Length-weight relationship of 73 fish species caught in the southeastern inner continental shelf region of Brazil

. The a and b parameters of the length-weight relationship (LWR) of the form W = aL b were estimated for 71 species of Actinopterygii and 2 Elasmobranchii, caught in the coastal region and inner shelf of southeastern Brazil. Estimates of b varied from 2.151 to 3.882. For the first time LWR for eight fish species is reported. Significant differences were observed among b values obtained for the same species caught in different ecosystems. Moreover, significant different results for b were observed among species caught in different ecosystems and between sexes of 12 species. Therefore, in order to obtain a reliable biomass estimate it is necessary to choose LWR data close in time and region with estimates for each sex.


INTRODUCTION
Fish population biomass estimates, or of an individual fish of the ichthyofauna, depends on the measurement of individual weight of these organisms.However, in most cases, weighing each organism individually under field conditions is a very difficult task and not always possible (Kimmerer et al., 2005).
The lenght-weight relationship (LWR) estimates are used to calculate the weight of the individual from length frequency data, allowing spatial and temporal comparisons among populations and species (Salles & Feitosa, 2000;Vianna et al., 2004).Therefore, the LWR may be considered an essential tool in the studies of fish stock assessment and management of fisheries resources (Haimovici & Velasco, 2000a;Ilkyaz et al., 2008;Rodriguez-Romero et al., 2009;Rojas-Herrera, 2009).
On the other hand, the historical review carried out by Froese (2006) shows that the intra-specific variance of LWR may be quite large and that users should follow some recommendations when using this relationship.Among the problems that may contribute to increase the variability of LWR, one can mention: the narrow range of body lengths in the sample, the use of non-random samples and of one specific size gear to select specimens and the LWR calculation with no regard of differences between the sexes.Despite these recommendations, the application of LWR for individuals of the same size class for the same species still persists (Muto et al., 2000).According to Kimmerer et al. (2005), it is highly recommended to use the LWR relationship with data collected in the same area and close to time of the study to minimize bias in the weight estimate.
LWR data are available in the literature for the majority of fish species from Europe and North America.Although publications regarding the LWR for marine tropical species and, in particular, in the Brazilian coast have increased (Araújo et al., 1998;Bernardes & Rossi-Wongtschowski, 2000;Haimovici & Velasco, 2000a, 2000b;Muto et al., 2000;Sales & Feitosa, 2000;Frota et al., 2004;Santos et al., 2004;Vianna et al., 2004;Giarrizo et al., 2006), these works are restricted to specific and isolated regions with no comparison among the data.
The Baixada Santista region, located in the central area of São Paulo state, southeastern Brazil, is characterized by intense industrial and port activity and human occupation, and is considered one of the most impacted areas of Brazil (Lamparelli et al., 2001).This coastal region features a diversity of ecosystems such as the estuary, the Santos Bay, and three main channels, namely Santos, Bertioga and São Vicente, connecting the estuary with the bay (Fig. 1).Two variables are mainly responsible for the changes in the ichthyofauna of the region: the shrimp fishing with artisanal fishing trawlers (Paiva Filho & Schmiegelow, 1986;Ávila da Silva et al., 2005), with by-catch composed mainly of young sciaenids; and the temporal variability of the occurrence of water mass in the inner continental shelf (Rossi-Wongtschowski & Paes, 1993;Castro & Miranda, 1998).
This work aims at describing the LWR of 73 fish species collected in three different coastal ecosystems of southern Brazil, that is, one bay, one channel and the inner continental shelf.Moreover, for the specimens observed in two or three ecosystems, a comparison of the LWR parameter estimates will be carried out following some of the recommendations proposed by Froese (2006).
Although samplings in the bay as well as in the channel were carried out only with one fishing gear, the size classes were found to be representative according to the frequency of distribution of the length classes.Larvae or juveniles were not considered in the analysis as to minimize errors in the estimate.No subsamples were carried out and all specimens were examined.
Each specimen of the ichthyofauna was identified, measured (total length-TL in cm) and weighed (total weight-TW in g).The specimens TL and TW pairs that had at least 14 individuals were plotted to identify and exclude possible outliers.The LWR was calculated using power regression W = aL b (Haimovici & Velasco, 2000a, 2000b), where a is the intercept and b the slope, W the weight and L the length.The degree of association between W and L was measured through the coefficient of determination (R 2 ).A Student's ttest (H 0 : b = 3) with ± 95% (α = 0.05) confidence level was carried out in order to verify if b values estimates are significantly different from the isometric value (b = 3) (Zar, 1998).The estimated values of the same species from different ecosystems were tested in order to check if there were significant differences among them.

