Biometric relationships between body size and otolith size in 15 demersal marine fish species from the northern Brazilian coast

The relationships between fish size and sagitta otolith measurements were calculated for the first time for 15 species belonging to six families from the northern Brazilian coast. A total of 220 fish were sampled from the bycatch landed by the bottom-trawl industrial shrimp-fishing fleet between August and September 2016. All species had strong relationships between otolith measurements and fish total length with the coefficient of determination (r2) ranging between 0.71 and 0.99. The variable most strongly related to fish total length was found to be the sagittal otolith length (OL) with 98% of the variability. These relationships are a useful tool to estimate length and mass of preyed fish from otoliths found in stomach contents of marine predators.


INTRODUCTION
Otoliths are structures composed mainly of calcium carbonate, located in the inner ear of Osteichthyes, which have body balancing and hearing as main functions (Campana 2004). These structures are arranged in pairs, called sagitta, asteriscus, and lapillus in bony fish, and vary widely in size and shape among species (Campana 2004;Popper et al. 2005). Due to its largest size in the majority of bone fishes, sagittae otoliths are the most suitable for systematic and ecological studies, for taxon identification, age estimation, and life history tracking (Harvey et al. 2000;De La Cruz-Agüero et al. 2016;Assis et al. 2018). Their nondigestible calcified structure has allowed them to be widely used to identify fishes ingested by different predators such as aquatic mammals, seabirds and fishes (Battaglia et al. 2010;Tuset et al. 2010). Furthermore, relationships between fish size and otolith measures are useful to elucidate the feeding behavior of piscivorous fauna, providing subsidies for the management of these species (De Pierrepont et al. 2005;Lombarte et al. 2006;Battaglia et al. 2010).
Studies on otoliths in marine fish from the Western South Atlantic are scarce (Waessle et al. 2003;Assis et al. VOL. 49(4) 2019: 299 -306 ACTA AMAZONICA 2018; Souza et al. 2019). The high nutrient and sediment load from the Amazon River, near the Northern Coast of Brazil favors the occurrence of abundant fishery stocks, mainly shrimp (Penaeidae) and several fish species (Isaac and Braga 1999;Marceniuk et al. 2019). The ichthyofauna is functionally important as an intermediate trophic level for many consumers, however, its importance is not well understood (Barletta et al. 2010).
The present study aimed to determine the relationship between fish size (i.e. length and weight) and sagittae otolith measurements (i.e. length, width, and weight) for the 15 most abundant demersal species captured along the northern Brazilian coast.

MATERIAL AND METHODS
Fish were captured between August and September 2016 in an area characterized by the estuarization of inshore waters, due to the proximity to the Amazonas River (5°02'21.6"N, 47°49'33.9"W; 0°51'02.0"N, 47°50'30.0"W northern and southern limits of the sampling area, respectively; Figure 1), and is inserted in the world's second largest mangrove (~700 000 ha), which is an important fishery area (Isaac and Braga 1999;Giarrizzo and Krumne 2008).
Samples were randomly collected from the bottom trawl of industrial shrimp trawlers using a 30 x 21 mm mesh bottom trawl of 22.4 m length towed at velocity of ~2.5 knots at 35 -49 m depth. Bycatch were taken to the laboratory and kept frozen until processing. Sampled fish were identified to species level, and measured (standard length, SL, and total length, TL, precision 0.01 cm) and weighed for total body weight (BW, 0.01 g). Sagittae otoliths were removed, cleaned and stored dry in coded microtubes. Each otolith was weighed (WO, 0.0001 g) using an analytical balance, and measured for maximum length (OL, 0.001 cm), as the horizontal distance between the anterior and posterior tips of the sagitta, and width (OW, 0.001 cm), as the greater distance between the dorsal and ventral margins of the otolith (Harvey et al. 2000;Battaglia et al. 2010).
Vouchers of each species were fixed in 10% formalin after processing, then preserved in 70% alcohol and deposited in the ichthyological collection of the Grupo de Ecologia Aquática (GEA) at Universidade Federal do Pará (UFPA). Potential differences between the dimensions of the right and left sagittae otoliths were tested using a paired Student's t-test per species (Park et al. 2018). The length-length relationship (LLR) was determined by the method of least squares to fit a simple linear regression model: TL = a + bSL. The length-weight relationship (LWR) was determined as: W = aSL b , and was fitted to the data using a linear regression of the log 10 -transformed data. Morphometric relationships between TL and otolith dimensions were calculated using linear (Y = a + bX) and linearizable (Y = aX b ) regression models, which best fit the data. When present, outliers were removed by graphical inspection of the plot before performing the regression analyses (Froese et al. 2011). The coefficient of determination (Pearson r-squared, r 2 ) was used as indicator of regression quality and to check if fish growth (b) was statistically different from isometric growth, a t-test (H 0 : b = 3) (Froese et al. 2011). A significance level of α < 0.05 (confidence level ± 95%) was routinely adopted.

