types of weight (round weight, different types of gutted weight or dressed weight/carcass

weight, etc.) may be used. However, these details are rarely reported in full, so that apparent differences between

studies regarding the size-weight relationships obtained from data sets may be due to the different criteria

applied rather than intrinsic differences in the biology of the species within the same stock. Even in the case of

swordfish stocks assumed to be distinct units and where little mixing has occurred, genetic differences are

minimal or insignificant and one would not expect significant differences in this biological parameter due to

factors in the natural environment. The evolutionary history of this species over millions of years and its long

life-span would not a priori lead one to anticipate substantial changes in its basic biological parameters over a

relatively short time scale. Yet the availability of samples and the methods followed to obtain and analyze

observations can vary from one study to another, which may lead to differences in the size-weight relationships

recorded. As has been pointed out in various studies, the differences between the constants a and b, which define

the size-weight relationship, within reasonable degrees of variability, can be a function of the range of sizes

considered in each case, which implies indirectly that different proportions of the sexes will be used for each fit,

as swordfish larger than 200 cm are very likely to be females.

Since the 1980s various studies have proposed size-weight relationships for Atlantic swordfish based on data

obtained from the Spanish surface longline fleet in oceanic areas in different months of the year (see references

above). These relationships were mainly derived from samples taken when fish were landed. It was considered

that this option is less subject to bias than if data are obtained in commercial vessels at sea, as in the latter case

the reliability and variability of the weights recorded can be affected by working conditions on board, the system

used for weighing and its accuracy, and adverse weather conditions during the trip. Some of the equations

proposed in the 1980s have been used by ICCAT for certain areas and weighing procedures. However, other

equations empirically proven in this fleet have been omitted in scientific reviews and manuals or are regularly

incorrectly referenced.

The 2017 Swordfish Working Group recommended that in the course of 2018-2019 studies should be undertaken

to validate the size-weight relationships commonly assumed in the assessment of Atlantic swordfish stocks. In

the light of this recommendation, this study analyses information compiled by means of intensive size-weight

data-mining using information collected during scientific sampling at landing points over a 30-year period. The

results are also compared with relationships previously determined in the same fleet. This paper thus sets out to

verify and validate the length-weight relationships previously provided and used in the assessment of the North

Atlantic swordfish stock, as well as reviewing the status of the matter in view of the different relationships

proposed, considering the recent recommendations in this regard.

2. Material and methods

Size-weight observations of swordfish (Xiphias gladius) individuals were obtained during landing from broad

fishing areas of the North Atlantic stock during the period 1984-2018. The lower jaw-fork length size (LJFL cm)

was measured in a straight line, mostly with calipers or in some cases with a tape measure, to the nearest lower

centimeter. The corresponding round weight (RW kg) was obtained in port regularly using digital scales.

Information associated with each size-weight observation, such as date of catch (year-month), fishing area

during the trip and gender (sex) of each fish was also recorded. Gender (male/female) could not be identified in

all cases since the gonads of some of the individuals were not accessible to the sampler. In this case, gender was

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classified as “unk.” and those individuals were only included in sex-combined analyses. BIL areas (BIL94A,

BIL94B and BIL94C), quarters and the five-year periods used in some analyses were obtained from the fishing

area recorded, month and year; respectively.

Data obtained from formats other than round weight (such as gutted weight or dressed/carcass weight) were not

converted into round weight and were excluded from the analyses. The use of average constants to convert one

type of weight to another was not considered valid for RW analysis, as the same conversion factor would be

assumed for all sizes and this would not adequately reflect the natural variations one would expect between

different sizes, sexes or vessels.

A base-case analysis of deviation (GLM-GENMOD SAS 9.4) was conducted fitting a sequence of models,

beginning with a simple model with only one intercept term and continuing through a model of specified

complexity, fitting one additional effect in each step to test the significance and importance of the additional

explanatory variable by the difference in deviations obtained from the different factors considered. Year, quarter,

BIL area, sex (male/female), size Ln(LJFL) and their interactions were considered in order to determine the

significance and % deviation explained by each main factor and their interactions with the weight Ln(RW).

