Population dynamics of Scomberomorus brasiliensis from a small-scale fishery off Southern Brazil Ocean and Coastal Research

Scomberomorus brasiliensis is the most important fish species of the small-scale fishery off the southwestern Atlantic north of the La Plata estuary. For management purposes, this study evaluated their reproductive biology, size, age and growth along the Paraná coast. Monthly samples (March 2018-June 2020) from the fishery comprised 933 specimens (413 males, 520 females), 210-779 mm fork length, corresponding to a size smaller than in the northern areas. It presented negative allometry ( b = 2.69159, length-weight relationship). Specimens in all stages of maturity occurred during the study period, indicating spawning in the area from October to June, peaking from January to March. The gonad–length relationship was suitable to confirm this assessment. Individual fecundity varied between 34,484 and 390,786 oocytes. Maturity occurred at L 50 = 446.46 mm, t 50 = 1.4 years, and L 100 = 588.79 mm, and t 100 = 2.3 years. The growth parameters were L ∞ = 771.68 mm, k = 0.65 year -1 and t 0 = -0.102 years, with cohorts aged from 0.5 to 6.5 years. Scomberomorus brasiliensis along the Paraná coast constitutes a self-sustaining group, not directly related to that from northeastern Brazil. This small-scale fishery is not currently negatively affecting stock level; it is essential to monitor these attributes to detect future changes or impacts. dot-plot by sex, gonad maturity and month was used to investigate individual variations, and (ii) a confidence interval plot was used to analyze averages (excluding immature individuals) by sex and month. Monthly averages of GLR’ were tested using a one-way analysis of variance, and assumptions were tested and confirmed in the residual analysis. The variance inflation factor was used to detect extreme averages with mul-ticollearinity, considering a cut-off value of 5 (Zuur et al., 2009; Legendre and Legendre, 2012). A post-hoc Tukey test was applied to detect differences among monthly averages.

The Brazilian Spanish mackerel is an important fishery resource mainly for the small-scale (artisanal) fishery (Fonteles-Filho, 1988;Batista and Fabrè, 2001;Collette et al., 2011). According to the last reliable Brazilian fishery statistic (IBAMA, 2007), it is one of the most valuable fishery resources, attaining above average prices for commercialization in the fish production chain. In 2007, 8,873 tons of Brazilian Spanish mackerel were landed, 99.7% from the small-scale fishery. Higher landings (~94%) occur in northern and northeastern Brazil (~4°50'N to ~13ºS), where S. brasiliensis is called "serra" in Portuguese and is targeted by a specific gillnet named "serreira" (Maia et al., 2015). In the southwestern Atlantic (22°S-34°S), it is named "sororoca" in Portuguese and 462 tons were landed in 2007 (IBAMA, 2007). From 2009 to 2011, the average annual production of 433.9 tons was an underestimated value (MPA, 2011) due to the progressive dismantling of fishery statistics promoted by deficient federal policies. There have been no national fishery statistics in Brazil since 2012; however, from 2016 this situation changed in some parts of southern Brazil owing to the commencement of the Fisheries Activity Monitoring Project. This project was demanded by an environmental agency (IBAMA) to the Petrobras oil company and was undertaken by researchers from diferent institutions. This project has provided a reliable source of data from both industrial and small-scale fisheries in the area between 22°S and 29°S.
The small-scale fishery is a common and well-developed activity throughout the Brazilian coast and is sometimes neglected and the victim of deficient policies similar to other fishery activities in Brazil (Oliveira and Silva, 2012;Isaac et al., 2013). Its importance is highlighted in the estuarine complexes and adjacent areas of the tropical and subtropical regions, including the Paraná coast (Chaves and Robert, 2003;Chaves and Silva, 2019). It is relatively short (~100 km in a straight line); however, it plays a significant role in fish populations, providing areas for reproduction, feeding, and growth, highlighting the Paranaguá Estuarine Complex and the Guaratuba Bay (Andriguetto-Filho et al., 2006;Lana and Bernardino, 2018).
