An osteometric approach to reconstruct the length and weight of Lutjanus argentiventris (Perciformes: Lujtanidae) for archaeological and ecological purposes

Lutjanus argentiventris presents a large intertropical distribution within the Eastern Pacific, which is as important to fisheries now as it was in the pre-Hispanic period. The purpose of this article is to present an allometric model that enables the size and weight of L. argentiventris to be predicted, using the isolated bones found in archaeological and paleontological contexts or the stomach contents of ichthyophagous species. A modern collection of L. argentiventris from Ecuador was used, composed of 37 individuals covering a wide range of sizes and weights. The total length (TL), standard length (SL), and total fresh weight (W) of each individual was gathered. The TL of the sample ranged between 210 and 760 mm, the SL between 164 and 627 mm and the W ranged between 123 and 6550 g. The most frequent bones (15) and otoliths were chosen and 39 measurements were taken. The total length-weight relationship was W = 6E-06 TL3.1513 with R2 = 0.997. In general, it was observed that the relationships between the TL and the bone measurements had a strong correlation (R2 > 0.95). The allometric model will be useful not only for archaeologists but also for biologists working on historical ecology.

Just as the weight increases with the size of the fish, bone size also increases with body size. The growth rate of each body part varies depending on species ontogeny and morphology (Teissier, 1948). In archaeology, fish body size and weight are used to study human diet, and to infer on fishing strategies and techniques, human exploitation and the overexploitation of fish faunas (e.g. Reitz et al., 1987;Lambrides, Weisler, 2015;Thieren, Van Neer, 2016;Prestes-Carneiro, Béarez, 2017;Lidour et al., 2018;Rurua et al., 2020). In particular, some aspects of fishing can be studied in depth: (1) changes in the geographic ranges of species, (2) reductions in their abundances, (3) signatures of trophic cascades and (4) marine fisheries trophic level changes (Erlandson, Rick, 2010).
On the other hand, Karachle, Stergiou (2012) summarize the importance of lengthweight models in three aspects of modern ecology studies: (1) use of length data as an estimation of biomass; (2) to ascertain the condition of the species; and (3) to compare the life history of different populations of the same species. In fisheries management, the weight and the size of fish are used to estimate population parameters, life history characteristics and to develop programs for the protection and management of the species (Castellanos-Galindo, Zapata-Padilla, 2019). This kind of information could be used to determine the minimum permissible lengths of capture and identification of suitable periods for a closed fishing season. The identification of age-classes and male to female ratios are relevant to evaluate the status of an exploited stock and to establish future harvest levels, and the relationship between fish-size and its life-history traits and habitats (Castellanos-Galindo, Zapata-Padilla, 2019; Froese, Pauly, 2019).
In modern fisheries, the concept of baseline is understood as the fish population that was present before human influence (Pauly, 1995). This author addresses the shifting baseline syndrome, but this can only be resolved by developing a pre-industrial baseline that extends beyond the origins of modern fishing, both artisanal and commercial (Froyd, Willis, 2008;Betts et al., 2011Betts et al., , 2014Barrett, 2019). Baselines should not assume static environments but rather dynamic systems (Rick, Lockwood, 2012). It is in this point where zooarchaeology and particularly ichthyoarchaeology can contribute with information to manage modern fisheries (Betts et al., 2011(Betts et al., , 2014Barrett, 2019). Fish size comparison between modern, historical and archaeological data could be used to regulate marine protected areas and to propose clear conservation objectives. For example, if archaeological data are used as baselines, new indicators could be proposed, 4/16 ni.bio.br | scielo.br/ni and compared over time. Similarly, reference levels of objectives, thresholds or limits could be developed to inform the management of marine resources and ecosystems (Schwerdtner-Máñez et al., 2014). At the same time, it could determine the absolute magnitude of the changes that can occur in a heavily exploited fish stock. Analysis of long-term trends in fish size can provide a key indicator of changes in ecological baselines (Betts et al., 2011(Betts et al., , 2014Barrett, 2019). Other contributions of the study of the archaeological fish size are to measure fluctuations in the aquatic environment and the intensity of exploitation (Betts et al., 2011(Betts et al., , 2014Barrett, 2019).
