The brown sea cucumber Isostichopus fuscus (Ludwig, 1875) is the most important commercial holothurian species in Latin America (^{Purcell et al., 2012}). For that reason, there have been multiple studies of its biology and ecology, including data on abundance (^{Wolff et al., 2012}; ^{Glockner-Fagetti et al., 2016}), growth (^{Herrero-Pérezrul et al., 1999}; ^{Mercier et al., 2012}), reproduction (^{Fajardo-León et al., 1995}; ^{Toral-Granda & Martínez, 2007}) and aquaculture (^{Hamel et al., 2003}; ^{Mercier et al., 2004}). Also, good information on the status of the fisheries has been published (^{Ramírez-Soberón et al., 2001}; ^{Herrero-Pérezrul & Chávez, 2005}; ^{Toral-Granda, 2008}), and in general the findings point out that although management efforts have been steered, the stocks have decreased considerably in Ecuador and Mexico, mostly because of exceeding quotas and illegal catches due to the high market value of this resource.

Among the topics that have received less attention from the researchers are the physiology and relative condition of the specimens of I. fuscus. These data have ecological relevance as in holothurians they can be linked to the reproductive effort and long-term success of the populations (^{Watanabe et al., 2012}), and also have been used as indicators of fishing yields of the brown sea cucumber (^{Herrero-Pérezrul & Reyes-Bonilla, 2005}). From the commercial perspective, a stock with organisms that are heavier related to their length, it is more productive than another with a less adequate physical status (^{Watanabe et al., 2012}). Biologically, the healthier and robust individuals might have a better chance to be reproductively successful as the parents can improve the quality of the yolk, and contribute with extra energy that allows the larvae to be better armed to survive, metamorphose and eventually recruit to the adult population (^{Glockner-Fagetti & Benítez-Villalobos, 2017}). A straightforward but efficient way to define the relative condition of a marine invertebrate is the analysis of the weight and length of the individuals, and from there to calculate the relative condition index Kn (^{Cone, 1989}; ^{Poot-Salazar et al., 2014}). This measure signs how heavy is an individual in relation to the expected weight at a given size, and the comparison is made in perspective with another member of the same population (^{Murphy et al., 1991}).

The objective of this paper was to examine the relative condition of populations of the brown sea cucumber I. fuscus resident at rocky reefs of the northwestern Gulf of California, Mexico, using three indicators: length, weight and relative condition. The region was of particular interest to conduct this study because in the 1990s was the most productive in the country in relation to the total holothurian catch (^{Fajardo-León & Velez-Barajas, 1996}; ^{Singh-Cabanillas & Vélez-Barajas, 1996}). Unfortunately, the situation changed by the following decades because of overexploitation of the stocks (^{Glockner-Fagetti et al., 2016}), and populations are still not able to recover, even when stronger management measures have been put in place (^{Toral-Granda, 2008}).

For this study, a total of 702 specimens of I. fuscus were collected by scuba diving in 86 sites of the northern Gulf of California, México (from 28°17’N, 112°51’W to 29°33’N, 113°33’W in October and November 2016, and at depths of 3 to 22 m. The organisms were placed in individual bags and taken to a boat where their length from mouth to anus was recorded with a precision of ±0.1 cm, and the weight was measured with spring scales (precision ±10 g); this was done after the organisms were left untouched for about 30 min in buckets in order to avoid or at least diminish body contraction. Afterward, the animals were returned to suitable areas at the bottom and placed carefully to avoid physical damage.

We calculated the length-weight relationship by the general equation W = a L^b, where W = weight in g, L = body length in cm, a = the ordinate, b = the slope of the regresion (^{Haddon, 2011}). The estimation was conducted in an iterative way using the Levenberg-Marquardt algorithm to find the best model. Afterwards, with the parameters of the equation and the weight and length data, we determined the relative condition (Kn) for each specimen by using an index which conveys the deviation from the actual weight of a given individual, from the expected value calculated for the entire field sample (^{Herrero-Pérezrul & Reyes-Bonilla 2005}; ^{Glocker-Fagetti & Benítez-Villalobos, 2017}). The index was calculated as Kn = W/aL^b.

For the statistical analyses, Kn of individuals of the sampled populations was compared using one-way analyses of variance, as data were homoscedastic and normal, according to Levene and Kolmogorov-Smirnoff tests (^{Sokal & Rohlf, 1995}).