Sensitivity analyses of deviation were also conducted considering five-year periods instead of years (excluding

the year effect, since annual changes are a priori considered biologically implausible for size-weight constants in

this species), omitting the temporal variable or excluding fish where LJFL ≥ 200 cm because of the low/null

occurrence of males in these largest size classes.

Based on the results of the analysis of deviation, the relationship between size and weight of the type RW= a *

LJFLb was obtained by two different types of fit. A first approximation was made by linear fit (linearization) (R-

vers.3.4.2) based on the logarithmic transformation of the size and weight variables: Ln(RW)= Ln(a) + b *

Ln(LJFL), where “a” and “b” are the constants for establishing this linear relationship (Sparre and Venema

1997). A second approximation was conducted using a non-linear Gauss-Newton fitting model (Anon. 2009) and

also tested using the NLS function (R-vers.3.4.2). The results obtained were compared with each other and with

those obtained in other studies for data obtained in the same fleet, using an equivalent type of size-weight

measurement. The quantitative impact on predicted weights was also assessed using four selected LJFL-RW

equations: (1) The estimated constants obtained by linear fit in this paper. (2) The estimated constants obtained

by non-linear fit in this paper. (3) The estimated constants for LJFL-RW provided in Garcés and Rey (1984). (4)

The estimated constants for LJFL-RW combining three North Atlantic areas considered in Mejuto et al. (1988).

The weight at size predicted from each equation was plotted vs. the weights at size observed. The estimated

whole weight predicted from the set of size data used in this paper was compared with the whole weights

observed in the same data set. Additionally, in order to assess the relative impact of using the four different

relationships selected on a real set of Task2-size data, 8 years of Task2-size data from Northern stock were

randomly selected for the 1990-2017 period and the four different length-weight relationships applied to predict

the respective whole round weight. In this last case, the whole weights predicted were compared with those

obtained using the non-linear estimated parameters provided in this study.

3. Results and discussion

A total of 38,660 observations of the size (LJFL cm) and round weight (RW kg) of swordfish (14,308 females,

12,740 males and 11,612 unk.) were analyzed as well as the associated variables. Tables 1 and 2 summarize the

number of observations by year and BIL area for the three sex levels recorded. Data for 2018 are partial because

only figures from the first quarter were available. However, sensitivity analyses including and excluding 2018

data did not show any difference, so data for 2018 were kept in the final runs. Most of the observations came

from the BIL94B and BIL94C areas where most fishing activity was historically carried out by this fleet in the

North Atlantic stock, defined by latitude 5ºN.

Table 3 summarizes the available size and weight data for the analyses. Sizes LJFL 80-284 cm (weights 5.9-

380.0 kg) for females and sizes LJFL 65-247 cm (weights 3.0-255.0 kg) for males were available for this

analysis. The respective average sizes and weights of the observations were 142.85 cm (Std.= 25.89) and 42.40

kg (Std.= 29.94) for females and 135.17 cm (Std.= 19.97) and 33.68 kg (Std.= 17.97) for males.

Figures 1 and 2 provide the size frequency distribution by sex and the respective box-plot of size variability by

sex. As expected on the basis of previous studies of size, sex-ratio at size (SRs) and growth by sex, the range of

sizes recorded for females was greater than that for males. This should not be seen as a limitation of the sample,

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as the range of sizes identified for each sex reflects those selected by this gear and the presence of each sex in

this stock as a whole, probably due to differential growth, females normally attaining larger sizes than males.

The number of samples available per size category was a good reflection of the sizes most frequently observed in

all fisheries and in ICCAT Task2-sizes for combined fleets. The fish selected by the surface longline fleet in the

areas sampled include fewer of the largest and smallest individuals.