In this article, the attention will focus on the yellow snapper, L. argentiventris, which has a subtropical distribution, ranging in the Eastern Pacific from southern California to northern Peru, including the Galapagos Islands (Allen, 1985) ( Fig. 1). The species is found in coral and rocky reefs at a depth range of 3-60 m and also in estuaries and river mouths, being tolerant to freshwater. It is characterized by a pinkish red colour of the anterior part of the body, which becomes bright orange to yellow in its posterior part. The fins are mainly yellow or orange. The yellow snapper is an active predator, feeding mainly at night on fish, shrimp, crabs and mollusks (Allen, 1985). Individuals can form small aggregations during the day or shelter in caves. The species also form seasonal spawning aggregations, a trait that makes many species vulnerable to overfishing (Sala et al., 2003). The species has been recorded up to a TL of 760 mm and a maximum weight (W) of 6550 g (Béarez, 1996: 44). For Gorgona Island in Colombia, Rojas et al. (2004) reported that the average size at sexual maturity was 515 mm TL and that the length-weight relationships were not significantly different between sexes. In the case of the central Mexican Pacific, the size range at sexual maturity was 260-330 mm for females and 240-320 mm for males (Lucano-Ramírez et al., 2014).
Our purpose is to present an allometric model that enables the length and weight of Lutjanus argentiventris to be predicted, using the isolated bones from archaeological and paleontological contexts or the stomach contents of ichthyophagous species. Lengthweight relationships for L. argentiventris can be found for Mexico (González et al., 2004;Aburto-Oropeza et al., 2009;García-Contreras et al., 2009;Piñón et al., 2009;Velázquez-Velázquez et al., 2009), Panama (Bonilla-Gómez et al., 2014 and Colombia (Rojas et al., 2004) but not for Ecuador. As there is no information available for the southernmost part of the range of L. argentiventris, it is useful to check whether this relationship is similar or different from those already known in more northern countries. Rojas et al. (2004) reported that the species is moderately slow growing, appears to be long-lived and has a low natural mortality rate, making it easily vulnerable to overfishing. It is therefore important to build osteometric models that could be used for in-depth long-term studies of L. argentiventris populations, with the aim of proposing management strategies.

MATERIAL AND METHODS
All the skeletons came from the fish collection of the Muséum national d'histoire naturelle in Paris. The modern collection of Lutjanus argentiventris is composed of 37 individuals covering a wide range of sizes and weights: 36 are from Ecuador and one is from Panama. The TL of the sample ranged between 210 and 760 mm, and the SL between 164 and 627 mm. The W ranged between 123 and 6550 g. The fish from 5/16 ni.bio.br | scielo.br/ni Ecuador (MNHN-ICOS-1776 to -1811) were sampled between 1992 and 1998 in the vicinity of Puerto López (Fig. 1) mostly over rocky reefs, and using harpoons. The specimen from Panama (MNHN-ICOS-1812) was sampled at Isla del Rey (Pearl Island Archipelago) in 2000. All individuals have complete information about their total length (TL) and standard length (SL), which were recorded in millimeters (mm), and their total fresh weight (W) in grams (g).
Specimens from other Lutjanus species were also used, such as: L. novemfasciatus (n = 3); L. colorado (n = 1); L. peru (n = 1); L. guttatus (n = 4) and L. argentimaculatus (n = 1). These specimens were also collected from the same locations and at the same time period as L. argentiventris, except for the last one which comes from Kenya (Indian Ocean). For this study, all the specimens were used, including the Panamanian specimen and the other species individuals, to test the model. We included other species because in the archaeological record it is sometimes very difficult to arrive at a species level Image represents a 645 mm TL individual).
6/16 ni.bio.br | scielo.br/ni determination, at times we only succeed to determine the genus, which is quite often the case within the genus Lutjanus (e.g. Guzmán, 2008).
Among the most frequently preserved bones in the archaeological archives, 15 were selected, 39 measurements were taken, and otoliths were included (Tab. 1, Fig.  2). Measuring points were chosen in such a way that they had a good probability of being found among archaeological remains; for this reason, the slender and fragile parts were discarded and the robust parts were preferred (Desse, 1984). The measurements were taken using a digital caliper with a precision of two decimal points. Following convention, the left side bones were measured. However, in the case of the otoliths, both sagittae (left and right) were measured and a two-sample (paired samples) t-test was performed in order to identify eventual differences between sides (the null hypothesis being that the means of two populations are equal). An allometric regression model was employed to determine the length-length and length-weight relationships for the L. argentiventris collection. This model assumes that the growth of each body part is relative to its total body length and weight, but with distinct growth rates (Teissier, 1948;Reitz et al., 1987;Marean et al., 2001). The lengthweight relationship is represented by a power function: Where "Y" is the total weight of the fish, "X" is the total length, "a" a constant and "b" the allometric coefficient. To create this model, we also used 11 more specimen data (TL, SL, W) measured in Ecuador from fresh fishes that could not be preserved. The total sample was 48 (37 collected and preserved fishes + 11 fresh fishes not preserved).
