Age and growth of Spanish mackerel ( Scomberomorus brasiliensis ) off the northeastern coast of Brazil

Age and growth of the Spanish mackerel (Scomberomorus brasiliensis) caught off northeastern Brazil were determined. A total of 831 otoliths were examined 296 from males (12 75 cm FL), 212 from females (11.5 72 cm FL) and 323 from specimens of undetermined sex (12.4 75 cm FL). There was a high percentage of juveniles in the catches, resulting mainly from the use of gillnets. Marginal increment analysis of the otoliths indicated that the shortest distances from the last ring to the edge occurred from November to May, laying down just one ring annually. One to eight rings were found, with specimen lengths ranging from 11.5 to 75.8 cm. The Schunute model was used to determine what model was best fit the data, demonstrating that the specialized von Bertalanffy growth equation is the most appropriate. Curves were established for males (L∞ = 79.52 cm, K = 0.189, t0 = -0.384 year) and females (L∞ = 109.18 cm, K = 0.114, t0 = -0.414 year), which resulted in distinct growth patterns between sexes. Based on the parameters estimated for the sexes separately, males have an approximate longevity of 15.5 years, whereas female longevity is 25.9 years. Specimens between 2 and 6 years of age represented 86% (n = 5,290) of the catch composition, characterizing the species as a catchable stock in the region. The present study updates essential information for assessing the stock of this important resource, for which the last growth studies in the region were carried out approximately thirty years ago.


Introduction
The Spanish mackerel (Scomberomorus brasiliensis, Collette, Russo & Zavalla-Camin, 1978) occurs along the Atlantic coast of Central America, the Caribbean and South America from Belize to the State of Rio Grande do Sul in southern Brazil (Collete & Nauen, 1983).It is a neritic species that inhabits the epipelagic zone, living mainly on the continental shelf in large schools (especially juveniles).There are currently three recognized species from the genus Scomberomorus along the Atlantic coast of South America: S. brasiliensis, S. cavalla, and S. regalis.
For a long time, S. brasiliensis was confused with S. maculatus, from which it differs by having a lower number of vertebrae (47-49) and smaller pelvic fin (3.6-5.9% of its length) (Collete et al., 1978).In 2003, a total of 6,642 tons of S. brasiliensis were caught in its areas of occurrence (FAO, 2003).It is also an important resource for the artisanal fishing fleet in Brazil, especially in the northeastern region, where 3,071 tons were landed in 2003 (IBAMA, 2003), representing 46.2% of all landings of the species in the Caribbean and South America.In Trinidad, S. brasiliensis is considered the most abundant neritic pelagic fish (Julien-Flus, 1988).
Growth studies are important in interpreting population dynamics and the impact of fishery exploitation.Estimates on the age structure of fishery resources allow the construction of age-length keys and the estimation of growth parameters for the application of stock assessment models.This enables comparative studies on growth in different stocks (Pauly, 1987), which allows the identification of indirect evidence of the population structure (Ihssen et al., 1981;Sutter et al., 1991).Most growth studies on Scomberomorus species are based on otolith analysis (Table 1).
In northeastern Brazil, S. brasiliensis is exploited especially by the artisanal fleet, between the 10 and 50 m isobaths, catches undertaken with gillnets predominating (81%) and, in a lesser proportion, those with surface lines (19%) (Lessa, 2006).Nóbrega & Lessa (2009a) assessed the exploitation status of the stock and estimated a mean annual biomass of 4,761 t for a mean yield of 1,437 t/year, indicating that the stock is near its maximal exploitation limit.In the present study, whole otoliths were used to estimate age and analyze the age structure of Scomberomorus brasiliensis caught off northeastern Brazil, thereby contributing essential information (growth parameters) for future assessments of exploitation levels and sustainable catch rates for this important fishery resource in the region.