Table 4 shows the results of base-case deviation analysis. The variables year, quarter, area, sex (male, female),

Ln(size) and their interactions were those initially considered in this base-case, while in the sensitivity analyses

for deviation an alternative variable of five-year period was considered, the temporal variable was omitted, or the

analysis was restricted to a more homogeneous range of sizes for both sexes (LJFL < 200 cm). The variable

Ln(size) contributed in all cases between 90.4% and 96.5% of the total deviation observed. Most of the other

factors and their interactions contributed less than 1% of total deviation. In the base-case analysis, the variables

year and sex contributed 5.3% and 2.7% of total deviation, respectively; however, the result of their interactions

with Ln(size) suggests that the % of deviation explained by the main factors year and sex could be due to the

difference in size-weight data for different years or sexes, as their respective interactions with Ln(size) were

irrelevant from the point of view of % of deviation. The analysis carried out using five-year periods instead of

single years reduced the deviation of the time variable and increased the % deviation of the most important

variable Ln(size). When the time variable was omitted from deviation analysis there was a corresponding

increase in % deviation for the main variable Ln(size). The sensitivity analysis of deviance based on a more

homogeneous range of sizes for both sexes (LJFL < 200 cm) also suggested that much of the deviation assumed

to be due to sex as a main factor in the base-case analysis could really be due to the effect of including the largest

fish in the analysis as the great majority, if not all, are females. In this particular sensitivity case, the % of the

total deviance explained by sex was reduced to 1.7% and all interaction of sex with other factors contributed

0.0% of the total deviation observed.

Based on these results, it was not considered justifiable from the statistical viewpoint, plausible from the

biological viewpoint or practical from an operational viewpoint to formulate size-weight equations by year, area,

quarter or sex using this data set. For purely descriptive purposes a linear fit by sex was calculated, the

differences being minor and quantitatively insignificant in the data set used (Table 5, Figure 3).

Table 5, Figure 4 shows the linear fit of size-weight data for all data combined and the coefficients “a” and “b”

obtained, with their respective confidence intervals. Figure 5 shows diagnosis of the residuals of the size-round

weight linear fit obtained by sex-combined (female+male+unk.) as well as the residuals vs. fitted values, qq-plot

and leverage. The model using a linear fit for all data combined was highly significant and explained 94% of the

weight variability in terms of size. In view of these results it was considered that the equation RW= 3.71811E-06

* LJFL 3.245243 can describe the relationship and predict average weight from size (RW= kg, LJFL= cm for 1 cm

size categories defined by their lower limit), for all the areas and periods sampled in this North Atlantic fleet.

This result for linear fit is almost identical to that provided by previous studies of the same fleet using the same

methodology and type of data. Although Rey and Garcés (1979) were probably the first to record biometric

relationships for swordfish in the NE Atlantic and the Mediterranean Sea, these size-weight relationships were

established between size (LJFL cm) and gutted weight (GW kg), considering completely different size ranges for

the two stocks analyzed, making it difficult to compare the results in the two stocks with each other and with

those obtained in the present study. However, Garcés and Rey (1984) provided the first LJFL-RW relationship

for the NE Atlantic, applying the same methodology as that used in this study and obtaining values of 3.800E-06

and 3.242775 for the constants “a” and “b”, respectively (r-squared= 0.9766), from N= 2,306 individuals of both

sexes. Subsequently, Mejuto et al. (1988) also developed LJFL-RW relationships considering a larger number of

observations in three regions in the North Atlantic over quarterly and annual periods. The annual constants for

the three regions combined, both sexes, with LJFL-RW data were 3.78054E-06 and 3.245067 for “a” and “b”

respectively (r-squared: 0.983), based on N= 6,666 individuals from the North Atlantic stock. The difference

between the constants “a” and “b” in the two studies referred to -both of which used RW- and those obtained in

the present study is practically negligible and reinforces our belief that these relationships are good

approximations to describe and predict average weight in this fleet from straight-line LJFL size, considering 1