The Paraná coast only presents a small-scale fishery (Andriguetto-Filho et al., 2006), comprising approximately 5,000 artisanal fishers and an average landing of 2,573 tons per year (2017-2019) (PMAP, 2020). These recent data improved the previous lack of information reported by different authors (IBAMA/CEPSUL, 2000;Robert and Chaves, 2006;Mendonça and Miranda, 2008;Mendonça and Lucena, 2014;Chaves and Silva, 2019), and confirmed the importance of S. brasiliensis in the small-scale fishery of Paraná. During 2017-2019, the Brazilian Spanish mackerel occupied the third prodution position, with an average of 113 tons per year, after the shrimp Xiphopennaeus kroyeri (first) and the molusk Anomalocardia flexuosa (second) (PMAP, 2020). Although it is landed the year-round, both as a target species and as by-catch (Chaves and Silva, 2019), higher frequencies are recorded during warmer months (October to March) (UNIVALI, 2013).
Despite the importance of S. brasiliensis, the amount and focus of available studies on its fishery and biology are heterogeneous. This species has been well studied in northeastern Brazil, where there is a single stock Isaac et al., 2013); however, in southern Brazil (22°S-34°S), including the Paraná coast, there are no studies. The species does not perform remarkable migrations like tunas, undergoing only seasonal and reproductive displacements (Collette et al., 1978(Collette et al., , 2011Batista and Fabrè, 2001). Therefore, it is reasonable that the individuals along the Paraná coast and adjacent areas caught by the small-scale fishery constitute a self-sustaining group (stock) not directly related to that from northeastern Brazil. Cadrin et al. (2014) defined stock as "an exploited fishery unit. A stock may be a single spawning component, a biological population, a metapopulation, or comprise portions of these units. For management purposes stocks are considered discrete units, and each stock can be exploited independently or catches can be assigned to the stock of origin". Thus, patterns of size, age, and growth (Ximenes, 1981;, reproductive biology (Silva et al., 2005;Lima et al., 2007;Lima et al., 2009), feeding (Menezes, 1970;Fonteles-Filho, 1988;Lopes et al., 2016), parasites (Alves and Luque, 2006;Eiras et al., 2014), and fisheries and management (Almeida et al., 2007;Brito and Furtado Júnior, 2010;Leão et al., 2018) described for this species in other areas cannot be assumed the same for management purposes along the Paraná coast (Moksness et al., 2013;Cadrin et al., 2014).
3 Chaves et al. Considering this scenario, it is possible to establish the following premises: (i) S. brasiliensis is the most important fish species for the small-scale fishery along the Paraná coast; (ii) the small-scale fishery is an important, essential and complex activity whose management requires relevant information regarding fisheries resources; and (iii) population dynamics parameters are intrisic for each stock and subsidisize proper management measures. Therefore, the present study aimed to estimate the population parameters of S. brasiliensis along the Paraná coast, verifying which population component was accessed by the fishing activity. Techniques for investigating reproductive biology, size, age and growth were applied, considering the hypothesis that the self-sustaining group along the Paraná coast had its own biological patterns.

MeTHODs saMplINg aND DaTa aCqUIsITION
Scomberomorus brasiliensis samples were obtained from small-scale fishery landings at the Fishery Market of Matinhos (FMM), Paraná coast, southern Brazil (25°49'S, 48°32'W) (Figure 1). Catches   Chaves et al. usually occurred with gillnets of varying mesh sizes (from 50 mm to 400 mm, usually 70 mm to 170 mm mesh), 2-3.5 km of extension, varied soak time (usually 20-30 h), with local modalities named "fundeio" and "caceio" in Portuguese (Chaves and Robert, 2003;Andriguetto et al., 2006;Afonso and Chaves, 2021). FMM is the centre of the landings and processing of fishery resources in coastal adjacent areas up to 40 m in depth. As a gross estimate, fishing occurs in a surface area of 2,000 km 2 and a volume of 40,000 km 3 of the neritic region, corresponding to the inner continental shelf. The inner shelf is characterized by the coastal water, a water mass with salinities less than 35 and varying temperatures, limited by the bottom temperature boundary, an intersection between the mixed coastal waters and subsurface cold-water intrusions (< 18ºC) that seasonally occur at the mid and outer shelf (Piola et al., 2018). During the study period, the atmospheric temperature in this region varied from 10.0ºC (August 2019) to 38.5ºC (January 2020) (DHN/Marinha do Brasil, 2021). The average values of sea surface temperature are available in the Supplementary Material, characterizing the seasons (summer = January, February, and March; autumn = April, May, and June; winter = July, August, and September; and spring = October, November, and December).
