Interannual variability in mantle length structure, recruitment, and sex ratio of jumbo squid, Dosidicus gigas, in the central Gulf of California, Mexico.
Article Type: Report
Subject: Squids (Physiological aspects)
Sex ratio (Research)
Veterinary physiology (Research)
Authors: Velazquez-Abunader, Jose Ivan
Hernandez-Herrera, Agustin
Martinez-Aguilar, Susana
Diaz-Uribe, Juan Gabriel
Morales- Bojorquez, Enrique
Pub Date: 04/01/2012
Publication: Name: Journal of Shellfish Research Publisher: National Shellfisheries Association, Inc. Audience: Academic Format: Magazine/Journal Subject: Biological sciences; Zoology and wildlife conservation Copyright: COPYRIGHT 2012 National Shellfisheries Association, Inc. ISSN: 0730-8000
Issue: Date: April, 2012 Source Volume: 31 Source Issue: 1
Topic: Event Code: 310 Science & research
Product: Product Code: 0912198 Squid NAICS Code: 114112 Shellfish Fishing SIC Code: 0913 Shellfish
Geographic: Geographic Scope: Mexico Geographic Code: 1MEX Mexico
Accession Number: 288172745
Full Text: ABSTRACT Changes in the number and abundance of the cohorts of jumbo squid are a demographic response associated with high variability in recruitment, and have implications for availability and accessibility to the fishing fleets. In this study, we analyzed the interannual changes in the size structure, recruitment, and sex ratio of jumbo squid Dosidicus gigas in the central Gulf of California, Mexico. Data were analyzed for the 2000 to 2009 fishing seasons (from March to November). The biological data were collected biweekly at the port of Santa Rosalia, Baja California Sur, during each fishing season. We recorded mantle length and mantle weight, and sex (male or female) was identified from morphochromatic properties of fresh gonads. We concluded that the mantle length structure of jumbo squid changed between 1 cohort and 3 cohorts from 2000 to 2009. In the study zone, the presence of 2 cohorts is common. The species shows positive allometric growth, and the females are more abundant than the males in the region. The comparison between the most important fishing grounds in the central Gulf of California (Santa Rosalia and Guaymas) showed similar patterns, such as the number of cohorts, sex ratios, growth pattern, and migration pattern identified between both coasts. We believe that this could be evidence of one population that is widely distributed in the central Gulf of California.

KEY WORDS: jumbo squid, Dosidicus gigas, mantle length structure, cohorts, recruitment, sex ratio, growth

INTRODUCTION

The jumbo squid (Dosidicus gigas d'Orbigny 1935) is widely distributed in the eastern Pacific, from Alaska to Chile (Cosgrove 2005, Wing 2006, Zeidberg & Robison 2007). This new distribution pattern was observed between Monterey, CA, and Chile (Ehrhardt 1991). The presence of this species in Monterey has always been assumed to be a temporal invasion; the first reports of this phenomenon were documented during the 1930s (Croker 1937). Consequently, jumbo squid is identified as an endemic species to the eastern Pacific Ocean (Nesis 1983, Nigmatullin et al. 2001).

In Mexico, most commercial catches of jumbo squid are harvested from the central Gulf of California (between 22[degrees]N and 28[degrees]N, and 109[degrees]W and 113[degrees]W). However, fishing areas can vary depending on squid distribution and oceanographic conditions. For example, during 1998, when a strong ENSO occurred, high catches were reported from the southern Gulf of California, beyond traditional fishing areas (Morales-Bojorquez et al. 2001a). Unusual catches from Loreto, Bahia de La Paz, Bahia La Ventana, and even in Bahia Magdalena on the Pacific coast account for a probable range expansion of the Gulf of California jumbo squid population. Recent occurrences of jumbo squid in Ensenada, near the northern border of Mexico from 2007 to 2009, and in Bahia Magdalena during 2009 and 2010, have resulted in an increased demand for squid-fishing permits along the occidental coast of the Peninsula of Baja California.

In this fishery, there are different fishing fleets. The fishing effort was increased as follows: 2 fleets from Baja California Sur (Santa Rosalia and Bahia Magdalena), 3 fleets from Baja California (Ensenada), and 2 fleets from Sonora, Mexico. In the Gulf of California, the landings vary seasonally as a function of the availability of squid. Off Baja California Sur, fishing occurs during spring and summer, and off Sonora, during fall and winter (Fig. 1). Baja California Sur and Sonora have artisanal fleets. The traditional artisanal fleets consist of small open boats (known locally as pangas), each operated by 2 fishermen. The fishing gear is a hand jig with 6 rings of barbless hooks; only 1 jig (14 cm) per line is attached to the end of a nylon line (300-400 m). In addition, Sonora has a fishing fleet of shrimp trawlers of various characteristics equipped with a manual jigging system or hand jigs. The Ensenada region has different fleets: an artisanal fleet similar to those observed in Sonora, commercial trolling, and trawler (midwater) vessels; both fleets are adapted and use a manual jigging system with a light system.