cm size categories defined by their lower limit. Moreover, García and Mejuto (1988), as part of a study of

swordfish reproduction, obtained linear LJFL-RW relationships by sex based on N= 649 individuals whose

gonads were analyzed, the values being a = 2.386E-06 and 3.073E-06, b = 3.332 and 3.281 for males (N = 297, r-

squared = 0.971) and females (N = 352, r-squared = 0.981), respectively. Although the sample was small in this

case, no significant difference between the sexes was identified. Another similar study of the Spanish fleet,

which used DW units, is included in the literature referred to above (García-Cortés and Mejuto 2002) but it has

not been compared with the results obtained in the present study as the type of weight analyzed in the two cases

is different.

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Table 6 provides a summary of the parameter statistics obtained by non-linear fit for all data combined (Figure

6). The estimated values obtained were: RW= 7.8485161E-06 * LJFL 3.099438. These constants “a” and “b” differ

from the values obtained by linear fit. Nevertheless, four LJFL-RW relationships obtained in the same fleet

(Table 7) were charted for comparative purposes (Figure 7) and were applied to both the 38,660 size

observations available in this study and the selected Task2-size sets for this fleet. Comparative analysis suggests

that the use of the four different size-weight relationships selected has low impact on predicting average

individual weight by size category for those size ranges most frequently observed in the fleet as a whole in the

North Atlantic (Figure 7). However, all the equations compared appear to show a less satisfactory fit for some

size categories LJFL>215 cm. This deviation between predicted and observed weight in the case of the largest

individuals could be caused by various factors. They include a small number of samples of these largest sizes

and the individuals normally being large females found in temperate water areas during trophic periods after

reproduction-spawning. However, we should also bear in mind that the difficulty of handling, measuring and

weighing individuals larger than 100 kg may have some influence on the reliability of weight records for these

largest fish. The large fishes sampled in the early years of the series sometimes had to be measured with tape and

weighed on scales that did not probably provide the same accuracy as the digital scales normally used to collect

data.

From the point of view of estimating total weight for the set of sizes sampled, the deviations recorded between

the total weight predicted using the four equations selected and the total weight observed ranged from +0.497%

to -1.083%, according to the size-weight equation considered (Table 7). On the other hand, from the point of

view of estimating total weight based on the different size-weight equations selected and applied to selected

Task2-size data, the relative difference in estimates of total weight displayed average values between +1.032%

and -0.540% with respect to the weight obtained by applying the non-linear fit equation taken as the reference in

this case (Table 8).

Size-weight relationships based on the linearization of size and weight data are often criticized. However, in this

type of biometric size-weight relationship linearization could provide a good approximation when the samples

are truly representative of the sizes present in the catch. Linearization is not a bad alternative in simple models

that can be easily linearized. Linear models are used to determine a single unique solution based on the smallest

sum of squares. In the case of non-linear models, incorrect specification of the model, poor initial starting values,

insufficient data and/or insufficient interactions could affect convergence. In this particular study, the results

obtained using two different non-linear software packages have provided almost identical results using different

starting values. The results obtained from both fit types indicate that the fitting methods applied in this case had

a marginal impact on the mean individual weight predicted from the size distribution considered for this

particular data set. Furthermore, the predicted individual mean weights are in practice very similar to those

obtained using equations considered as reference in some cases for this species-stock and similar areas of the

Northern stock. However the lack of alignment between predicted and observed weight for the largest fish

should be further investigated despite the low prevalence of these sizes in this fishery.

The primary purpose of determining size-weight is usually to define a biometric relationship that is

representative of all individuals in the stock, relatively stable over time in these highly migratory species with a

long life. This relationship may be very similar, or even identical in practice, in stocks with a common

evolutionary history except, perhaps, during very specific parts of the life cycle or when very unfavorable

environmental conditions occur lasting throughout the lifetime of individuals, such as a lack of prey in the area

of distribution, or during and after their concentration for biological processes involving a high energy cost.

