Introduction

More than half of the species (30) in the family Loliginidae Lesueur, 1821 are commercially important (^{Roper et al. 1995}), though most of them are captured as bycatch in numerous coastal trawl fisheries (^{Zeidberg et al. 2006}, ^{Arkhipkin et al. 2015}). In Mexico, loliginid squids are incidentally captured in shrimp and demersal-fish fisheries, with no management regulation. Because this squid group is scarcely known in Mexico, all squids caught as bycatch are generalized as “unidentified squid” in national fishery statistics (^{Alejo-Plata et al. 2001}, ^{Judkins et al. 2009}, ^{CONAPESCA 2018}).

The length-weight relationship (LWR) is one of the most important fishery parameters in statistical modeling, for example in executing catch-at-age or catch-at-size models and the stock synthesis model (^{Quinn and Deriso 1999}, ^{Zepeda-Benitez et al. 2017}), since LWR is a useful tool in analyzing key biological aspects, for example in estimating biomass from length observations and converting biomass to number of individuals, which is advisable for stock assessment of fast-growing species such as squid (^{Le Cren 1951}, ^{Alford and Jackson 1993}, ^{Froese 2006}). Another significant biological parameter is the condition factor, which reveals the physiological status of individuals and can be related to growth rate, phenotypic variability, or the health status of aquatic ecosystems inhabited by the species under study (^{Blackwell et al. 2000}). In this study, we aimed to estimate the LWR and condition factor for loliginid squids captured in Mexican waters.

Materials and methods

Loliginid squids (N = 1,105) captured on the Pacific and Atlantic coasts of Mexico were evaluated in our study. Squids were sampled along the coast from the state of Baja California to the state of Oaxaca, including the Gulf of California (32º37′75″-16º24′36″N; 117º01′95″-92º24′31″W), and along the coast of the state of Tamaulipas, in the Gulf of Mexico (22º12′31″-27º40′42″N; 97º08′38″-100º08′51″W). Squids were captured with typical fishing nets used for catching demersal fish and shrimp, and specimens were obtained from landing areas and local markets and during oceanographic cruises conducted in the period from 2011 to 2014. Species were identified using specialized identification guides (^{e.g., Jereb et al. 2010}). The dorsal mantle length (DML) and total weight of each squid were recorded.

To assess the relationship between weight increase and DML, the following potential equation was employed: W = a × DML ^b , where W is squid weight, a is the coefficient of proportionality, and b is the allometry coefficient. To estimate the type of growth, Student’s t test was performed using the b values that were obtained from the model and compared with the theoretical value of b = 3, which represents isometric growth. Fulton’s condition factor (K) was estimated for species having isometric growth using the following formula: K = 100 × (W/DML³). The relative condition factor (Kn) was calculated for species having allometric growth using the following formula: Kn = W/a × DML ^b .

Results

The following species were identified: Doryteuthis pealeii (N = 50, DML= 67.7-213.0 mm), Doryteuthis plei (N = 50, DML = 33.0-638.0 mm), and Lolliguncula brevis (N = 11, DML = 40.0-71.0 mm) on the Atlantic coast, and Lolliguncula diomedeae (N = 263, DML = 44.7-98.4 mm), Lolliguncula panamensis (N = 467, DML = 20.1-112.0 mm), Lolliguncula argus (N = 64, DML = 40.4-45.7 mm), and Doryteuthis opalescens (N = 200, DML = 17.6-55.4 mm) on the Pacific coast. The largest squid was a D. pealeii individual (213.00 mm DML), and the smallest a D. opalescens individual (17.61 mm DML). For all loliginid squids, except L. argus and L. brevis, the allometry coefficients obtained with Student’s t test were statistically different from the theoretical value of 3 (P < 0.05), indicating negative allometric growth. The low coefficient of determination (<0.60) values estimated with the potential LWR model for L. diomedeae, L. argus, and D. opalescens demonstrated that the populations of these species are comprised of different intraspecific groups or stocks (Fig. 1). Kn values were >1.00 for all species except L. panamensis, though its corresponding value was close to 1.00 (0.99). The highest value (10.64) was detected for D. opalescens, evincing its great size in terms of weight and DML. K values were <1.00 for the 2 species analyzed (Fig. 2).