Material and Methods
Length (fork length -FL, cm) and weight (TW, g) of the Spanish mackerel were collected daily from the artisanal fleet operating with hand lines and gillnets off northeastern Brazil (Fig. 1) between February 1998 and April 2001.The fishing areas had depths from 4 to 204 m (mean = 36.3m; SD = 26.9m), with the distance from shore ranging from 1.37 to 54.42 km (mean = 15.72 km; SD = 11.4).Potential regression between the FL and TW was calculated for combined sexes.
To determine growth, specimens (n = 1,041) were measured and weighed.Sex was determined through a macroscopic analysis of the gonads (Vazzoler, 1996).Sagittal otoliths were removed, washed and dry stored.
The right otolith of each pair was examined whole in vegetable oil on a black background under transmitted light.Otoliths were classified into age groups based on the number of translucent bands.Distances from the nucleus to the edge (otolith radius -OR) and between translucent bands were measured (Fig. 2) with a stereoscopic microscope equipped with ocular micrometer at 10x magnification (1 micrometer unit = 1 mm).A single reader analyzed each otolith on different occasions with no knowledge on the size of the individual or the previous bands count.Average percentage error (Beamish & Fournier, 1981) was used to compare the concordance of age determination between two readings.
Marginal increment analysis was performed to determine the periodicity of ring formation by subtracting the otolith radius (OR) measurement from the last growth ring (r n ).For monthly marginal increment analysis, the sample was divided into juveniles (< 3 years) and adults (> 4 years) based on the maturity scale proposed by Gesteira & Mesquita (1976).Analysis of variance (ANOVA) and a post-hoc least significant difference test were used to determine significant differences between months.Potential regressions between the OR and FL were calculated for males, females and combined sexes.Analysis of covariance was used to compare the correlation between the OR and FL for males and females.Measurements of the distance between the otolith nucleus and the last band were back-calculated using the Monastyrsky equation ( 1) for the body proportionality hypothesis (BPH) (Francis, 1990): (1) in which L i = the back-calculated length at last age; S i = otolith radius at the time of the last band; S c = the otolith radius at capture; L c = the length at capture; and b = the slope coefficient of the relationship between OR and FL (potential relationship for combined sexes).
To determine which growth model best fit the observed and backcalculated lengths of males, females and combined sexes in northeastern Brazil, the growth equation formulated by Schnute (1981) was employed, using the nonlinear least squares method (2).Relative growth rates z 1 and z 2 were also  calculated (3 and 4) (Schnute, 1981): )./ ) (( where L t is predicted length at age t; τ 1 = first specified age; τ 2 = second specified age; a = constant relative rate of relative growth rate; b = incremental relative rate of relative growth rate; y 1 = size at age τ 1 ; y 2 = size at age τ 2 ; z 1 = relative growth rate at age τ 1 ; z 2 = relative growth rate at age τ 2 . Growth parameters were calculated for males, females and combined sexes using the specialized von Bertalanffy equation with p = 1/b (5), with individual observed lengths and lengths backcalculated to the last band of each specimen: (5) where L t is predicted length at age t; L ∞ = mean asymptotic fork length; K = growth rate constant; t 0 = the age when length is theoretically zero; b = incremental relative rate of relative growth rate.
Variability in the estimated growth parameters for males, females and combined sexes was determined using 95% confidence intervals generated from normal bivariate distribution for the L ∞ and K parameters, conditioned to the estimated t o value (conditional distribution) using the parameter vector, its covariance matrix and a function that provides the p density contours for a normal bi-dimensional variable (Kimura, 1980;Cerrato, 1990).To compare the estimated growth parameters for males and females, the Hotelling T 2 test was employed and 95% confidence intervals were constructed for the difference between the L ∞ , K, t 0 growth parameter vectors in order to graphically represent the test according to the following hypotheses (Cerrato, 1990): An age-length key was constructed from the entire sample of otoliths (n = 831), thereby establishing the age structure of the overall sample (n = 6,148).To estimate the longevity of the Spanish mackerel in northeastern Brazil was used the equacion (6) proposed by Taylor (1958): (6) Age max = t 0 + 2.996 / K where K = growth rate constant; t 0 = the age when length is theoretically zero.