RESULTS
The number of individuals captured according to species varied from 14 to 20,123.The LWR of 73 species belonging to 32 families, totaling 47,373 individuals, were estimated (Table 1).The families, the species and their descriptors, the sampling locations, the sample sizes (n), the length and weight variations, length median (Md), the a and b parameters of LWR, the lower and upper confidence limit (LCL-UCL) of the intercepts and slopes, and the coefficient of determination (R 2 ) are also shown in the Table 1.
The median lengths values of the species that have occurred in more than one environment were bigger in the inner continental shelf and smaller in Bertioga Channel or in Santos Bay.On the other hand, specimens were found to be smaller in the channel when the median length values of the species were compared with those captured in the bay.
All LWR were highly significant with the coefficient of determination (R 2 ) varying from 0.747 to 0.999 (P < 0.01).The b values estimates varied from 2.151 for Chilomycterus spinosus to 3.882 for Anchoviella lepidentostole, both captured in the inner continental shelf, but most of the b values estimated ranged from 2.6 and 3.5.The LWR b coefficient distribution exhibited symmetry (0.418) and kurtosis (0.781) (Fig. 2).
Regarding the types of growth (positive/negative allometry or isometry), it was observed that the members of the same family presented similar patterns.For instance, Carangidae exhibited a higher number of species with negative-allometric growth (b < 3), while Achiridae, Ariidae, Haemulidae, Paralich-thyidae, Sciaenidae and Serranidae were characterized with more species with positive-allometric growth (b > 3).Two species of Pristigasteridae, although captured in different environments with different abundance values, exhibited an isometric growth (b = 3), that is, the individuals keep the same body form and proportional growth in all size classes.
The estimated b values were found to be significantly different from b = 3 in 16 out of 30 species observed in the continental shelf.For two species that were exclusively observed in Bertioga channel, b was found to be significantly different in one of the species.In addition, b was found to be significantly different from b = 3 in eight out of 12 species exclusively observed in Santos Bay.The LWR b values estimates for Lagocephalus laevigatus, Micropogonias furnieri and Pellona harroweri were not significantly different from 3. Nevertheless, the b Table 1.Sample characteristics (local, number, minimum, maximum and median length, minimum and maximum weight) and estimated parameters of the length-weight relationship (a, b, lower confidence limit, upper confidence limit and coefficient of determination) for 73 fish species caught in the tropical southeastern inner continental shelf and estuarine region of Brazil.Bold numbers indicate significant differences from b = 3. LCL: lower confidence limit, UCL: upper confidence limit, B: Bay, C: Channel, S: Shelf.2).Among five species, four belonged to the Sciaenidae family (Micropogonias furnieri, Stellifer brasiliensis, Stellifer stellifer and Stellifer sp.) and Stephanolepis hispidus.For these species the LWR estimates were obtained for each sex.

DISCUSSION
General data of LWR of 73 actinopterygian species were estimated for a tropical region of southwestern Atlantic according to recommendations of Froese (2006).From these 73 species, information about the LWR parameters for 23 species is not available in the FishBase data base (Froese & Pauly, 2004).
Smaller median lengths values of the species occurred in Bertioga Channel or in Santos Bay in comparison to the occurrences in the inner shelf.This result may be related to the fact that many fish species use the estuarine regions as a spawning and growth areas, remaining in these regions in the early stage of their life cycle (Fuiman & Werner, 2002).
Those extreme b values estimated for Chilomycterus spinosus (2.151) and for Anchoviella lepidentostole (3.882) account for the species body form, that is, species with height bigger or equal for a given length and species with low height relative to length.In this study no species presented long caudal fins that could interfere in the b values, as shown by Ilkyaz et al. (2008).
Carangidae exhibited a higher number of species with negative-allometric growth (b < 3), while Achiridae, Ariidae, Haemulidae, Paralichthyidae, Sciaenidae and Serranidae were characterized with more species with positive-allometric growth (b > 3).Two species of Pristigasteridae, although captured in different environments with different abundance values, exhibited an isometric growth (b = 3), that is, the individuals keep the same body form and proportional growth in all size classes.Similar growth patterns for Carangidae and Ariidae species were obtained by Giarrizzo et al. (2006) in the northeastern Brazilian estuary.
The observed intra-specific variations found in b values justify the use of LWR obtained in the same area and close to the time of sampling (Kimmerer et al., 2005).Differences in b values for some species when compared to other studies from other locations (Haimovici & Velasco, 2000b;Muto et al., 2000;Gomes & Araújo, 2004;Giarrizzo et al., 2006) can be explained by several factors, such as variations in the parameters of hydrographic properties (e.g., temperature, salinity), food availability, number of specimens and variation in the length of the individuals collected from the sampled populations, or to procedural and statistical reasons (Pauly, 1984;Weatherley & Gill, 1987;Kimmerer et al., 2005), or any other variable that can affect the body weight indicates a difference in growth or condition.
The hydrographic pattern of the southeastern continental shelf region of Brazil comprises three water masses: the Tropical Water (TW) (T > 24, S), the Coastal Water (CW) and South Atlantic Central Water (SACW) (T < 18, S > 36.4) (Castro & Miranda, 1998).The SACW is the water mass responsible for carrying nutrients to the pelagic system mainly in summer (Gaeta & Brandini, 2006).Therefore, the penetration intensity of the SACW and the deep thermal front location may be responsible for the occurrence of higher b values in this period.As the b exponent corresponds to the allometric condition factor, the bigger the value the better the conditions of the individuals.Moreover, these values are also influenced by the degree of repletion of the digestive tracts of the specimens.
The intercept estimates may also be affected by individual features or processes such as reproduction, sex, size, and even the sample size (Haimovici & Velasco, 2000b;Frota et al., 2004;Vianna et al., 2004).
This study reinforces data presented by Froese (2006), in that variations among sex, size classes, seasons and sites should be considered in the studies where weight data are needed to provide fish biomass estimates.

Figure 1 .
Figure 1.Map of the southwestern Atlantic showing sampling areas of Brazil: Santos Bay, Bertioga Channel and inner shelf.Black dots indicate sampling stations.

Figure 2 .
Figure 2. Distribution of b values estimated for 73 species collected in the tropical southeastern inner continental.