Figure 1 Length-weight relationship for the loliginid squids evaluated in this study. (a) Lolliguncula panamensis, (b) Lolliguncula diomedeae, (c) Lolliguncula argus, (d) Doryteuthis opalescens, (e) Lolliguncula brevis, (f) Doryteuthis plei, (g) Doryteuthis pealeii. 

Figure 2 Relative condition factor and Fulton’s condition factor for the loliginid squids evaluated in this study. (a) Lolliguncula panamensis, (b) Lolliguncula diomedeae, (c) Lolliguncula argus, (d) Doryteuthis opalescens, (e) Lolliguncula brevis, (f) Doryteuthis plei, (g) Doryteuthis pealeii. 

Discussion

In this study, the LWR and condition factor were determined for Loliginidae individuals captured on the Atlantic (3 species) and Pacific (4 species) coasts of Mexico. Considering the swimming strategies of other aquatic organisms, ^{Helfman et al. (2009)} found that, in most fish, the energy cost of locomotion in a water mass decreased as fish size increased. The type of growth detected in most of the squid species examined in our study (negative allometric growth) can be explained by their daily and seasonal swimming habits. Several loliginid species undertake significant daily migrations, congregating in bottom waters (some species at 700 m depth) during daylight and ascending and dispersing in the water column at night. Moreover, some loliginid species perform seasonal migrations in relation to water temperature (e.g., D. pealeii seasonally travels up to 600 km) (^{Roper and Young 1975}, ^{Roper et al. 1984}). Therefore, the negative allometric growth of these loliginids is favorable in terms of the energy cost of their migration habits. On the other hand, L. argus and L. brevis tended to increase body thickness in proportion to size, and their swimming behavior is accordingly related to the type of growth we detected (isometric growth). Given that both are coastal, shallow-water dwellers (e.g., L. brevis is a slow swimmer, regularly restricted to very shallow waters) (^{Roper and Young 1975}, ^{Brakoniecki and Roper 1985}, ^{Bartol et al. 2001}), the swimming energy requirements for these 2 species are not as demanding as for the rest of the taxa analyzed; however, it is worth noting that the observations made for L. brevis in this study are not conclusive because of the low number of examined individuals. Another explanation for the types of growth exhibited by teuthids was posed by ^{Bazzino-Ferreri (2014)}, who analyzed length-weight data for the Humboldt squid, Dosidicus gigas, over a 10-year period (1996-2006). This author concluded that the type of growth and the condition factor of this squid vary according to latitude, year or season, population size range, and environmental conditions. Since ours is the only study addressing the LWR and condition factor for loliginid squids in Mexican waters, we have no point of comparison, but it is highly likely that these 2 factors are affected by the same variables affecting D. gigas growth and condition. Further systematic studies should be performed to confirm this statement considering that the Humboldt squid and our loliginids belong to different orders.

Regarding the condition of loliginid squids, the species with isometric growth showed a poor condition (low K values), while the rest of the species showed a good relative condition (Kn > 1.00). The K and Kn values we report here can be employed as reference for comparative purposes in further research (e.g., aquaculture). Doryteuthis opalescens showed the best condition (Kn > 10) among the species analyzed, and this can be related to intense gonad activity, given that maturation and growth of reproductive organs in this species depend directly on the energy obtained from food; in addition, the excellent condition of this species indicates that it is highly likely that squid were collected in spawning areas (^{Jereb et al. 2010}).

In this study, most loliginid species collected in Mexican waters showed negative allometric growth. The type of growth found in each of the taxa could be related to their migration habits in the water column or otherwise be affected by latitude, population size range, environmental variables, and year or season. The LWR and condition factors for these squid species are now available to be incorporated in further fishery stock assessment models.