Biological samples were obtained monthly at FMM from March 2018 to June 2020, comprising biometry and gonads of 933 S. brasiliensis specimens (Table 1), with limited numbers in some months due to non-capture. Specimens were measured for total length (TL, mm) and fork length (FL, mm) and, whenever possible, total weight (TW, g) depending on immediate filleting. Sex (male and female) and maturity were identified based on visual inspection of the gonads (Vazzoler, 1996;Brown-Peterson et al., 2011) as follows: immature (A), developing (B), spawning capable (C), spawning capable with preovulatory hydration (Ch) only for females, and regressing (D). Morphological details of gonad features in each developmental phase are described in the Supplementary Material. From December 2018, gonad weight (GW, g) was recorded.
For fecundity estimates, between December 2018 and February 2019 the left and right ovaries of 42 individuals, previously fixed in 10% formalin, were separated and weighed, and a medial, small portion of each was obtained and weighed too. The two dry portions were mechanically dissociated, aiming to identify, under a steromicroscope, the vitellogenic oocytes recognized by their opacity, resulting from yolk deposition (Vazzoler, 1996;Brown-Peterson et al., 2011). The opaque oocytes were counted, and the number found in each portion was extrapolated for the total ovary weight. The total number of oocytes in both ovaries was summed, constituting the individual fecundity (F i ).

DaTa aNalysIs
The results are presented based on FL data. Regressions between TL and FL were fitted for males and females together and separate, allowing for conversions. Linear models were adjusted by the iterative least squares method with the Levenberg-Marquardt algorithm and 9,999 iterations (Motulsky and Christopoulos, 2003). Residual analysis was performed and outliers (|Z|>1.96) were removed. The models were re-adjusted, and regressions for each sex were compared with an analysis of covariance (Zar, 2010). The length-weight relationship was fitted for males and females together (Froese, 2006), and using the iterative method. A t-test was applied to verify the isometric pattern (β = 3) of the coefficient b value. All statistical procedures were performed with α = 0.05.
The spawning period was verified based on the overall monthly distribution of gonad developmental phases (Lowerre- . For a detailed diagnosis, monthly frequencies of females and males in reproductive activity (combined frequency of C+Ch+D) were tested using a heterogeneity chisquare test (Zar, 2010). The gonad-length relationship (GLR = GW / FL × 100) was individually estimated from December 2018, helping the spawning period diagnostic. Because of the GLR dependence on FL, the size effect was removed by calculating GLR' = GLR × (FL 0 / FL) b , where the reference values for standardization were FL 0 = 516.05 mm (average FL), and b = 3.0208 from the model GLR = aFL b (Lombarte and Lleonart, 1993). Then, a confidence interval plot (95% t-distribution) of GLR' values by sex and gonad developmental phase was created to ascertain the representativeness of gonad maturity. After checking, individual values were graphically analyzed: (i) a dotplot by sex, gonad maturity and month was used to investigate individual variations, and (ii) a confidence interval plot was used to analyze averages (excluding immature individuals) by sex and month. Monthly averages of GLR' were tested using a one-way analysis of variance, and assumptions were tested and confirmed in the residual analysis. The variance inflation factor was used to detect extreme averages with multicollearinity, considering a cut-off value of 5 (Zuur et al., 2009;Legendre and Legendre, 2012). A post-hoc Tukey test was applied to detect differences among monthly averages.
Individual fecundity (y) was evaluated by fitting linear models between FL and gonad weight (x) by the aforementioned iterative method. The average length at first maturity (L 50 ) was estimated based on a logistic model (Haddon, 2011), in which the frequencies of adult females (P) were plotted against the bottom limit of length classes (L) following the formula P = 1 / [1 + e -r (L -L 50 ) ]. Previously, two approaches were verified: one considering C + Ch + D as adults, and the other with B + C + Ch + D as adults, the former being inadequate due to the mix between individuals for the first time as developing and reccurrent ones. The non-linear iterative least squares method with the Levenberg-Marquardt algorithm and 9,999 iterations was applied to fit the model (Motulsky and Christopoulos, 2003). Based on the model, the length at which all individuals could reproduce (L 100 ) was estimated.