However, this possible limitation due to the effect of the environment is relatively unlikely for this species in the

Atlantic in view of its great migratory adaptability and its widely diverging opportunistic feeding patterns from

surface waters to depths of hundreds of meters. The possible difference between size-weight relationships in the

Atlantic and the Mediterranean swordfish is not easy to verify from literature, given the very different ranges of

sizes normally found in each stock and in the catches of the respective fleets (e.g. Rey and Garcés 1979). Even

so, obtaining size-weight relationships for each fleet/area/season may have a practical application in some cases,

as they can be useful for weighting in order to determine CAS figures for each fleet, so that each relationship can

be adapted to the sizes and characteristics of the individuals caught by each fleet. In the case of swordfish, it has

been determined empirically that the equation representative of the stock as a whole allows one to make a

reliable average prediction based on size when this is measured correctly, so that the relationship can be used to

obtain CAS for each fleet or for combined fleets. In the case of other species or fleets (some tuna and tuna-like

species in particular or areas where catches predominantly consist of very specific ranges of sizes, etc.) it may be

useful to develop specific relationship per fleet when they target fish with specific features and/or there are

significant and relevant differences between the individuals caught and the average values for the stock as a

whole. The development of size-weight relationships by fleet/area/season may thus be useful when catches are

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concentrated in certain periods, during biological processes that lead to substantial changes in individuals’

condition or when landing figures are not in round weight (e.g. GW or DW), as not all fleets apply the same

procedures to process fish, nor there is any reason why conversion factors should a priori be identical for

different fleets or markets.

In the literature we often find different estimated values for the constants a and b in size-weight equations for the

same species or stock. As we have pointed out, these differences can have various causes that are not necessarily

produced by hereditary or environmental factors. Even when the same methodological approaches are used, the

difference between observations of the range of sizes considered in each fleet-study, or other conditioning

factors or limitations related to the sampling, or the quality of the data recorded, etc. could explain the

differences (usually slight) in the results obtained by different authors for this species when data that are really

equivalent are used. In other cases there are substantial methodological differences between authors in the way

they obtain field data, define criteria for analysis, eliminate data they consider to be outliers, etc., or assume sizes

and/or weights that are not strictly equivalent among studies. In this sense, the comparison of the observed

weight at size data between different fleets pointed out in some cases significant differences probably caused by

methodological inconsistencies between fleets and protocols (see e.g. Hanke et al. 2018-in press).

Whatever the cause, the representativeness of observations regarding the size-weight intervals considered in each

case can make an important contribution to the differences between studies, especially when data are compared

for fleets and gear with very different selective patterns (e.g. longline vs. harpoon) so that different size intervals

and sex, and frequencies are analyzed for different gear-fleets-areas. In this study we are probably using an

unprecedented amount of observations obtained from landings over 30 years, providing a balanced

representation of the sizes and sexes present in the different months and areas in which this longline fleet has

targeted North Atlantic swordfish stock.

Another element receiving little attention in comparisons between size-weight relationships is the definition of

the size categories used for each study and their subsequent use in procedures to compare predictions of weight

according to size category. In the case of swordfish, size-weight relationships have often been obtained assuming

size intervals of 1 cm, generally defined by their lower limit. However, in subsequent applications or

comparisons 5 cm intervals could be used. This implies that to predict the average weight corresponding to each

5 cm class the equation must be modified as follows: RW=a*(LJFL+k)b, k being a constant according to the size

category limit used for the size-weight fit, this constant being properly adapted to other larger size categories

used to predict their mean weights.