Finally, we used kriging (Matlab, GLOBEC kriging Software Package - EasyKrig V3.0) to map the spatial distribution of the relative condition of specimens along the study region, based on the geographic position of the field survey and the condition of the specimens found there. Doing that, we prior used Matlab 7.7, the program GEODAS-NG Smart Start Center and topography and line coast from “Global Self-consistent, Hierarchical, and High-resolution Geography Database” (GSHHG, National Center for Environmental Information, NOAA).

The results indicate that the length of the specimens was 22.32 ± 5.25 cm (average ± SD), with a minimum and a maximum sizes of 5.2 and 38.2 cm, respectively (Fig. 1a). The organisms were relatively smaller than those reported for other populations of I. fuscus which range in average size from 23 to 25 cm in areas such as the Galapagos Islands, Ecuador (0°N; Hearn et al., 2005; ^{Toral-Granda & Martínez, 2007}), and Santa Rosalía (27°N), Loreto (25°N) and La Paz (24°N), in Mexico (^{Herrero-Pérezrul et al., 1999}; ^{Reyes-Bonilla & Herrero-Pérezrul, 2003}; ^{Herrero-Pérezrul & Reyes-Bonilla, 2005}), but similar to the ones found in the tropical Mexican coast at Jalisco (20°N) and Huatulco (15°N), according to ^{Glockner-Fagetti & Benítez-Villalobos (2017)}. At the same time, the reported sizes for Bahía de Los Ángeles (Fig. 3b) in the 1990s was 23 cm (^{Salgado-Castro, 1994}), but for 2005-2007 was just 13.91 ± 3.47 cm, then increased to 17.78 ± 3.78 cm in 2013 (^{Glockner-Fagetti et al., 2016}), and in 2016 was 22.3 cm. The slightly smaller size of the brown sea cucumber in our study, when compared with other locations in the Gulf of California, may be a consequence of the overexploitation that the stocks suffered in the last two decades, an idea suggested by ^{Glockner-Fagetti et al. (2016)}. Nevertheless, it is also clear that the stock is recovering, as local fishers are much more aware of the need to protect the resource for the future.

Figure 1 Frequency distribution of a) length, b) weight and c) relative condition index of analyzed specimens of the brown sea cucumber Isostichopus fuscus in the northwestern Gulf of California. 

In the fieldwork conducted for this paper, the individual weight of I. fuscus specimens was 420.61 ± 192.48 g (range from 8 to 960 g; Fig. 1b). This is one of the highest figures reported anywhere in the eastern Pacific (^{Herrero-Pérezrul et al., 1999}; ^{Reyes-Bonilla & Herrero-Pérezrul, 2003}; ^{Hearn et al., 2005}; ^{Herrero-Pérezrul & Reyes-Bonilla, 2005}; ^{Toral-Granda & Martínez, 2007}; ^{Glockner-Fagetti et al., 2016}; ^{Glockner-Fagetti & Benítez-Villalobos, 2017}), as they ranged from 251 to 396 g in average. The only exception appears in the study by ^{Fajardo-León et al. (1995)}, for Santa Rosalía, Mexico (27°N), where the mean weight of over 200 sampled specimens along a year was 458 g. This finding points out the excellent state of the holothurians at the study region, and is one of the reasons why the condition index reach values higher than 2.0 (Fig. 1c), the highest reported for this species (^{Herrero-Pérezrul & Reyes-Bonilla, 2008}; ^{Glockner-Fagetti et al., 2016}; ^{Glockner-Fagetti & Benitez-Villalobos, 2017}).

According to the nonlinear adjustment, the length-weight relationship coefficients (±SE) were: a = 3.27 ± 0.50 and b = 1.56 ± 0.05; this latter constant is the slope of the curve and has been referred as the “isometry coefficient”, as it represents an indication of the symmetry in body form of an organism as it grows (^{Haddon, 2011}). The results of this study show that the studied populations of I, fuscus in Baja California had a negative allometric growth (Fig. 2a), a finding that is not surprising, since all published studies on this species found a similar result (^{Fajardo-León et al., 1996}; ^{Herrero-Pérezrul et al., 1999}, ^{Reyes-Bonilla & Herrero-Pérezrul, 2003}; ^{Herrero-Pérezrul & Reyes-Bonilla, 2005}; ^{Glockner-Fagetti et al., 2016}, ^{Glockner-Fagetti & Benítez-Villalobos, 2017}). The conclusion is that the shape of this holothurian changes ontogenetically, becoming more elongated as they grow (^{Herrero-Pérezrul et al., 1999}).