In the case of the length-length relationships the same function was used; however, "Y" is the total length, and "X" is the body part measurement. The quality of the relationship is given by the coefficient of determination (R 2 ). The best fitted measurements allowed us to reliably estimate the length and the weight of the fish from its isolated bones. Desse et al. (1989) proposed to establish Global Rachidian Profiles (GRP) to identify the position of the vertebrae along the spine. This approach is really helpful in archaeological cases where the vertebrae are the most common element. At the same time, by knowing the height of an archaeological vertebra it is possible to estimate the size of an individual. To construct the GRP of L. argentiventris, four individuals with different sizes were selected, and measurements were taken on the caudal (diameters M1 and M2) and ventral faces (M3) of the vertebrae (Tab. 1, Fig. 2).
In general, it was observed that the relationships had a strong correlation (R² > 0.95) (see Tab. 1, Fig. 2 for bone measurements). The measurements relating to the maximal length of the element were well correlated with the TL. However, other measurements, based on small parts of the bones, which are the most frequently preserved, were also well correlated (see Fig. 4 for other Lutjanus species and the Panamanian specimen).  Regarding the GRP, four M2 profiles from four individuals are represented in Fig.  5A, and profiles for the M1, M2 and M3 of a single individual are represented in Fig.  5B. In both figures, two main zones could be distinguished: the anterior zone from 8/16 ni.bio.br | scielo.br/ni vertebrae 1 to 7, and the posterior zone from vertebrae 8 to 24. The anterior zone is more heterogeneous while the posterior zone is more homogeneous.
In the case of the otoliths, it was observed that the exponent of the allometric equation was superior to 1 (Tab. 2). This implies that they grow more slowly than the rest of the body. There were no significant differences between the length, height and weight of the right and left otoliths (Tab. 3).
Some degree of similarity was observed between the "b" values of the length-weight relationship obtained in this study and those from previous studies from Mexico, Panama and Colombia (Tab. 4). These results indicate that Lutjanus argentiventris has a similar, often isometric, growth all along its range.   The tests made using other species of the same genera (Fig. 4) showed that the model could be used, at least in some instances, at genus level without much distortion. This is an important issue when dealing with Lutjanus species from other geographic areas. With regards the GRP profiles, the similar M2 values of the vertebrae of the posterior zone (Fig. 5) allowed us to use their measurement without knowing their exact rank in the rachis, which is often difficult to determine with isolated caudal vertebrae.
The otoliths on both sides can be used to estimate the size of the fish (Tab. 3).

DISCUSSION
The relationships between bone measurements and body-length were robust (Tab. 2), which makes us confident that they can be used with archaeological samples. Also, it is interesting to point out that the model also works with small fish, such as the 109 mm TL Panamanian specimen (Fig. 4). Such applications have already been carried out and have shown their interest. This is notably the case of recent studies in the fresh waters of South America (Peña-León, 2011, 2013Prestes-Carneiro et al., 2019) or in the marine waters of the Persian Gulf (Yeomans, 2015;Lidour et al., 2018). However, this kind of study is not frequent in Latin American archaeological literature of despite its great informative potential. The study of the body length of the archaeological L. argentiventris could provide information on where the specimens were captured, depending on their size, and on ancient fishing techniques. The early life stages of L. argentiventris are found in mangroves, estuaries or shallow bays, which provide them with food and protection from large predators; adults then move to the outer rocky reefs where they continue to grow (Rojas et al., 2004). With this in mind, small-sized archaeological fish are expected to have been captured in mangroves, or at least close inshore, while larger fish came from deeper waters. The proportion of   juveniles to adults can also provide information about fishing grounds and/or the health of nurseries and, beyond that, mangroves. However, these inferences should be accepted with caution because different populations of the same species may present different life history characteristics (e.g. Rojas et al., 2004, Lucano-Ramírez et al., 2014, and direct interpolation with the past could be risky. Ancient size data obtained from  archaeological material could be helpful in modern ecological studies and fisheries management, given that such information could provide insight into: (1) the long-term effects of human activities on fisheries and aquatic ecosystems; (2) the acceleration and geographical extension of these effects over time; (3) the distribution and ecology of past fish populations (Erlandson, Rick, 2010). The allometric model presented here can be used to predict the size and weight, not only of L. argentiventris, but also of its congeners, using isolated bones found in archaeological and paleontological contexts or the stomach contents of piscivorous species. This model could be useful not only for archaeologists but also for biologists working in historical ecology.