LENGTH – WEIGHT AND LENGTH – LENGTH RELATIONS , AND RELATIVE CONDITION FACTOR OF RED LIONFISH , PTEROIS VOLITANS ( ACTINOPTERYGII : SCORPAENIFORMES : SCORPAENIDAE ) , FROM TWO NATURAL PROTECTED AREAS IN THE MEXICAN CARIBBEAN

Background. Biological invasions are often listed among the main threats to the ecosystem and are considered drivers of biodiversity loss. The Indo-Pacifi c lionfi sh, Pterois volitans (Linnaeus, 1758) (hereafter lionfi sh), invaded the Atlantic Ocean where it threatens the stability of the marine ecosystem. It would be crucial to know its biological characteristics to understand how environmental parameters could affect its growth. It is also important to continue the earlier efforts of management and control. In this study, we described the L–W and L–L relations and the relative condition factor of lionfi sh in two natural protected areas in the southern coast of Quintana Roo, Mexico. Materials and methods. Lionfi sh were captured during 2012 and 2013 from the Reserva de la Biosfera Banco Chinchorro (RBBC) and the Parque Nacional Arrecifes de Xcalak (PNAX). The length–weight relation was calculated based on the equation W = aTLb. The relative condition factor was calculated through the relative weight. Results. A total of 817 lionfi sh were caught in the frames of this study. In this number, there were 449 individuals from the RBBC (282.1 ± 62.1 mm TL) and 368 from the PNAX (249.2 ± 77.6 mm TL). The L–W relation for lionfi sh from the RBBC was W = 0.0041 TL3.258 and that for the PNAX was W = 0.0049 TL3.191. There was a signifi cant difference between these relations (ANCOVA, F = 3.91; P = 0.0481). The growth type was positive allometric. The L–L relation was signifi cant. The relative condition factor differed between areas only in 2013, but a high value was determined in 2012. Conclusions. The L–W relations were different between locations (RBBC and PNAX) but no between years. The relative condition factor showed high values (>100) for both locations which may imply that lionfi sh is in good shape, in the studied location, due to environmental factors providing good food supply and because of the lack of predators. These results may be useful as a baseline to document the population dynamics of lionfi sh in the region.


INTRODUCTION
The Indo-Pacifi c red lionfi sh, Pterois volitans (Linnaeus, 1758) (thereafter lionfi sh), invaded the eastern coast of the Atlantic Ocean, the Caribbean Sea, the Gulf of Mexico (Schofi eld 2010), and also the Brazilian coast (Ferreira et al. 2015).Lionfi sh represents a threat to the biodiversity and stability of the marine ecosystems due to its high voracity (Morris and Akins 2009) causing reduction in the abundance of native fi sh and invertebrates (Albins and Hixon 2008, Côté et al. 2013, Ballew et al. 2016).In Mexico, lionfi sh was detected in the late 2009, both in the Mexican Caribbean and southern Gulf of Mexico (Aguilar-Perera and Tuz-Sulub 2010, Sabido-Itzá et al. 2012), where now it is considered as established (López-Gómez et al. 2014, Sabido-Itzá et al. 2016).Thus, it is imperative to know further its biology to understand the ecological effects due to its invasion in the marine ecosystem of the region.
The length-weight relation (L-W) is an important tool (Le Cren 1951, Giacalone et al. 2010) to estimate attributes of the population, such as: • The fi sh weight based on length; • Fish weight based on growth; • Biomass; and • The condition factor (Petrakis and Stergiou 1995, Gonçalves et al. 1997, Kimmerer et al. 2005, Froese 2006, Froese et al. 2011).
Length-length (L-L) relations are used for conversion between lengths (Klassen et al. 2014).The L-W relation may differ between individuals of the same species in regions, seasons and sex (Okgerman 2005, Froese 2006).While it is important to know this relation for either native species or species under population threat (Vega-Cendejas et al. 2012, Hossain et al. 2014), when an invasive species is established it is crucial to document this relation in order to detect temporal and spatial fl uctuations of the population in the invaded ecosystem.
This work aimed to calculate the L-W and L-L relations, and the relative condition factor, of lionfi sh in two natural protected areas off the southern coast of Quintana Roo, Mexico.