This study uses data from samples obtained in port. Weights obtained in port using scales are a priori considered

less susceptible to bias or increased variability for reasons unconnected with the strictly natural variability of the

species. However, the means to obtain the weight of each individual are not necessarily the same between years

due to improvements implemented over the years. In this sense, the results obtained in the present work suggest

the importance of the observations identified as "unk", which mostly belong to the first two years of the analyzed

series whose weight data was obtained with old scales. The elimination in the analysis of that subset of the years

before 1989 produces slight changes in the constants obtained by linear fit: a = 3.03027E-06, 3.12858E-06 and

2.95793E-06; b = 3.289428 (CI95%: 3.279295-3.299561), 3.283821 (CI95%: 3.270295-3.297347) and 3.293327

(CI95%: 3.276813-3.30984), for the case of combined sexes, females and males, respectively. Anyway, the data

used come from one fleet and no transformation constants were used to convert other weight types to round

weight.

The different proportion of genders in the samples - when significant differences are identified - may be another

source of size-weight diversity in some large pelagic species. However, in the case of swordfish and considering

the present data set and previous studies in the same fleet, the importance of sex seems to be irrelevant when the

same size ranges by sex are considered and compared.

In summary, a review of the literature previously cited highlighted an apparent diversity of results between

authors in some cases, which may be due to various factors, some of which have been previously discussed.

Among other factors, we would underline the different quantity and quality of raw data used, the inclusion or

exclusion of “outliers” in the respective fits, the size-weight interval and frequencies by size class used in each

study, and the methods used for fitting data. In some comparisons, there could be unclear definitions of the type

of length, size classes and weight used in the fits, and in some other cases there may be confusion regarding the

equations obtained from the total or round weight, and other types of weight: gutted, gutted and gilled, dressed-

carcass, etc. When such confusion is conveyed from one study to another, this could occasionally lead to some

inappropriate comparisons or to the presentation of comparative summaries without considering the real type of

size-weight data used in each case. The different ways of processing the catches – when units other than live

707

weight are used – is an element that frequently contributes to the confusion and the diversity of relationships in

studies, while constant conversion factors may be used in some data sets before fitting procedures. Subsequent

studies should incorporate detailed descriptions of the type of size and weight used in each case and, in the event

of using weights other than live weight, relationships by fleet are especially recommended and should be

evaluated.

The ICCAT swordfish Working Group has recently noted the importance of this type of length-weight

contribution. The relationships described in this paper cover a substantial proportion of the regularly reported

full-size spectrum of swordfish for all gears combined and specifically for the fleet analyzed in this paper. At the

same time, non-linear and linear fits of the length-weight relationships have been tested and compared with those

more regularly used for assessment. The result obtained in this study for linear fit is almost identical to the LJFL-

RW relationships previously provided by equivalent data obtained in the same fleet, using similar

methodological approaches. Although the linear and non-linear fits provide different constant values, the

practical impact for the prediction of mean weight at size and predicted total weight sizes combined seems to be

minor for most size ranges fished by this fleet or combined fleets, as it probably is from the point of view of the

overall impact on data preparation procedures for stock assessment.

Acknowledgements

The authors wish to thank the staff of the IEO and of the sampling network for compiling the information to

carry out this analysis. Special thanks go to the skippers and sailors of the Spanish longline fleet for the facilities

to carry out sampling in port over several decades.

708

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711

Table 1. Number of size and weight observations available by year for each sex category considered (female,

male, unk. and total)

Year Female Male Unk. Total

1984 902 902

1985 9874 9874

1989 942 735 65 1742

1990 756 752 142 1650

1991 625 550 79 1254

1992 734 623 36 1393

1993 786 1140 95 2021

1994 944 1003 21 1968

1995 767 532 32 1331

1996 810 726 57 1593

1997 551 513 39 1103

1998 647 572 42 1261

1999 533 462 12 1007

2000 210 182 3 395

2001 436 390 30 856

2002 358 365 9 732

2003 410 398 6 814

2004 369 312 2 683

2005 223 164 1 388

2006 355 219 37 611

2007 463 338 51 852

2008 441 404 26 871

2009 339 323 662

2010 306 315 621

2011 343 245 6 594

2012 347 229 22 598

2013 338 243 9 590

2014 366 251 11 628

2015 265 199 2 466

2016 269 247 516

2017 333 257 1 591

2018 42 51 93

Total 14308 12740 11612 38660

Table 2. Number of size and weight observations available by BIL area and sex category (female, male, unk.

and total)

BIL Area Female Male Unk. Total

BIL94A 1531 1356 820 3707

BIL94B 10035 8613 6817 25465

BIL94C 2742 2771 3975 9488

Total 14308 12740 11612 38660

712

Table 3. Summary of the intervals, mean values and standard deviation of the size and weight observations for

each sex considered (female, male) and all data combined (female+male+unk.).