The von Bertalanffy growth model (VBGM) parameters were estimated. After simulations, the maximum theoretical length (L ∞ ) was calculated using the Powell-Wetherall method and the growth rate (k) with the Shepherd length composition analysis (SLCA) (Isaac, 1990), considering fine adjustments in the routine introduced by Gayanilo et al. (2005). The theoretical age at zero length (t 0 ) was estimated using the Pauly formula (Pauly, 1984). The instantaneous growth rate (G = [(ln FL 2 -ln FL 1 ) /(t 2 -t 1 )]× 100) was calculated, and for age zero approximated values were FL 1 = 5 mm (based on Jenkins et al., 1984;Shoji et al., 2002) and t 2 =0.5 years. Based on the growth parameters, an inverse VBGM was used to estimate the average age at first maturity (t 50 ) and the age at which all individuals could reproduce (t 100 ).

ResUlTs
The 933 individuals of S. brasiliensis comprised 413 males (range of 210-740 mm FL), and 520 females (range of 282-779 mm FL) ( Table 1). The FL-TL relationships did not show significant differences between males and females (F = 0.88; p = 0.35), thus ensuring representativeness for the grouped model ( Table 2). The length-weight relationship (Table 2 Specimens from all maturity stages were found, although with varying proportions during the study period. Juveniles (immature, A) of S. brasiliensis were Table 2. Scomberomorus brasiliensis: summary of regressions involving total length (TL), fork length (FL), weight (TW), individual fecundity (Fi), gonad weight (GW), and proportion of adult females (P) for individuals landed at Fishery Market of Matinhos, southern Brazil, years 2018-2020 (a and b -regression coefficients; in the logistic model r = a and L 50 = b, SE -standard error, N -number of data, F -regression statistics, p -probability, r 2 -coefficient of determination). . Individuals in the developing (B) phase occurred in all months of the year, and from April (beginning of autumn) and August (winter) their frequencies were higher than 30% over the two years ( Figure 2). Scomberomorus brasiliensis specimens in reproductive activity (C + Ch + D) presented more than 30% of the frequency between November and December (end of spring) up to February 2019 (summer) and June 2020 (winter) ( Figure  3a). There were differences between sexes and years (χ 2 = 50.30, p = 2.65 × 10 -6 ) due to the predominance of females. This predominance was remarkable in January 2019 (χ 2 = 24.40, p = 7.43 × 10 -7 ), April 2019 (χ 2 = 4.00, p = 0.0455), January 2020 (χ 2 = 7.20, p = 0.0073), April 2020 (χ 2 = 15.21, p = 9.61 × 10 -5 ) and June 2020 (χ 2 = 14.23, p = 0.0002), evidencing a reccurrent pattern. Detailing the frequency of females, during the summer of 2019 and summer-autumn of 2020 there was a gradual decrease of spawning capable individuals (C + Ch) and an increase of regressing ones (D) (Figure 3b).
The gonad-length relationship (after size-effect removal) varied significantly among the gonad developmental phases (Figure 4 and referential values in the Supplementary Material). Higher individual values were recorded during the summer and autumn for both sexes (Figure 5a and 5c), related to reproductive activity. Average values of GLR' (Figure 5b and 5d) presented significant variation among months for both females (F = 13.78; p < 0.001) and males (F = 9.96; p < 0.001). Increases in GLR' indicated periods of intense reproductive activity. Alternate patterns of increases and decreases presented differences (p < 0.05 from Tukey tests, cf. Supplementary Material), although sequential values of these "sets" of high and low values did not differ, indicating homogeneity during intense and non-intense periods of reproductive activity.
Individual fecundity varied between 34,484 (410 mm FL) and 390,786 oocytes (650 mm FL), progressively increasing in relation to FL and ovary weight ( Figure 6 and Table 2). The first maturity corresponded to an average length of 446.46 mm FL (Figure 7, Table 2), corresponding to t 50 = 1.4 years, and based on the model, L 100 = 588.79 mm FL and t 100 = 2.3 years.
The estimated growth parameters were L ∞ = 771.68 mm, k = 0.65 year -1 , and t 0 = -0.102 years (Figure 8). The score function plot revealed a single peak corresponding to the estimated k value, ensuring its representativeness. Scomberomorus brasiliensis individuals presented ages from 0.5 to 6.5 years, predominating individuals of 1 year (32%), 1.5 years (45%) and 2 years (16%). The instantaneous growth 7 Chaves et al. rate evidenced a rapid growth up to 2.5 years, corresponding to 629 mm FL, which then decreased significantly ( Figure 8).