MATERIALS AND METHODS
Study area.The Reserva de la Biosfera Banco Chinchorro (RBBC) (18°47′-18°23′N, 87°14′-87°27′W) is a coral reef complex (144 360 ha) located at 30.8 km off the coast of Quintana Roo (Carricart-Ganivet and Beltrán-Torres 1998).The Parque Nacional Arrecifes de Xcalak (PNAX) (18º30′-18º11′N, 87°43′-87°50′W) (17 949 ha) is located along the southern coast of Quintana Roo, close to Belize (Anonymous 2004) (Fig. 1).Fieldwork.Lionfi sh were collected by local fi shermen and divers with spear guns from February through November 2012 and from January through May 2013.At laboratory, each fi sh was taxonomically identifi ed to species, according to Schultz (1986), measured in total length (TL) and standard length (SL) in mm, and weighed in g to total and eviscerated weight using an electronic scale.Data analysis.Size-frequency distributions were built based on intervals of 20 mm TL to compare the size distribution between localities using D max from Kolmogorov-Smirnov (K-S): where D max is the max imum cumulative difference from samples, F 1 is the proportion of values lesser or equal to x in the fi rst distribution, and F 2 is the proportion of values less or equal to x in the second distribution.
The L-W relation was calculated based on the equation where W is the total weight of fi sh, L is the total length in mm, a is the intercept, and b is the regression coeffi cient (slope) (Le Cren 1951, Froese 2006).The coeffi cients a and b were estimated by a lineal regression on logarithms: The 95% confi dent intervals of a and b, and the coeffi cient of determination (r 2 ) were also calculated.Outliers were addressed based on Froese (2006).The b value of each relation was evaluated with a Student's t-test to determine the difference to isometry (b = 3).The relation TL-SL was also estimated through a lineal regression.The slopes of the L-W relation were compared between years and area through analysis of covariance (ANCOVA).In order to estimate the relative condition factor between space and time, the relative weight (W r ) was used according to Froese (2006)

RESULTS
A total of 817 lionfi sh was captured, of which 449 were from the RBBC and 368 from the PNAX.For the RBBC, the fi sh length ranged between 100 and 395 mm TL (282.1 ± 62.1) and weight-between 9 and 845.7 g (363.9 ± 217.2), while for the PNAX the corresponding values were between 60 and 380 mm TL (249.2 ± 77.6) and 3 and 804 g (277.3 ± 198.1), respectively.The size distribution of the fi sh from RBBC showed a main modal group between 260 and 3340 mm TL, while that from the PNAX showed two peaks where the main was 240 and 280 mm and a second one reached 80 to 120 mm TL.There were signifi cant differences between size distributions from the RBBC showing larger sizes compared to those from the PNAX (K-S; D max = 0.18, P < 0.01) (Fig. 2).
The relative condition factor for lionfi sh in the RBBC ranged between 149.1 ± 19.4 in 2012 and 136.9 ± 16.9 in 2013 (t-test = 6.9, P < 0.01), while in the PNAX ranged