Size (LJFL cm ) Weight (RW kg)

Min. Max. Average Std. Dev. Min. Max. Average Std. Dev.

All 65 292 145.0570 26.1224 3.0 380 43.5126 28.3858

Female 80 284 142.8507 25.8846 5.9 380 42.5041 29.9388

Male 65 247 135.1756 19.9732 3.0 255 33.6882 17.9745

Table 4. Results obtained for base-case GLM-GENMOD deviation for each main factor considered: year,

quarter, BIL area, sex (female, male), Ln(size) and interactions.

Model factors

d.f.

Residual

deviation

Change

in

deviation

% of

total

deviation p chi-sq

1 81563235

Year 29 77481247 4081988 5.3% < 0.001 0.00E+00

Year Quarter 3 77236695 244552 0.3% < 0.001 0.00E+00

Year Quarter BIL_Area 2 76829785 406910 0.5% < 0.001 0.00E+00

Year Quarter BIL_Area Sex 1 74744539 2085246 2.7% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ 184 4693564 70050975 90.4% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ Quarter*Sex 3 4691831 1733 0.0% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ BIL_Area*Sex 2 4691741 1823 0.0% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ Year*Sex 29 4682447 11117 0.0% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ Sex*lnSZ 141 4663912 29652 0.0% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ Quarter*BIL_Area 6 4658823 34741 0.0% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ Year*BIL_Area 45 4635052 58512 0.1% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ BIL_Area*lnSZ 277 4629997 63567 0.1% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ Quarter*lnSZ 447 4576029 117535 0.2% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ Year*Quarter 83 4527095 166469 0.2% < 0.001 0.00E+00

Year Quarter BIL_Area Sex lnSZ Year*lnSZ 2830 4090416 603148 0.8% < 0.001 0.00E+00

713

Table 5. Summary of the parameter statistics of the linear fit for each sex considered (females, males) and all

data combined (female+male+unk.). Note: see discussion for linear fit parameters excluding data before 1989.

Linear fit SEX

All Female Male

Residuals:

Min. -0.8880 -0.91312 -0.71480

1Q -0.0909 -0.9046 -0.09165

Median 0.0009 0.00072 -0.00371

3Q 0.0904 0.09192 0.09088

Max. 1.8925 1.89647 0.84090

Res. Stand. Error 0.1385 0.1417 0.1378

Multiple R-squared 0.9433 0.9403 0.9228

Adjusted R-squared 0.9433 0.9403 0.9228

F-statistics 6.459E+05 2.254E+05 1.523E+05

p-value < 2.2E-16 < 2.2E-16 < 2.2E-16

Coefficients:

Coef. a 3.71811E-06 3.11297E-06 2.95028E-06

LCL95% 3.57485E-06 2.91086E-06 2.72059E-06

UCL95% 3.86711E-06 3.32912E-06 3.19935E-06

Coef. b 3.245243 3.284868 3.293896

LCL95% 3.237329 3.271305 3.277350

UCL95% 3.253157 3.298430 3.310443

Table 6. Summary of the parameter statistics of the non-linear fit for all data combined.