Results
The size structure of the overall sample ranged from 9.5 to 96 cm (mean = 46.7 cm; SD = 12.33 cm) (Fig. 3a).Gillnets caught individuals ranging from 9.5 to 76 cm FL (mean = 43.7 cm; SD = 10.99 cm), whereas hand lines caught individuals ranging from 32.1 to 96 cm FL (mean = 58.3cm; SD = 15.58 cm).Approximately 60% and 29% of catches carried out by gillnets and hand lines are immature specimens, respectively.
There was no significant difference in lengths between males and females (ANOVA, p = 0.26); however, females had a greater maximum length (86.5 cm) than males (76.5 cm) (Fig. 3b).The weight of the specimens ranged from 12 to 7,640 g (mean = 912 g; SD = 777 g).The potential model showed good fit to the regression between the FL and TW (Fig. 3c).
Among the total number of otoliths examined (n = 1,041), 79.8% were used -296 from males (12 -75 cm), 212 from females (11.5 -72 cm) and 323 from specimens of undetermined sex (12.4 -75 cm).The average percentage error (APE) between readings ranged from 0% to 15.98% of 0 to 8 bands, whereas the overall sample had an APE of 12.6%.The coefficient of variation (CV) between the two readings was 11.88%.The number of translucent bands ranged from 0 to 8 in the 831 specimens, with sizes between 11.5 and 75 cm FL.
There was a similar pattern for juveniles and adults in marginal increment averages from the last growth ring in relation to the otolith radius, resulting in significantly lower values (ANOVA, p < 0.001) between November and February (Fig. 4a) for juveniles and statistically significant differences between the period from November to May and the period from June to September (Post-hoc, p < 0.05).In adult specimens, significantly lower average marginal increment values (ANOVA, p < 0.001) were found between November and May (Fig. 4b) and there was a statistically significant difference between the period spanning from November to June and the period spanning from July to October (Posthoc, p < 0.05).Thus, an annual growth band deposition pattern was considered.
The potential model showed reasonably fit to the regression between the OR and FL for males (Fig. 5a), females (Fig. 5b) and combined sexes (Fig. 5c).There were no significant differences (ANCOVA, p = 0.39) in relations between the OR and FL by sex.Mean observed and backcalculated lengths for the ages exhibited similarities (Fig. 6), indicating that the bands interpreted on the otoliths may be used to estimate growth and establish the age structure of the S. brasiliensis caught off northeastern Brazil.Absolute ages were calculated considering the month of January as that in which the species changes age.
The growth model proposed by Schnute (1981) estimated a > 0 and b > 1 for both sexes separately and combined (Table 2), indicating the specialized von Bertalanffy with p = 1/b to be the best growth model for the species.The growth rates (z 1 , z 2 ) for τ 1 and τ 2 demonstrated considerable variation, indicating extremely high growth at the ages established for τ 1 and very low growth for older specimens (τ 2 ), with a being an estimate of the constant relative growth rate (Table 2).
The growth curves established for separate and combined sexes provided residuals that fit reasonably well to normal distribution (KS, p = 0.16).Curves from observed and backcalculated data resulted in similar coefficients of determination and standard error for the estimated parameters in both the Schnute model (Table 2) and the von Bertalanffy equation (Table 3).Thus, the estimates obtained  for the observed data were chosen as those that best represent the growth of S. brasiliensis in waters off northeastern Brazil.
The established growth parameters indicate that males have a higher growth rate than females and achieve a lower L ∞ (Fig. 7).The confidence interval for the K and L ∞ parameters conditioned to the t 0 value (conditional distribution) provided a 95% likelihood between L ∞ values from 87.76 to 130 cm and K values from 0.085 to 0.143 year -1 for females; L ∞ from 68.59 to 90.44 cm and K from 0.152 to 0.226 year -1 for males (Fig. 8); L ∞ from 87.4 to 101.8 cm and K from 0.141 to 0.173 year -1 for combined sexes.
In the comparison of female and male growth parameters using the Hotelling T 2 test, significant differences were found  (T 2 = 751.012;F = 374.76;d.f.= 3.013; p < 0.001).This result is graphically illustrated in Fig. 9, in which the H 0 point (δ = 0) is not contained within the 95% confidence interval created for the difference between female and male growth parameters (δ = 0).
Employing the age-length key for the sample used in the growth study, the age structure was calculated for the overall sample (n = 6,148).Individuals between two and six years of age represented 86% of the total (Fig. 10).Based on the parameters estimated for the sexes separately, males have an approximate longevity of 15.5 years, whereas female longevity is 25.9 years.