Population dynamics studies on jumbo squid in the Gulf of California have shown that the number of cohorts is variable. Although Ehrhardt et al. (1983) reported 5 cohorts in the Gulf of California from January to September 1980, Hernandez-Herrera et al. (1998) found only 1 cohort between November 1995 and November 1996. More recent studies over a wider time frame have shown a variable interannual number of cohorts from 1-3 (Morales-Bojorquez et al. 2001b, Morales-Bojorquez & Nevarez-Martinez 2010, Nevarez-Martinez et al. 2010, Velazquez-Abunader et al. 2010). The origin of the cohorts has been proposed to be either a phenotypic (Nesis 1983, Keyl et al. 2008, Keyl et al. 2011) or genetic response (Nesis 1983). Nigmatullin et al. (2001) explained the complicated intraspecies size structure of jumbo squid along the latitudinal gradient in the eastern Pacific. They suggested the presence of 3 groups on the basis of mantle length (ML): small, ML of 13-26 cm in males and 14-34 cm in females; medium, ML of 24-42 em in males and 28-60 cm in females; and large, individuals with an ML of 50-120 cm. In this last group, the females are larger than the males. Some mechanisms that can, in theory, cause variability in the size structure included environmental factors (Hill 1985), the population area, the spatial distribution of individuals (Winters & Wheeler 1985), the abundance (MacCall 1976), density dependence of the squid population and fishing by different fleets, and schooling behavior (Ye & Mohammed 1999). Changes in the number and abundance of the cohorts of jumbo squid are a demographic response that have implications for availability and accessibility to the fishing fleets. In this study, we analyzed the interannual changes in the size structure, recruitment, and size at first capture of jumbo squid in the central Gulf of California, Mexico.

[FIGURE 1 OMITTED]

MATERIALS AND METHODS

Data from the 2000 to 2009 fishing seasons in the Gulf of California were analyzed. Two biological sampling sessions per month were carried out during each fishing season (usually from April to November) at the port of Santa Rosalia, Baja California Sur (Fig. 1). Random samples of squid in commercial catches were selected to record the individual ML ([+ or -] 0.1 cm) and mantle weight (MW; [+ or -] 0.1 kg), whereas sex was identified from morphochromatic properties of fresh gonads (Diaz-Uribe et al. 2006). The number of squid sampled each month per fishing season is shown in Table I.

Statistical Analysis

To estimate the relationship between ML and MW, the power equation MW = [alpha][ML.sub.[beta]] was used for each fishing season and the total data, where [alpha] is the average condition factor and [beta] is the coefficient of allometry, indicating isometric growth when equal to 3 and allometric growth when significantly different from 3 (Esmaeili & Ebrahimi 2006, Aguirre-Villasenor et al. 2008). The estimated value of [beta] was analyzed with Student's t-test (Sokal & Rohlf 1995, Zar 1999) to determine whether growth was isometric or allometric. Sex ratio data were calculated monthly as the number of females divided by the sum of males and females, and the data were categorized by a 4-cm ML class. To determine whether the sex ratio can be regarded as 1:1, a chi-square hypothesis test was carried out (chi-square, [alpha] = 0.05) (Sokal & Rohlf 1995).

Mantle Length-Frequency Distributions

The mantle length-frequency distribution of jumbo squid in each fishing season was represented graphically as frequency histograms. In this way, the observed modes were fitted to a multimodal model defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [x.sub.i] is the number of times a type i event occurs in n samples, n is the sample size, and [p.sub.i] are the separate probabilities of each of the type k events possible. To estimate the model parameters, it is necessary to transform Eq (1) into a likelihood expression. Therefore, the new equation is

-In L{[x.sub.i]|n, [p.sub.1],[p.sub.2], .....,[p.sub.k]} = [n.summation over i=1] [[x.sub.i]In([p.sub.i])] (2)

The main assumption for the parameter estimation is that the size distribution for each mean ML or mode can be analyzed with a normal distribution, determining that each mode corresponds to a different size group or cohort in the squid population (Keyl et al. 2011). Using this condition, the estimations of the relative expected proportions of each ML category are described using the density function

