Length-weight relationship of fishes from an estuary of Abrolhos Bank, Brazil

Abstract: Aim We investigate the length-weight relationship estimates of seventeen species caught using an artisanal purse seine in the Abrolhos Bank, a tropical estuarine complex in eastern Brazil. Methods From February 2012 to November 2013, fish were collected monthly using an artisanal small purse seine with a total of 84 fish landings. The fish were captured in mangrove margins during high tide and retrieved after six hours at depths ranging from 1.2 to 3 meters. Results A total of 4433 fish specimens from 17 species and nine families were sampled. The coefficient of determination ranged from 0.904 for Centropomus parallelus to 0.987 for Lutjanus cyanopterus. Species presented allometric growing, with Caranx latus, Lutjanus cyanopterus and M. curema exhibing negative allometric while all the other species presented positive allometric growing. We present first data in Brazil to L. cyanopterus and first data in the literature to Lutjanus alexandrei. Conclusions Our results provide novel data of biological attributes for 17 species. By understanding the length-weight relationships and growth patterns of these species, data at stock level may subside proper management initiatives such as fishing restrictions in fishing sites or seasons and mesh size limits.

region, encompassing a large mid to outer shelf hard bottom domain with reefs and rhodolith beds (~20,900 km2) (Leão et al., 2003;Moura et al., 2013). Moreover, it is an ancient and important fishing area in Brazil (Cordel, 2006;Fogliarini et al., 2022), with fish being the primary income source of thousands of families. Fisheries in estuarine environments support the livelihood of hundreds of families, providing animal protein and generating income.

Study area and sampling
The study was conducted at the Caravelas-Nova Viçosa estuarine complex, located on the extreme south coast of the state of Bahia and mid portion of Abrolhos Bank, eastern Brazil (17° 38' 08.89" S; 39°15'41.87" W; Figure 1). The Cassurubá Extractive Reserve has an area of 100.767 ha in total, being created in 2009, aiming to assign exclusive fishing rights to local fishers and guarantee the maintenance of fish stocks at sustainable fishing levels (Nobre & Schiavetti, 2013).
Fishes were collected monthly from February 2012 to November 2013. We sampled the fish catches during 84 fish landings of a small-scale fisher using an artisanal small purse seine fishing named "camboa" [see details in Giglio & Freitas (2013)]. The net contained on the purse net had 400 meters in length, 3 meters in height, and 40 millimeters in mesh size. Specimens were entangled in the mangrove margins during the high tide and collected after six hours in the low tide, at depths of 1.2 to 3 meters.

Introduction
Biometric data like length-weight relationship (LWR) is basic information in fishery biology (Froese, 2006). These parameters are essential for fisheries, being used to calculate the weight of the individual from length-frequency data, estimation of biomass, growth pattern, general health, habitat conditions, fish fatness, morphological characteristic of the fish and fish condition factor in studies where weighing the fish is not possible (Ritcher et al., 2000;Froese, 2006;). For instance, LWR data is commonly used to calculate biomass of fish to analyze fish stock or verifying the fish density. The examination of the length-weight data is basic in fisheries research, providing information that informs stock assessments and aid in making informed decisions for sustainable exploitation.
Although there were LWR studies for many places along the Brazilian coast (Frota et al., 2004;Joyeux et al., 2009), there needs to be more data on LWR for fish stocks caught in the estuarine environments of eastern Brazil. Obtaining LWR data from local fish stocks, instead of from other stocks, is important for informing local management as it ensures that strategies are tailored to the specific characteristics and dynamics of the local fish populations, thereby increasing the accuracy and effectiveness of harvest regulations (Froese, 2006). Herein, we investigated the LWR of 17 fish species caught in an estuary off the Abrolhos Bank. The Abrolhos Bank extends ~ 200 km offshore and is Southwestern Atlantic's most biodiverse After the collection, individuals from each species were immediately photographed and identified with the use of keys and descriptions provided by Cervigón et al. (1992), Carvalho-Filho (1999), and Nelson (2006).

Statistical analyses
Specimens were individually measured in Total Length (TL) to the nearest millimeter and weighted through Total Weight (TW) at a precision of 0.01g. All measurements were conducted immediately after the fishing in the field. The length-weight relationship (TW = a TL b ) was determined for all species that had sampled sizes ≥ 13 individuals. The data check for outliers was the determination of the coefficient lower than 0.95 (Barnett & Lewis, 1994). Parameters of the growth model TW = aTL b were estimated by least squares linear regression on log10 transformed data (Froese, 2006), where a is the intercept of the regression, and b is the allometric coefficient. The degree of association between variables was calculated by the determination coefficient (r 2 ) and confidence interval (95%) of a and b were calculated. The type of growth was determined through a Student t-test where H0: b = 3 (isometric growth) and H1: b ≠ 3 (allometric growth) (Zar, 2010). Metric relationships of all species were plotted using the R software v. 4.1.2 (R Core Team, 2019).

Results
We analyzed 4433 fish specimens belonging to 17 species and nine families. Gerreidae and Centropomidae had higher numbers of individuals caught, representing 45% and 24% of the total catches. The number of individuals varied from 13 for green moray, Gymnothorax funebris Ranzani (1839)     Three species presented positive allometric growth (b > 3): C. latus, L. cyanopterus and M. curema while all others presented negative allometric growth (b < 3) (Table 1).

Discussion
Our result provides an adequate estimation of the LWR according to the guidelines for data collection and analysis of length-weight relationships described by Froese (2006). The calculated b values of the regression for all species are within the acceptable range of ~2.5-3.5 (Froese, 2006). Variations in length-weight relationship parameters may be related to multiple environmental, biological and fishing conditions such as habitat, season, sex, maturation, growth phase, temperature, salinity, food availability and fishing gear (Froese, 2006;Hossain et al., 2019). However, these characteristics were not considered in our study.
This study provide novel data on LWR for fishes in an estuary from the most biodiverse reef complex in south Atlantic, the Abrolhos Bank. We provided the first of length-weight relationship published for Brazil to the Cubera Snapper, Lutjanus cyanopterus, and Brazilian Snapper, L. alexandrei. Such species are commercially important and data from local stocks are basic to understanding specific characteristics and dynamics of the local fish populations. This local level data informing proper management initiatives such as fishing gear of mesh size restrictions using accurate biological attributes information. Lutjanus cyanopterus is listed as endangered (EN), being overexploited since the 2000s, with no sign of population recovery (Motta et al., 2022). For Brazilian Snapper L. alexandrei we also provide the first reference available in the literature for LWR. Such species was described in 2007 (Moura & Lindeman, 2007), and show few biological data available.
Fishes presented allometric growth, and most species had negative allometric growth which suggests that the weight of the fish increases at a slower rate compared to its length. However, it is important to acknowledge that our study did not account for potential variations in growth patterns between sexes and different life phases, highlighting the need for further investigation to understand these factors' influence on the length-weight relationship in fishes. For instance, for Ocyurus chrysurus in Mexican waters, while young male and female individuals presented negative allometry, adult females presented an isometric pattern (Renán et al., 2015). Such a pattern may be related to gonadal development since females need more energy for gonadal maturation while males have smaller gonads and invest less energy in somatic growth (Lester et al., 2004). In addition, we have a small sample size (less than 30 individuals) to six species which need more samples to inform accurately the biological attributes.
This study provides data on the length-weight relationship and growth mode for 17 species. The biological data presented in this study provided basic data on the biological aspects of commercially important fishes. This can be a useful insight for fisheries management such as fishing gear and mesh size restrictions, especially in Cassurubá estuary who fish stocks are declining.