DIsCUssION
Biological sampling of fish landings is crucial for understanding the population strata accessed by fishing activity, information that subsidizes stock assessment and proper management measures (Cadima et al., 2005;Murie et al., 2012). The practical sample unit in the present study was the FMM, the focal point of a small-scale fishery, and sampling effort comprised the size range available of S. brasiliensis, similar to the procedures described by Batista and  Fabrè (2001). Thus, the population parameters of S. brasiliensis along the Paraná coast were properly estimated, revealing that the small-scale fishery caught mainly adults at and just after the first maturity.
The range of observed FLs was influenced by gillnet selectivity, explaining the low incidence of individuals less than 300 mm FL and larger than 700 mm FL. In the Caribbean Sea and the northern Chaves et al. and northeastern Brazil, maximum lengths recorded were larger than 900 mm FL (Froese and Pauly, 2019) and attained a 1360 mm FL ), which does not occur in the small-scale fishery of Paraná. These individuals either cannot occur at this latitude or are not accessed by the fishing activity. The former has support; otherwise, larger individuals would be common in other small-scale fisheries and in the industrial fishery that occurs in adjacent areas far from the coast, which has not happened either historically (Andriguetto et al., 2006;IBAMA, 2007) or recently (PMAP, 2020). However, S. brasiliensis along the Paraná coast is caught mainly by gillnets (Chaves and Robert, 2003), and 99% came from this fishing gear during 2017-2019 (PMAP, 2020). Therefore, the samples in the present study well represented the adults of the area, in view of the different mesh sizes of gillnets and fishing gears used in the Paraná coast and adjacent areas (Andriguetto et al., 2006), even under selectivity effects (Hubert et al., 2012).
Size structure influences the sex-ratio. Data from the present study showed that S. brasiliensis females were larger than males, similar to that in northeastern Brazil Maia et al., 2015). This dimorphism was not evidenced in the relative growth pattern (FL-TL relationship), only in the predominance of females (0.8:1, males:females), which varied compared to other studies. In northeastern Brazil, in coastal areas between 04°39'S and 06°29'S, the sex-ratios observed were 1.1:1 (n = 145) in a beach (from beach trawls) (Lima et al., 2007), and 2:1 (Oliveira et al., 2015), from joining samples from various beaches and omitting the number of individuals analyzed. The former represents a local proportion between males and females; however, the latter cannot be considered owing to the lack of information. In contrast,  found a sex ratio of 1.4:1, sampling a large area of the continental shelf (02°30'S-13°S, macro-scale study), evidencing different patterns of S. brasiliensis from northeastern Brazil compared to the Paraná coast.
Length-weight relationships also present intrinsic patterns related to biological and methodological aspects (Froese, 2006). Biological aspects include stock-population identity and density-dependent processes related to population dynamics (McBride,  2014). Methodological aspects are related to the size range analyzed, number of fishes, and model adjustments (i.e. algorithm used, linear vs. non-linear procedure, checking of assumptions). Thus, although direct comparisons among different studies require caution, some insights emerge. The b coefficient of the Caribbean Sea and northeastern Brazil ranged between 2.800 and 3.264, mean 2.97 (n = 9) (Silva et al., 2005;Tagliafico et al., 2015;Froese and Pauly, 2019), suggesting a conservative pattern of negative allometry also detected in the present results. In S. brasiliensis, these b values (< 3) were closely related to their elongated body shape, which predominates growth in length (Froese, 2006).
