Length-weight and length-length relationships for rockpool fishes on the Brazilian coast

Fifty-nine length-weight (LWR) and length-length (LLR) relationships were estimated for 18 fish species, belonging to 10 families. The fish specimens were captured in rockpools of 21 sites along a stretch of 4,900 km of the Brazilian coast, between latitudes 00° and 22°S, in 2012. This study represents the first reference available for five fish species (Gobiesox barbatulus, Bathygobius geminatus, Labrisomus nuchipinnis, Malacoctenus delalandii, Lutjanus alexandrei) in LLR and six (Gobiesox barbatulus, Bathygobius geminatus, Hypleurochilus fissicornis, Omobranchus punctatus, Entomacrodus vomerinus, Diplodus argenteus) in LWR.


Introduction
In most fishery studies length-weight relationship (LWR) equations have been extensively used to estimate the fish weight from length given the technical difficulties (e.g., bobbing motion of the boat) and the amount of time required to record weight in the field (Morato et al. 2001, Morey et al. 2003).However, the LWR of the same species could vary in space (e.g., habitats and regional variation), so the use of a single equation throughout a large geographical area could introduce a bias in the estimates of weight (Morato et al. 2001, Mendes et al. 2004, Joyeux et al. 2008).Therefore, obtaining accurate local LWR parameter estimates is an important factor in the assessment of fish stocks and to subsidize the ecosystem modelling (Vaz-dos-Santos & Gris 2016).Additionally, length-length relationship (LLR) is very important for fisheries management and for comparative studies of population growth (e.g., Moutopoulos & Stergiou 2002).In this study we report 59 LWR and LLR for 18 fish species caught in rockpools of 21 sites along a stretch of 4,900 km of the Brazilian coast, between latitudes 00° and 22°S.

Material and Methods
A Brazilian coastal sector between the Amazon estuary (0° of latitude) and Rio de Janeiro (22° S) was sampled between March and December 2012, in 21 rockpool sites spaced in average ~210 km apart (Figure 1).
The rockpool fish fauna was caught at low tide using anesthetic clove oil (40 ml from anesthetic dissolved in 1000 ml of ethanol) and small hand-nets (length 150 mm; mouth 101.6 mm and mesh 3 mm).The specimens were fixed in 10% formalin, preserved in 70% alcohol and identified at the lowest taxonomic level possible (Figueiredo & Menezes 1978, 1980a, 1980b, Menezes & Figueiredo 1985, Carvalho-Filho 1999, Carpenter 2002a, 2002b, Eschmeyer et al. 2016).Specimens were measured (nearest 0.01 cm standard length, SL and total length, TL) using digital slide calipers and weighed (nearest 0.01 g total weight, TW) using a digital balance.
The length-weight relationships (LWR) were calculated using the equation TW = aTL b .Data were log transformed into: log TW = log a + blog TL (plots were performed for visual inspection of outliers, with extremes being excluded from the regression analyses) where TW is weight in grams, TL is total length in centimeters, a is a constant, and b is the slope of the linear regression that sets the allometric growth (Froese 2006).Furthermore, length-length relationships (LLR) were estimated by the method of least squares to fit a simple linear regression model using the equation TL = a + bSL (Hossain et al. 2006).The association degree between variables (TW and TL for LWR and SL and TL for LLR), was measured by the coefficient of determination (r 2 ).In order to verify if b was significantly different from the isometric value (i.e., b = 3 for LWR), the one-tailed Student's t-test (H0: b = 3) with a confidence level of ± 95% (α = 0.05) was employed (Sokal & Rohlf 1987, Froese et al. 2011).