Non-linear fit Estimate LCL95% UCL95%

Coef. a 7.8485161E-06 7.69942E-06 7.99761E-06

Coef. b 3.0994379946 3.09576763 3.10310835

Approx. Stand-error (a) 1.49096E-07

Approx. Stand-error (b) 0.00367036

MSE 48.7333

RMSE 6.9809

714

Table 7. Relative difference (%) between the weights observed in the total of 38,660 size-weight observations

analyzed in this document and the weights predicted for these sizes applying four different size-weight

relationships (LJFL-RW) obtained in the same fleet.

Equation Reference a b Effect on weight (%)

(1) Linear fit (this paper) 3.718110E-06 3.245243 + 0.497

(2) Non-linear fit (this paper) 7.848515E-06 3.099438 - 0.357

(3) Garcés & Rey (1984) 3.800000E-06 3.242775 - 0.431

(4) Mejuto et al. (1988) 3.780540E-06 3.245067 - 1.083

Note: equations (1), (3) and (4) were obtained by linearization procedures.

Table 8. Relative difference (%) between predicted weights based on eight Task2-size sets calculated by

applying four different size-weight relationships (LJFL-RW) obtained in the same fleet. The non-linear fit of the

present study was considered as a reference equation for comparison with other equations tested.

Note: equations (1), (3) and (4) were obtained by linearization procedures.

Equation Reference a b

Mean effect

on weight

(%)

LCL95% UCL95%

(1) Linear fit (this study) 3.718110E-06 3.245243 +1.032 +0.732 +1.333

(2) Non-linear fit (this study) 7.848515E-06 3.099438 Reference Reference Reference

(3) Garcés & Rey (1984) 3.800000E-06 3.242775 +0.107 -1.91 +0.405

(4) Mejuto et al. (1988) 3.780540E-06 3.245067 -0.540 -0.844 -0.235

715

SEX = All

SIZE_LJFL

frequency

100 150 200 250 300

02000

4000

6000

SEX = Female

SIZE_LJFL

frequency

100 150 200 250 300

02000

4000

6000

SEX = Male

SIZE_LJFL

frequency

100 150 200 250 300

02000

4000

6000

Figure 1. Size (LJFL cm) frequency distribution of the available size-weight data for obtaining length to weight

ratio. Sex: All includes females+males+unknown (see tables for details).

Figure 2. Box-plot of size (LJFL cm) for each sex category (all combined, female and male) and for each BIL

area (BIL94A, BIL94C and BIL94B) considered. All includes females+males+unknown.

716

Figure 3. Size (LJFL cm) - round weight (RW kg) linear relationships of swordfish from North Atlantic stock.

Left panel: for each sex considered (female, male) and all data combined (female+male+unk.). Note: fit lines of

females and males (red and green) are superimposed. All data combined (black line). Right-upper panel: for

females. Right-lower panel: for males. See Table 5 for details.

Figure 4. Size (LJFL cm) - round weight (RW kg) linear relationship of swordfish from North Atlantic stock

obtained for years and sexes combined (female+male+unk.) and 95% confidence intervals. See Table 5 for

details.

717

Figure 5. Diagnosis of the residuals of the size (LJFL cm) - round weight (kg) linear relationship of swordfish

from North Atlantic stock obtained for sexes combined (female+male+unk.): Residuals vs. fitted values, qq-plot

and residuals vs. leverage.

Figure 6. Size (LJFL cm) - round weight (RW kg) non-linear relationship of swordfish from North Atlantic

stock obtained for years and sexes combined (female+male+unk.). See Table 6 for details.

718

Figure 7. Comparison between average values and variability of weights (RW kg) observed for each size class

of 5 cm (LJFL cm) represented by box-plots (in gray) vs. average predicted weight by size category based on

four size-weight equations tested (colored lines). Eq.1-Black = Linear fit (this study). Eq.2-Green = Non-linear

fit (this study). Eq.3-Red = Garcés & Rey (1984). Eq.4-Blue = Mejuto et al. (1988). Note that there are

superimposed lines in some of the predictions of weight where the graphic differences are almost imperceptible.

Eq. 1,3,4

Eq. 2

Size-class (5cm)

RW

(k

g)