GROWTH AND MORTALITY OF RED LIONFISH , PTEROIS VOLITANS ( ACTINOPTERYGII : SCORPAENIFORMES : SCORPAENIDAE ) , IN THE PARQUE NACIONAL ARRECIFE ALACRANES , SOUTHERN GULF OF MEXICO , AS DETERMINED BY SIZE-FREQUENCY ANALYSIS

Background. Biological invasions represent a threat to the ecological stability of the ecosystem. Two lionfi sh species, the red lionfi sh and the devil fi refi sh—both tropical marine predators native to the Indo–Pacifi c—were introduced to the Atlantic Ocean. However, only one—the red lionfi sh, Pterois volitans (Linnaeus, 1758)—has reached the level of an invasive species so far. It is crucial to learn its biology and ecology to understand trends of its invasion and impacts on native fauna, and to determine ecological changes as the invasion progresses. This study reports the growth and mortality of P. volitans in coral reefs of the Parque Nacional Arrecife Alacranes, off the northern Yucatan Peninsula, Mexico, in Southern Gulf of Mexico. Materials and methods. Lobster diver fi shers participated in voluntary captures of lionfi sh during the lobster fi shing seasons of 2010–2012. In the laboratory, lionfi sh were taxonomically identifi ed, measured, and weighed. Their length–weight relation was determined according to the commonly used equation: W = aTLb. Fish total lengths were used to calculate the parameters of the von Bertalanffy growth function (VBGF) of lionfi sh based on the size-frequency analysis routine ELEFAN in the FiSAT II software. Results. A total of 776 lionfi sh (9.0 to 38.9 cm in total length, 7 to 874 g in total wet weight) were collected. The VBGF parameters estimated were L∞ = 42 cm, K = 0.88 –1, t0 = –0.107 years. The total mortality instantaneous rate (Z) calculated by the total length converted catch curve was 2.06 year–1. Conclusion. This study provides fi rst calculation of growth parameters and mortality of P. volitans in Southern Gulf of Mexico as determined by size-frequency analysis. Results contribute to the knowledge on the biology of P. volitans and to a better understanding of aspects of its biological invasion in the region.


INTRODUCTION
The red lionfi sh, Pterois volitans (Linnaeus, 1758), is an introduced species currently invading many coral reefs of the Western Atlantic (Schofi eld 2010, Côté et al. 2013).It is one of two lionfi sh introduced to the Atlantic Ocean (Hamner et al. 2007).The second species is the devil fi refi sh, Pterois miles (Bennett, 1828).Both are tropical marine predators native to the Indo-Pacifi c.Only P. volitans, however, has reached the level of an invasive species so far (Whitfi eld et al. 2002) representing 93% of the invasive population in the region (Hamner et al. 2007).More than 30 years after its suspected accidental introduction off the eastern coast of the United States (Whitfi eld et al. 2002), the specimens of red lionfi sh, P. volitans, grow larger now and its populations are more dense compared to those in their native coral reefs in the Indo-Pacifi c Ocean (Darling et al. 2011).
The red lionfi sh invasion poses a threat to the coral reef biodiversity because of its fast population growth and increased predation rate on native fi sh may cause native fi sh population to decline (Green et al. 2012).Thus, it is crucial to obtain as much biological information as possible of P. volitans for better elucidating how it is impacting the invaded marine environment (Barbour et al. 2011).
In the Western Atlantic, Potts et al. (2011) estimated growth parameters of the red lionfi sh, based on sagittal otoliths of specimens from Onslow Bay, North Carolina, United States, using the von Bertalanffy growth function (VBGF): -0.32 (t + 1.22) ] and Barbour et al. (2011) did the same from the same area: Recently in Cayman Islands, Edwards et al. (2014) calculated growth parameters using otoliths: In the Southern Gulf of Mexico, the red lionfi sh was detected late in 2009 (Aguilar-Perera and Tuz-Sulub 2010) where it has invaded the Parque Nacional Arrecife Alacranes off the northern Yucatan Peninsula (López-Gómez et al. 2014).So far, relatively little is known on its biological aspects in this area.Consequently, the objective of this work was to estimate growth parameters, based on size-frequency analysis, and mortality of Pterois volitans from the Parque Nacional Arrecife Alacranes, Southern Gulf of Mexico.