Results and Discussion
Overall, 4,299 specimens representing 18 different fish species belonging to 10 families were analyzed.The family Blenniidae were the most richness with four species, followed by Gobiidae and Pomacentridae (tree species each one), and Labrisomidae (two species).The five remaining families (Gobiesocidae, Carangidae, Gerreidae, Haemulidae, Sparidae and Lutjanidae) were represented by only one species.Sample size ranged from 9 specimens for Labrisomus nuchipinnis (Quoy & Gaimard, 1824) in Pirangi do Sul-RN (site 12), to 735 for Scartella cristata (Linnaeus, 1758) in Canoa Quebrada-CE (site 10).The inclusion of species with small sample size (< 20 individuals) is justified by using individuals with a spread in length broad enough to obtain the relationships (Froese 2006, Froese et al. 2011).
A total of 59 LLR and LWR were computed for all 18 fish species caught in one or more sampling sites (Table 1 and 2).All regressions were highly significant (p < 0.001), with the coefficient of determination r 2 ranging from 0.911 to 0.999.
The present study provides the first information on LLR and on LWR for five [Gobiesox barbatulus (Starks, 1913) 1 and Table 2), respectively.It also presents the LWR Table 1.Estimated parameters of length-length simple linear regression (LLR) to convert standard length (SL) to total length (TL) for 18 rockpool fish species in 21 sites along Brazilian coast.Conversions among length measurements are given in Table 1.The parameter b of the LLR ranged from 1.125 for Bathygobius geminatus from Castelhanos beach (site 20, Espírito Santo state), to 1.416 for Diplodus argenteus from Tartaruga beach (site 21, Rio de Janeiro state).The slope (b) of LWR ranged from 2.81 for Eucinostomus melanopterus (Bleeker, 1863) from Saco beach (site 15, Sergipe state), to 3.26 for Labrisomus nuchipinnis from Itapuã beach (site 17, Bahia state), thus within the expected range of 2.50-3.50, as suggested by Froese (2006).The calculated mean value of all 59 estimations of b (± SE) was 3.06 (± 0.09), thus indicating a tendency towards positive allometry, which is in agreement with the majority of fish species (Froese 2006).Concerning the type of growth, 39 estimations (66.1% of the overall 59 estimations species × sites) evidenced isometric growth (b = 3), 17 estimations (28.8%) showed positive allometry (b > 3), and three estimations (5.1%) negative allometry (Figure 2).The most represented families in terms of species richness did not show a consistent tendency in type of growth among species.

Family/Species
Almost 90% of all fish collected were juveniles of larger species or adults of small species.Samples of three species [i.e.Caranx latus (Agassiz, 1831), Diplodus argentus and Abdefduf saxatilis (Linnaeus, 1758)] were represented by small length ranges due to the nursery function of the sampled tidalpools.Therefore, LWRs biased by inclusion of small specimens, should be used with caution (Giarrizzo et al. 2006).As pointed out by Petrakis and Stergiou (1995), the application of these LWRs should be limited to the size ranges used to estimate the parameters.Geographical differences in type of growth were observed for nine fish species.Seven species presented isometry or positive allometry, depending on the geographic site sampled [Scartella cristata, Bathygobius geminatus, Labrisomus nuchipinnis, Malacoctenus delalandii (Valenciennes, 1836), Abudefduf saxatilis, Stegastes fuscus (Cuvier, 1830) and Stegaste variabilis (Castelnau, 1855)].One species presented isometry or negative allometry [Ctenogobius boleosoma (Jordan & Gilbert, 1882)] and the Bathygobius soporator species showed isometry and negative and positive allometry.The observed differences among localities could be explained by a number of factors including temperature, salinity, food availability, gonadal development, number of specimens, and the variations in the range of length of the sample populations (Pauly 1984, Weatherley & Gill 1987, Giarrizzo et al. 2006, Joyeux et al. 2008, Macieira & Joyeux 2008).
In conclusion, this study has provided baseline information on the LWR and LLR of rockpool fish fauna sampled along a wide coastal sector of Brazil.The results obtained from this study will be useful to fishery biologists to employ adequate estimations for specific geographic areas.

Figure 1 .
Figure 1.Geographic location of the 21 rockpools sites along the Brazilian coast.The names of locations are available in Table1.
information of Omobranchus punctatus(Valenciennes, 1836), an exotic fish species from Indo-Pacific region widely introduced in the Western Atlantic Coast (Lasso-Alcalá et al. 2011).

Figure 2 .
Figure 2. Frequency distribution of b values of 59 LWR estimations computed for 18 fish species caught in tidepool along the Brazilian coast.

Site/State Site Code n Regression parameters a b 95% CL of a 95% CL of b r 2
(Froese & Pauly 2016ns; CL, confidence limits; Species in bold have length-length relationships estimates included in fishBase database(Froese & Pauly 2016) and literature.

Table 2 .
Estimated parameters of length-weight relationships (LWR) for 18 fish species in 21 rockpool sites along Brazilian coast.TL. total length; TW. weight; CL.Confidence limits; Species in bold have length-weight relationships estimates included in FishBase database (Froese & Pauly 2016) and literature.