A remarkable diagnostic herein presented is the spawning of S. brasiliensis on the inner continental shelf of the Paraná coast, reinforcing the group identity in the area. In northeastern Brazil, there are two proposals, a high migratory pattern based on seasonal absences in some areas (Batista and Fabrè, 2001), and small-scale displacements in large areas (Colette et al., 2011). Both do not apply for the Paraná coast, where there is a continuous landing of individuals with 400-600 mm FL throughout the year, indicating the stock permanency in the area and small-scale fishery availability. Regarding the spawning period of S. brasiliensis on the Paraná coast (beginning in the spring, peaking in the summer, and finishing in the autumn), it was similar to historical records in northeastern Brazil (Gesteira and Mesquita, 1976). Nonetheless, more recent data from that area indicate spawning peaks in the summer and autumn (March to June), corresponding to the rainy season in that region (Lima et al., 2007) and matched with a higher abundance of S. brasiliensis (Brito and Furtado Júnior, 2010).   A methodological highlight deserves attention, the efficient use of the gonad-length relationship for spawning period diagnosis. Because of the difficulty in sampling weight data from small-scale fisheries, it was impossible to use the gonadosomatic relationship, i.e., the proportion between the gonad and total body weights (Brown-Peterson et al., 2011). Thus, the gonad index (GI = GW / FL b , b from the length-weight relationship), more often referred to as the gonad condition factor (Vazzoler, 1996), is a good indicator of reproductive activity, mainly for spawning periods (West, 1990;Lowerre-Barbieri et al., 2011). The GI denominator implies an estimated value (FL b ), and it can be calculated using the expected total weight (aFL b ), becoming the gonadosomatic relationship. Simulated values can be a source of bias, and thus this approach was disregarded. Initially, the size-dependence of the GLR values constituted a problem (West, 1990), which was easily solved adopting a sizeeffect removal procedure (Lombarte and Lleonart,   1993), efficient for GLR based on the present findings. Thus, the gonad morphological attributes and volume evaluated with the gonad-length relationship indicated an extensive spawning period at the inner continental shelf of S. brasiliensis.
Fecundity is an important component of reproductive strategies, operating on a spatial scale related to spawning and nursery areas, and enhancing the reproductive resilience of a stock (Lowerre- Barbieri et al., 2017). For S. brasiliensis, fecundity was higher Chaves et al. in heavier gonads and larger individuals, as expected. In northeastern Brazil, other estimates include a fecundity of 2,204,000 oocytes, and 350-790 mm FL, which were directly proportional to size, age and weight (Gesteira, 1972), and 871,523 oocytes, and 350-790 mm FL (Lima et al., 2007). More than the features of each stock, differences in relation to the Paraná coast (34,786, can be related to period, areas, and the criteria for counting oocytes. The fecundity results are the first referential for southern Brazil, showing the importance of larger and older females in the stock maintenance and other biological and environmental factors (Lowerre-Barbieri et al., 2017).
The average length at first maturity is a tool for stock management, and is usally a referential for establishing minimum legal sizes (Lowerre-Barbieri, 2009). The current estimate for S. brasiliensis (446.46 mm FL corresponding to 524.44 mm TL) was similar to that in most cases in northeastern Brazil. These other estimates include 410 mm FL (Gesteira and Mesquita, 1976), 419 mm FL , 410 mm FL (Lima et al., 2009), and 400 mm FL (Maia et al., 2015). These reveal a conservative pattern for the species in Brazil. In northeastern Brazil, there is an exception of 280 mm TL, which is a reduction in size due to overfishing (Lima et al., 2007). This last situation highlights the limitations of estimating catches of larger individuals or the use of L 50 values to restrict catches as management measures (Chaves, 2012). Especially for S. brasiliensis, larger females have a remarkable contribution to the reproductive success, ensuring egg availability. We refine this diagnostic with age and growth information below.
In northeastern Brazil, previous age and growth parameters of S. brasiliensis included values of L ∞ = 1067 mm FL and k = 0.16 year -1 (otolith analysis, Ximenes, 1981), L ∞ = 1360 mm FL and k = 0.29 year -1 (modal progression analysis, Gonçalves et al., 2003), and L ∞ = 957 mm FL, k = 0.15 year -1 , and t 0 = -0.212 years (otolith analysis, ). In these studies, age groups varied between one and eight years, matching the present findings. In contrast, the maximum theoretical length (L ∞ = 771.68 mm) was lower and the growth rate (k = 0.65 year 1 ) was higher than the other estimates. Differences in the results might be due to factors such as the methods applied, size structure with a predominance of juveniles in previous studies, time and area, once the analysis herein applied was properly conducted.