DISCUSSION
Size distributions of lionfi sh for both locations (RBBC and PNAX) mainly corresponded to reproductive capable adults (>189 mm TL) (Gardner et al. 2015).However, in the PNAX there was a modal group showing sizes representing juveniles (60-120 mm TL).Thus, it is probable that PNAX is a very important place for lionfi sh recruitment (Vásquez-Yeomans et al. 2011).In the PNAX, there was a change in modal groups into larger size classes from 80-160 mm TL in 2009-2011 (Sabido-Itzá et al. 2016) to 240-280 mm in 2012-2013.This may imply that lionfi sh population is experiencing a growth trend (Côté andMaljković 2010, Pusack et al. 2016).
The size of the largest lionfi sh collected in the Mexican Caribbean, specifi cally in the RBBC (395 mm TL), was relatively similar to that collected in the southern Gulf of Mexico (389 mm TL, Aguilar et al. 2013) and to that in the Cayman Islands (391 mm TL, Edwards et al. 2014).However, the largest lionfi sh size captured in the western Atlantic was 477 mm TL for Islamorada, Florida.
The L-W relations of lionfi sh from the Mexican Caribbean are described herewith for the fi rst time.These relations explain an allometric growth type for lionfi sh with some slight differences.These differences may be due to environmental factors in a given geographic location, reef health, and habitat type (Díaz-Pérez et al. 2016), but also to biotic factors such as differences in the native community and availability of potential prey (Gonzalez-Salas et al. 2003, García-Salgado et al. 2006).In general, the vast majority of b coeffi cients calculated for lionfi sh in different geographic areas show values greater than 3 (positive allometry), and only in two cases the coeffi cient b was lower than 3 (Table 3).
The relative condition factor for lionfi sh from the Mexican Caribbean differed between areas only in 2013, but a high value was determined in 2012.Values of relative condition factor lower than 100 indicate that fi sh is under low availability of food resources and high abundance of predators, while higher values indicate high abundance of prey and low predation (Froese 2006, Rypel andRichter 2008).In this case, lionfi sh from Mexican Caribbean with values higher than 100 imply a well-being of fi sh in both areas.This latter indicates that lionfi sh show a high rate of prey consumption in combination with a lack of predation for native fi shes (groupers and snappers) for its possible biological control (Côté and Maljković 2010, Green et al. 2011, Hackerott et al. 2013).
On its native reef, lionfi sh is relatively smaller compared to that on invaded reefs (Darling et al. 2011).Consequently, the invaded environment, in the Mexican Caribbean, is favourable for its growth.Our results suggest that the PNAX and the RBBC could offer a suitable habitat for the establishment of lionfi sh despite some of their population attributes (e.g., size distribution, condition factor and length-weight relation) may differ at close geographic proximity.This study provides suitable information useful as a baseline to delineate population dynamic models to assess the progression of the invasion of lionfi sh in the Mexican Caribbean.This latter is of particular importance for management practices, based on culling, to face the invasion.In fact, so far the RBBC and the PNAX are under culling program for lionfi sh with the collaboration of voluntary fi shermen.Such programs are expected to foster conservation efforts of these natural protected areas (Sabido-Itzá et al. 2016).In addition to continuing the culling program, it is recommended to conduct surveys to estimate lionfi sh density.Also studies on stomach content analysis are desirable in order to determine the possible impact of the lionfi sh invasion on the native fauna of the region.

ACKNOWLEGMENTS
The Comisión Nacional de Áreas Naturales Protegidas (CONANP), with the help of the personnel of the natural protected areas Reserva de la Biosfera Banco Chinchorro and Parque Nacional Arrecifes de Xcalak, provided logistic and fi nancial support.We thank local fi shermen who actively participated in lionfi sh removals from coral reefs.We thank Irving Chávez for helping in editing fi gures.

Fig 1 .
Fig 1. Location of the Natural Protected Areas, Parque Nacional Arrecifes de Xcalak and Reserva de la Biosfera Banco Chinchorro, on the southern Quintana Roo, México where W r is the relative weight, W and L are the weight and length of each fi sh, a m and b m are the mean values of a and b from the L-W relation of each location.The Student's t-test was used to compare W r between locations each year.

Table 1
Lineal relations (y = a + bx) between total length and weight of lionfi sh, Pterois volitans, in two natural protected areas in the Mexican Caribbean

Table 3
Mean total length and coeffi cients of the L-W relations estimated for lionfi sh, Pterois volitans, in Western Atlantic, Caribbean Sea, and Gulf of Mexico TL = total length, TL values are mean ± standard deviation (where available) and range, a = intercept, b = slope, r 2 = coeffi cient of determination.