Discussion
Whole otoliths of S. brasiliensis were used in the present study, as they offered good visibility of the bands (Fig. 2) and an acceptable average percent error (12.6%) between readings (Campana, 2001).This APE indicates that the aging protocol adopted is replicable.Whole otoliths have been used by a number of authors to estimate the age of species from the genus Scomberomorus (Nomura, 1967;Beaumariage, 1973;Johnson et al., 1983;Manooch et al., 1987;Collins et al., 1989;DeVries & Grimes, 1997;Begg & Sellin, 1998) due to the easy preparation and visualization of the growth bands (Manooch et al., 1987).
A pattern of a greater frequency of translucent bands on the edge of otoliths was observed between November and May, thereby evidencing annual band formation.This result is essential for the estimation of the age of S. brasiliensis in waters off northeastern Brazil, as the confirmation of the periodicity of growth band deposition is a basic requirement for the study of growth using hard structures (Casselman, 1983).Ximenes (1981) found similar results in northeastern Brazil, with reductions in the translucent margins occurring in the otoliths from December to March, coinciding with the period of smaller marginal increments observed in the otoliths of adult specimens in the present study.Nomura (1967) either found a greater frequency of translucent bands on the edge of otoliths from S. brasiliensis in the State of Ceará (northeastern Brazil) from January to April.
Reproduction occurs between September and March along the coast of the State of Ceará (Gesteira & Mesquita, 1976) and coincides with the change in age, which occurs from November to March.Seasonal marks on hard structures are generally associated to temperature in regions at high Table 2. Growth parameters calculated from observed lengths (OL) and back-calculated (BC) lengths, using Schnute model (1981).τ 1 = first specified age; τ 2 = second specified age; a = constant relative rate of relative growth rate; b = incremental relative rate of relative growth rate; y 1 = size at age τ 1 ; y 2 = size at age τ 2 ; z 1 = relative growth rate at age τ 1 ; z 2 = relative growth rate at age τ 2 (SE -standard error; r 2 -coefficient of determination).latitudes, whereas such marks in tropical fish are thought to be associated to environmental changes in the habitat, availability of food resources, life strategy history of the species and endogenous control (Longhurst & Pauly, 1987).Synchronization of band formation with gonad maturity and reproduction has been found for the king mackerel in waters off Trinidad (Sturm & Salter, 1990) as well as for the Spanish mackerel (Scomberomorus commerson) off the eastern coast of Australia (McPherson, 1992).Band formation has also been correlated to reproductive behavior in the school mackerel (S. queenslandicus) due to its coinciding with the reproductive peak in October through January.The same is true for the spotted mackerel (S. munroi) off the eastern coast of Australia, with peak reproduction between August and October (Begg & Sellin, 1998).Thus, the reproduction process may be related to the formation of growth bands in S. brasiliensis in the northeast Brazil.
The reasonable adjustment between the OR and FL resulting from the potential model (Fig. 5a-c) and the similarity between the mean observed and backcalculated lengths (Fig. 6) confirm the presupposition of proportionality between otolith size and length of the specimens (Carlander, 1981).The backcalculation method demonstrated an excellent fit to the data, with the lowest standard errors and coefficients of variation in relation to the observed data (Tables 2 and 3) for the majority of curves.Although a tendency toward underestimating mean lengths for the ages (Fig. 6), asymptotic size and overestimating the growth rate (Table 3) was found, the method generally demonstrated the viability of the use of growth marks on otoliths as age and growth estimators for the species in the region.
This sustains the preference for growth curves generated from observed lengths, as underestimations in the backcalculation model could cause variations in biomass estimates, for which the accuracy of growth parameters is a basic presupposition.The determination of age through growth bands is the most valuable information used in virtual population analysis, cohort analyses and catch curves (Hilborn & Walters, 1992).
The estimated von Bertallanffy growth parameters revealed that females achieve a greater asyntotic size and   have a slower growth rate than males, which corroborates findings described by Nomura (1967) and Ximenes (1981).There was a significant difference between male and female growth, which is in agreement with results described by other authors, who report the difference in male and female growth patterns to be a characteristic of Scomberomorus species (Beaumariage, 1973;Powell, 1975;Sturm, 1978;Johnson et al., 1983;Fable et al., 1987;MacPherson, 1992;Schimidt et al., 1993;DeVries & Grimes, 1997).
Differences in growth between sexes indicate that males have faster growth until approximately five years of age.Beginning at six years of age, females have larger sizes for the same age (Fig. 7).The accentuated growth rate of males in relation to females at early ages is also verified by the z 1 parameters estimated from the younger ages τ 1 by the Schnute model, which resulted in considerably higher values for males using both the direct and backcalculated methods (Table 2).According to Gesteira & Mesquita (1976), S. brasiliensis are ready for reproduction at 41 cm FL off the coast of Ceará State (3.5 years for males; 3.75 years for females).At age of first sexual maturity, females begin to have larges sizes than males for the same age and reach larger asymptotic sizes (Table 3, Fig. 7).These results suggesting that there may be a more influence of reproduction activity in females, promoting a redirection of energy to gonad maturity and reproduction, with a consequent reduction in somatic growth until the age of first sexual maturity.
Age distribution, calculated using the age-length key, indicated an accentuated catch rate of immature specimens.According to Nóbrega & Lessa (2009a) the FL at first maturity for S. brasiliensis off northeastern Brazil is 42 cm, when individuals are between 3.6 and 4 years of age, based on the estimated growth curves in the present study (considering the difference in growth between sexes).Thus, it can be concluded that approximately 58% of catches are immature specimens.Management measures that encourage an increase in the mesh size of gillnets are urgent, as is an increase usage of hand lines rather than nets in order to promote rational catches of this important fishery resource in waters off northeastern Brazil.
The growth model of Schnute, used to examine which model performed better adjustment to S. brasiliensis growth, in the northeastern Brazil, indicated, according the values obtained for a e b parameters, that the specialized von Bertalanffy model is the best to describe the species growth in the region.The collapses of important fishery stock resources in the entire world demonstrate that the methods for stock evaluation do not guarantee the resources sustainability (Schnute & Richards, 2001).However, the search for models which minimize variance and uncertainty in data analysis of fishery biology must be permanent, in order to maximize the quality of population estimates and their exploitation levels.
The growth parameters and characteristics estimated in the present study and the age structure for S. brasiliensis caught by the artisanal fleet in northeastern Brazil represent an important contribution to our knowledge of the species.
The present study updates essential information for assessing the stock of this important resource, for which the last growth studies (Ximenes, 1981) in the region were carried out approximately thirty years ago.