The Powell-Wetherall method is more accurate to estimate L ∞ in species that present prolonged spawning and recruitment, a trend that increases the individual variability of growth; in this situation, SLCA method is more accurate for estimating k values (Isaac, 1990). These features apply to S. brasiliensis, and their reproductive biology sustains the present findings regarding age and growth. In the modal progression analysis (SLCA), a new cohort appeared in January, matching the spawning peak identified here. Different cohorts were identified, despite some overlap in the interval of 400-600 mm FL (modal progression in Supplementary Material). Other elements can affect growth parameter estimation via modal progression analysis. Some species present schools structured by size, not by age (Murie et al., 2012). This probably does not apply to the present samples because, in addition to the absence of larger specimens of S. brasiliensis in other fisheries in the area, schools are more typical for juveniles (Maia et al., 2005;, and were not numerous in the present study where adults predominated. Regarding the environmental conditions affecting fish growth, considering the heterogeneity of the inner shelf of the Paraná coast (e.g., water mass, estuaries, and temperatures), it is reasonable to hypothesize that there was growth adaptation for local thermal conditions, resulting in individuals that grow faster than in low latitudes (Yamahira and Conover, 2002). This could explain the higher growth rate value compared to the northeastern Brazil estimates, a question that remains open for future studies.
Thus, the age structure and growth parameters of S. brasiliensis along the Paraná coast reflect its population structure, where it is smaller and grows faster than the stock in northeastern Brazil. Current data on age and growth are robust and suitable, and can reflect the high biological productivity and shelters of the Paraná coast, including its two estuaries (Lana and Bernardino, 2018), which are areas favorable for fish growth as well as spawning, nursery, and feeding. These population patterns have resemblance with the congeneric S. queenslandicus, a species that occurs in northern Australia in the same latitude as that of the Paraná coast whose patterns are similar to S. brasiliensis, an example that reinforces the Chaves et al. results obtained. Scomberomorus queenslandicus is relativelly small (L ∞ range = 628-651 mm), grows fast (k range = 0.59-0.71 year -1 ) and presents small displacements, with a number of stocks (Begg et al., 1997;Begg & Sellin, 1998).
Current findings and discussions attained the objectives and confirmed the hypothesis, i.e., along the Paraná coast S. brasiliensis has its own biological patterns in terms of size, reproductive biology, age, and growth, constituting a self-sustaining group for management purposes (a stock sensu Cadrin et al., 2014), which is not directly related to that from northeastern Brazil. Based on this, recommendations can be proposed and must be considered in future strategic management planning (Isaac et al., 2013). Juveniles are being preserved, considering their absence in the catches, as are the larger and older individuals, mainly females. A point that deserves attention is the predominance of individuals at one year of age and in first maturity at the landings. If there is a reduction in the resource availability, size reduction, earlier maturation, and other indicators of overfishing, it is recommended a legal-size range for catches, based on the maturity and age structure are provide (Chaves, 2012). Period restrictions of S. brasiliensis fishing would be desirable only if larger and older females become constant at landings during spawning periods. It is strongly recommended that all measures enforced emerge from participative management, involving all stakeholders, actors, and processes (Almeida et al., 2007;Mourão et al., 2014), considering the fishing complexity along the Paraná coast (Andriguetto-Filho et al., 2006). For non-English readers, a Portuguese version of this paragraph is available in the Supplementary Material.

CONClUsIONs
The importance of S. brasiliensis for the small-scale fishery along the Paraná coast is undeniable, and the present study provided relevant information regarding the population dynamic parameters of this species. The small-scale fishery accesses mainly "young adults", i.e., individuals between 400-and 650 mm FL, 1-2.5 years old, in the first maturity stage or just after this stage. Allied to the spawning period and area and growth parameters estimated, they constitute a first referential, standardizing the methods applied to monitor the species in the area. Future changes in these attributes could reliably indicate impacts due to fishing activity or other factors. These biological indicators are essential for proper management (McBride, 2014), highlighting that small-scale fishery is "our best hope for sustainable utilization of coastal resources" (Pauly, 2006).
Further studies focusing on the S. brasiliensis stock along the Paraná coast must expand the present analyses. These could comprise: (i) histological analysis of gonads and oocyte diameter concerning the gonad-length relationship, providing additional information regarding the maturation process (West, 1990;Lowerre-Barbieri et al., 2011); (ii) otolith analysis (and/or other calcified structures) to refine age and growth estimates (Vaz-dos-Santos, 2015); (iii) inspection of eggs and larvae in the area (Lowerre- Barbieri et al., 2017); and (iv) an accurate definition of stock limits and connectivity level among groups in the species distribution area (Cadrin et al., 2014