MATERIALS AND METHODS
Study area.The Alacranes reef (22°31′28N, 89°42′44W), the largest reef formation in Southern Gulf of Mexico, is located 135 km off the northern Yucatan Peninsula (Chávez et al. 2007).In 1994, due to its high biodiversity, the Alacranes reef was declared a natural protected area known as the Parque Nacional Arrecife Alacranes (PNAA).It must be emphasized, however, that the PNAA is a commercially important fi shery zone for the spiny lobster (Panulirus argus) where three fi shermen groups catch lobster from July to February each year (Rios-Lara et al. 2007).Fieldwork and laboratory.Diver fi shers collected lionfi sh using spear guns, from July 2010 to February 2012 at depths ranging from 5 m to 20 m.Participant fi shers received orientation briefi ngs during specifi c workshops where they were invited to collect red lionfi sh, as much as possible, during their fi shing journeys in the lobster fi shing season (July to February) in the PNAA.Instructions given to fi shers specifi ed that the lionfi sh collected should be kept frozen in labelled bags and basic information from the collection site should be recorded (see López-Gómez et al. 2014 for details).There was no collection of lionfi sh during the lobster closed season (March-June).Specimens caught were preserved frozen, kept in labelled polyethylene bags, and transported to the laboratory of the Campus of Biological Sciences of the Universidad Autónoma de Yucatán.At the laboratory, the specimens collected were taxonomically identifi ed to species according to Schultz (1986), measured in total length [cm], and wet weighed [g].It was not possible to determine the sex of specimens at the time of processing, so total length data of all specimens were pooled for the analyses.Parameter b is the exponent of the arithmetic form of the length-weight relation and the slope of the regression line in the logarithmic form, while parameter a is the coeffi cient of the arithmetic length-weight relation and the intercept of the logarithmic form (Froese 2006).When b > 3 (positive allometric growth), large fi sh increased in height or width more than in length since large fi sh in the sample are thicker than small fi sh.By contrast, when b < 3 (negative allometric growth) large fi sh change their body shape to become more elongated or small specimens were in better nutritional condition at the time of sampling.When b = 3 (isometric growth), small fi sh in the sample have the same form and condition as large specimens (Froese 2006).The 95% confi dence intervals for the parameter b (CI 95%) were calculated to determine if the hypothetical value of isometric growth (b = 3) fell between these intervals (Froese 2006).
Parameters of the von Bertalanffy growth function (VBGF) were calculated, based on lionfi sh length frequency distributions (class intervals of 2 cm in total length), using the ELEFAN routine of the software Fish Fisheries Stock Assessment Tools (FiSAT II) (Gayanilo et al. 1997).The VBGF is expressed as: where L t is the length at age t, L ∞ is asymptotic length, K is the growth rate (year -1 ), and t 0 is the hypothetical age of fi sh at zero length.For assessing the variability of K and taking into account the uncertainty in the estimation of asymptotic length, estimated values of maximum length and its 95% confi dence interval from the routine Maximum Length Estimation included in FiSAT II (Gayanilo et al. 1997) were used to obtain a range of possible values of K.
The instantaneous rate of total mortality (Z) was determined by the length converted catch curve which, in the absence of declared exploitation of lionfi sh in the PNAA, is equivalent to the instantaneous rate of natural mortality (M).Also, an independent estimate of M was performed using the empirical equation of Pauly (1983).The alternative to calculate this latter estimate is available in the FiSAT II package and is a commonly used indirect method of estimating natural mortality related to VBGP and mean environmental temperature T [ºC].This method assumes a relation between fi sh size and natural mortality.While the relation is relatively weak, the inclusion of mean environmental temperature increases the fi t since fi sh in warmer waters tend to have higher mortality rates compared to those in cooler waters (Pauly 1983).

RESULTS
Over the study period, 776 red lionfi sh were collected.Fish ranged from 9.0 to 38.9 cm in total length (TL) and from 7 to 874 g in total wet weight (W).Maximum length (38.9 cm TL) and maximum wet weight (874 g) were recorded in October 2012 and the smallest length (9 cm TL) and the smallest weight (7 g) in August 2010 (Fig. 1).Wet weights were related to total lengths (r 2 = 0.97; Table 1) according to the formula: W = 0.011• TL 3.33   The parameter b (3.33) in the combined length-weight relation was signifi cantly different from the isometric value of growth (t-student = -1.3606,n = 776; P > 0.05) (Table 1).The calculated VBGF based on observed TL at age was: The total mortality instantaneous rate (Z) calculated by the total length converted catch curve was 2.06 year -1 (1.22 -2.90; 95% confi dence interval).In the PNAA at least two cohorts were identifi ed from the curves since 2010 through 2012 (Fig. 1), with the highest frequency of adult sizes detected in October 2012.The instantaneous rate of natural mortality (M) was 1.46 year -1 in relation to the average temperature of the sampling period in the PNAA (26.7°C).