Fig. 2 .
Fig. 2. Characteristics of whole otoliths from Scomberomorus brasiliensis observed under transmitted light for age determination.Female specimen, six years of age, measuring 57 cm FL (OR = otolith radius; = translucent bands).

Fig. 3 .
Fig. 3. Length frequency distribution for overall sample (a); Frequency distribution of male and female lengths (b); Relationship between FL and TW (combined sexes) showing adjusted potential model (c) of Spanish mackerel off northeastern Brazil.

Fig. 4 .
Fig. 4. Marginal increment with mean and 95% confidence intervals for young specimens (a) and for adults (b) of Scomberomorus brasiliensis in the northeastern Brazil.

Fig. 5 .
Fig. 5. Relationship between OR and FL for males (a), females (b) and combined sexes (c), showing adjusted potential model for Scomberomorus brasiliensis collected off northeastern Brazil.

Fig. 6 .
Fig. 6.Mean observed and backcalculated lengths of Scomberomorus brasiliensis at different catch ages for males, females and combined sexes in the northeastern Brazil.

Fig. 8 .
Fig. 8. Cross sections of approximate 95% confidence regions around least squares estimates (L ∞ , K) for growth parameters of males and females of Scomberomorus brasiliensis collected off northeastern Brazil.

Fig. 9 .
Fig. 9. Cross section of approximate 95% confidence intervals calculated for the difference between the vectors of the growth parameters (L ∞ , K) (T 2 of Hotelling) for females and males of Scomberomorus brasiliensis collected off northeastern Brazil.

Table 1 .
Parameters of von Bertalanffy growth based on otolith analysis for Scomberomorus species carried out in the world (L ∞ in fork length; M = males; F = females; B = both sexes combined).

Table 3 .
Von Bertalanffy growth parameters calculated from observed lengths (OL) and back-calculated (BC) lengths of Spanish mackerel collected off northeastern Brazil (SE -standard error; r 2 -coefficient of determination).