Figure 2 a) Length-weight relationship and b) relative condition index of the brown sea cucumber Isostichopus fuscus in the study area. The regression models that describe the data are presented. 

Also, here we suggest another explanation of the negative allometric growth of I. fuscus; it is possible that as the organisms use seawater to maintain their form, and this liquid is less dense than any biological tissue, consequently the individuals are lighter than expected.

The b parameter of the weight-length equation presented in this paper (1.56) is one of the highest reported for a population of I. fuscus in the literature as the values fluctuate from 1.20 to 1.83 (see review in ^{Glockner-Fagetti et al., 2016}). As stated before, this finding suggests that the condition of the holothurians in the northwestern Gulf of California is excellent when compared with any other area of that inner sea, the tropical Mexican Pacific, and even the Galápagos Islands, and that may help explain the high biomass that characterized the fishery in the past (^{Fajardo-León & Vélez-Barajas, 1996}; ^{Herrero-Pérezrul & Chávez, 2005}).

The average ± SD condition index Kn of the I. fuscus specimens collected at Baja California was 0.96 ± 0.29, with a maximum of 2.14 and a minimum of 0.046 (Fig. 2b). ^{Glockner-Fagetti et al. (2016)} report that the monthly average of Kn in the population of I. fuscus from Bahia de Los Ángeles (Fig. 3b) was 1.08 ± 0.27 in 2013 (ranging from 0.11 to 2.62) and 1.05 ± 0.32 in 2005-2007 (from 0.08 to 2.26), while ^{Herrero-Pérezrul & Reyes-Bonilla (2008)} refer monthly means of 1.040 ± 0.027 (0.12 to 2.82) for Loreto (25°N), and ^{Glockner-Fagetti & Benítez-Villalobos (2017)} mentioned 1.04 ± 0.31 (0.92 to 1.34) in Huatulco, in the southern Mexican Pacific. As observed, there seems to be no statistical difference in all estimations, evidence of stability in the relative condition of the specimens regardless of region and time in the northern Gulf. In this region, it could be expected that with the reduction of the population sizes and the interannual stability in the primary ocean productivity (^{Brusca et al., 2017}), the potential increase of available food per individual might have improved the condition of the holothurians, but that was not the case. We suggest that as environmental factors seem to play minor roles, the constancy in the relative condition of I. fuscus may represent a physiological limit in the weight of the animals in relation to its length.

Figure 3 Interpolation maps of the relative condition index (Kn) of I. fuscus, along the study region. a) Angel de la Guarda Island, b) Bahía de los Ángeles, c) San Lorenzo Archipelago. The areas inside the black circles include the locations with significantly higher Kn than the rest (five sample sites in Fig. 3a and four in Fig. 3b; from a total of 85 sites). 

Moreover, the analysis of variance showed that specimens from different sites differ in their Kn (F(87, 614) = 3.5, P < 0.01): organisms in the outer coast of Angel de la Guarda Island (Fig. 3a) and north of Bahia de los Ángeles (Fig. 3b) had higher Kn, as shown in the interpolated maps of relative condition. The possible explanation hinges on the way the fishery is conducted. Many fishermen travel from Sonora (at the eastern coast of the gulf) to the east, but they usually work at San Lorenzo Island (Fig. 3c) and west of Angel de la Guarda Island. While on the other hand, local fishermen conduct their work mostly on the peninsular coast; this way, the northwest coast of Angel de la Guarda Island may receive less fishing effort than others. The case for north Bahía de los Ángeles is explained here by the management efforts conducted by authorities of the biosphere reserve.

In conclusion, this study demonstrated that average length in the populations of the brown sea cucumber I. fuscus in the northeastern Gulf of California is lower than that reported for other areas of the same region, but size has been improving from the lowest point in 2005-2007 when the fishery was at its apex. On the other hand, the average weight of the specimens was among the highest reported in the eastern Pacific, probably reflecting on the high local primary productivity of the study region (^{Brusca et al., 2017}). Finally, the average relative condition of the animals did not differ to that recorded in the Mexican Pacific coast, and in the study region, the value of the index has not changed in a decade; something that can be explained as a genetic limitation on the condition of the specimens.