RESULTS
The analyses were performed using 220 specimens from 15 species (see Figure 2 for otoliths) and six families. The most representative family was Sciaenidae with nine species, followed by Haemulidae, with two species, and the remaining four families, with only one species each (Table  1). Body weight ranged between 6.7 to 911.1 g, SL between 7.1 to 69.5 cm, and TL from 8.9 to 72.1 cm. Paired t-tests did not detect differences between left and right sagittae otoliths for OL, OW, and WO (p > 0.05 for all species). Hence, all further analyses were standardized by using only the left otolith measures.
Differences between the b values estimated by the different regression models were species specific. However, for species of the same family with similar body shape (e.g. Sciaenidae and Haemulidae), values were similar ( Figure 3). Length-weight relationships (LWR) were highly significant (p < 0.001) only for six species: Ctenosciaena gracilicirrhus, Macrodon ancylodon, Menticirrhus americanus (all Sciaenidae), Haemulon steindachneri (Haemulidae),

DISCUSSION
Body size and mass relationships are important tools for the functional understanding of a species at specific locations (Froese et al. 2011). Generally the length-weight relationships (LWRs) are used for converting lengths into fish mass and vice versa (Froese 2006;Froese et al. 2011), and length-length relationships (LLRs) are used to convert one length into another (e.g. standard length to total length). Additionally, assuming that otolith size is closely correlated to fish size, and its shape is species specific (Campana 2004), it is suggested that otolith analysis is a feasible and reliable method to identify fish species and to estimate fish size and weight (Battaglia et al. 2010;Park et al. 2018). Froese (2006) suggests that the angular coefficient does not differ from isometry when b = 3. Accordingly our b values of the BW-TL relationship were isometric for sciaenids, which, in addition, had coefficients of determination (r 2 ) higher than 0.90 (see Figure 3). However, VOL. 49 (4)   ACTA AMAZONICA despite the strong biometric relationships derived from our data, our estimated parameters should be used with caution, as our small sample sizes (mainly those ≤ 10 for B. ronchus, P. harroweri, N. grandicassis, Trichiurus lepturus, and Paralonchurus brasiliensis) and a selective effect of the mesh size used by the shrimp trawlers may have caused the size distributions in our samples to be underrepresented. The lack of statistical differences between left and right sagitta indicates that otoliths on either body side are indistictively usable for fish-size estimations (Battaglia et al. 2010;Mehanna et al. 2016;Park et al. 2018;Yilmaz et al. 2015). The high coefficients of determination for the relationships between otolith measurements and fish size in all our species indicates that length or weight of fish can be reliably estimated from otoliths found in stomach contents of predators. Our values of b varied considerably among the species, owing to the variable size and shape of the sagittae among the species. Yet, at family level (e.g. Scianidae), the b values tended to negative allometry in most relationships, as species within families are relatively more similar in shape. Most studies providing relationships between otolith and fish size have used only the width and length of the otolith (Giménez et al. 2016;Assis et al. 2018;Park et al. 2018). Considering the high values of correlation in our analyses, the inclusion of otolith weight in our estimations contributed to strengthen the relationship models.
The relationship between otoliths and fish size was estimated for species from different regions around the

CONCLUSIONS
This study is a contribution to the knowledge about the relationships between otolith and fish size in 15 fish species from the northern Brazilian coast for the reliable estimation of species-specific fish length or weight from otolith size. Our results form a baseline for future studies on trophic ecology and fish distribution, and will enable a more accurate evaluation of length and/or biomass of demersal fishes consumed by predators.