DISCUSSION
This study is the fi rst report of growth parameters of red lionfi sh, Pterois volitans, in Southern Gulf of Mexico as determined by size-frequency analysis.Growth parameters calculated before of specimens from North Carolina (Barbour et al. 2011, Potts et al. 2011) and Cayman Islands (Edwards et al. 2014) were based on readings of sagittal otoliths.The maximum size (39 cm TL) of P. volitans detected in this work is the largest ever recorded in the PNAA, and similar to that detected in a specimen from Cayo Arenas-a site located approximately 50 km to the east from the PNAA (Aguilar-Perera et al. 2013).This maximum size (39 cm TL) of P. volitans is the largest ever recorded in Southern Gulf of Mexico too.However, the maximum size of P. volitans ever recorded in the invaded Western Atlantic was 46.4 cm TL of a specimen taken off North Carolina (Potts et al. 2011).
The calculated b parameter (3.33) in the lengthweight relation indicated a positive allometric growth of P. voltians in the PNAA.However, a previous estimation (b = 3.30) from the same area shown isometric growth (n = 455 lionfi sh) (Perera-Chan and Aguilar-Perera 2014).(Barbour et al. 2011).In the Cayman Islands it amounted to 3.24 (Edwards et al. 2014) and in the Bahamas it was 3.29 (Green et al. 2011).In general, parameter b is subject to changes because of sample size, environmental factors, and seasonality (Froese 2006).
The VBGF parameters of lionfi sh in the PNAA showed similarities and differences with growth parameters of Pterois volitans from other areas in the Western Atlantic region.Barbour et al. (2011) calculated a value of L ∞ = 42 cm for the lionfi sh and Potts et al. (2011) of L ∞ = 45 cm; both of them off the North Carolina coast (USA).This parameter was relatively similar to that of the PNAA (L ∞ = 42.5 cm) but higher than that calculated (L ∞ = 34.9cm) in the Cayman Islands (Edwards et al. 2014).Lionfi sh from the PNAA appeared to reach their maximum length faster than fi sh from the Cayman Islands and North Carolina, with K values for fi sh from the PNAA equal to 0.88 and K values for lionfi sh from North Carolina equal 0.32 (Potts et al. 2011) and 0.47 (Barbour et al. 2011) and Cayman Islands equal to 0.42 (Edwards et al. 2014).In general, in comparison to growth rate values for other tropical fi sh (K = 0.1 to 0.3), the lionfi sh appears to reach their asymptotic maximum length faster (Edwards et al. 2014).Estimates of lionfi sh's growth parameters in the PNAA may have been affected since there is a lack of older and larger lionfi sh (since the recent establishment of lionfi sh in the area) which may produce a truncated growth curve.
Estimates of natural-(1.46 year -1 ) and total mortality (2.06 year -1 ) of red lionfi sh from the PNAA are the fi rst estimates in the Southern Gulf of Mexico.Estimates of total mortality by the length converted catch curve (Pauly 1983) can be considered equivalent to the natural mortality rate (Z = M) in the absence of formal fi shing practices in the area.In the particular case of the PNAA, however, special considerations have to be taken with this calculation because a removal of more than 700 lionfi sh in 18 months may indicate that fi shing mortality could be high.The natural mortality calculated (M) for lionfi sh in the PNAA (1.46 year -1 ) is very high compared to value of M for a typical of short-lived fi sh which it could be ranged from 0.2 to 0.5 (Froese and Pauly 2014).This inferred value of M has previously been used for modelling growth in lionfi sh (Barbour et al. 2011).Consequently, we suggest caution with this calculated value for M for lionfi sh in the Southern Gulf of Mexico.
We recommend using sagittal otoliths to calculate growth parameters of lionfi sh in the area, and then make comparisons with the growth parameters calculated in this work in the PNAA.We also recommend conducting studies to evaluate the impact the removals may have on the lionfi sh population by comparing possible changes in lionfi sh growth between removed and non-removed areas within the PNAA.
Data analysis.Based on log-converted total weight and total length, the parameters a and b of the length-weight regression analysis were calculated according to the equation: lnW = ln(a) + ln(b)TL and expressed as W = aTL b

Fig. 1 .
Fig. 1.Monthly growth curve variation of red lionfi sh, Pterois volitans, calculated through the ELEFAN-I model in FiiSAT II based on length frequency data (above) and restructured length frequency data (below), from the Parque Nacional Arrecife Alacranes, off the northern Yucatan Peninsula, Mexico; Data was available only in the period July-February each year which corresponds to the lobster fi shing season in the area

Table 1
Descriptive statistics and estimated length-weight relation parameters of red lionfi sh, Pterois volitans, in the Parque Nacional Arrecife Alacranes, off the northern Yucatan Peninsula (July 2010-February 2012) n = number of specimens in the analysis; Regression parameters: a, scaling constant; b, slope; CI, confi dence interval; SE, standard error; r 2 coeffi cient of determination.