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [[mu].sub.n] and [[sigma].sub.n] are the mean and SD of the ML of each size group. Expected frequencies were estimated with the logarithmic function of the multinomial distribution (Eq 2), and final values of the model parameters were assigned by comparing the observed and expected frequencies (Haddon 2001, Aguirre-Villasenor et al. 2006). The objective function for parameter estimation was defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where [[mu].sub.i] and [[sigma].sub.i] are the mean and SD of each modal group present during a fishing season. The initial values for parameters in Eq 4 were assigned using 2 criteria: (1) a visual inspection of the mantle length-frequency distribution (Montgomery et al. 2010) and (2) previous knowledge of the recruitment events (Nevarez-Martinez et al. 2006, Nevarez-Martinez et al. 2010). The model parameters were estimated when the negative log-likelihood function (Eq 4) was minimized with a nonlinear fit using Newton's algorithm (Neter et al. 1996). When the sample had more than 1 modal group, the separation index (SI) was used (Sparre & Venema 1992):

SI = [[[ML.sub.j] - [ML.sub.i]] / [([S.sup.2.sub.j] + [S.sup.2.sub.i] / 2) [greater than or equal to] 2]] (5)

where [ML.sub.j] and [ML.sub.i] are the mean MLs of j and i modal groups, and [S.sup.2.sub.j] and [S.sup.2.sub.i] are SDs for the j and i modal groups. If SI < 2, then it was not feasible to separate the normal components of the frequencies observed (Sparre & Venema 1992).

[FIGURE 2 OMITTED]

The previous analysis was used to determine the number of size groups and to estimate the recruitment of jumbo squid. We defined recruitment as the number of individuals at a certain age, size, or stage added to the exploitable stock each year as a result of growth and/or migration into the fishing area. The choice of the age and stage varies (Myers 2002). In marine fisheries, recruitment usually refers to the first age at which individuals are targeted for harvest (Hilborn & Walters 1992, Quinn & Deriso 1999, Haddon 2001). Boyle & Rodhouse (2005) defined recruitment as the number of individuals that reach a specified stage of the life cycle (e.g., metamorphosis, settlement, joining the fishery). Different measures of recruitment are valid, and the choice often depends on the ease of measurement. We used the accepted concept of recruitment given by Hilborn & Walters (1992), Quinn and Deriso (1999), Haddon (2001), and Myers (2002).

Mantle Length at First Capture

ML at first capture was calculated with the cumulative ML frequency of squid using 4-cm ML intervals. The ML at which 50% of the jumbo squid are captured (MLc) was determined by fitting the logistic model (Nevarez-Martinez et al. 2010):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where [P.sub.i] is the cumulative probability at i interval, [L.sub.i] is the midpoint of the ML at i interval, r is the intercept, and [L.sub.50] is MLc (in centimeters). Fitting was performed by nonlinear regression and minimizing the squared sum of residuals with a nonlinear fit using Newton's algorithm (Neter et al. 1996).

RESULTS

For the fishing seasons between 2000 and 2009, 11,429 individuals were analyzed. Most biological samples were obtained from May to October, when the squid are mainly distributed in the fishing grounds off Santa Rosalia, Baja California Sur. When the fishing season extended to November (2000, 2001, 2004, and 2008) or started earlier in March or April (2004 to 2009), sampling was also achieved for these months. For some fishing seasons such as 2001, 2007, and 2009, a hurricane and tropical storms prevented us from monthly sampling during September or October. In 2000 and 2003, some logistical problems prevented us from regular sampling throughout the entire fishing season (Table 1). The smallest individuals were observed during 2004 (ML = 27 cm), 2008 (ML = 28 cm), and 2009 (ML = 29 cm), whereas the largest ones were sampled during 2001 (ML = 93 cm) and 2008 (ML = 102 cm; Fig. 2).

The ML-MW annual relationships showed positive allometric growth for jumbo squid for all fishing seasons ([beta] [not equal to] 3; Student's t-test, P < 0.05). The [beta] values varied between 3.2 (2003) and 3.6 (2005); the parameters of the power equation during the study period are shown in Table 2. The same pattern of positive allometric growth was estimated during the entire study period; the comparison between the power equation from 2000 to 2009 ([alpha] = 7 x [10.sup.5], [beta] = 3.2, [R.sup.2] = 0.92, [F.sub.(1,11287)] = 0.13 x [10.sup.-4], P < 0.0001) and each fishing season is shown in Figure 3.

Estimates of the sex ratio showed that females were more abundant than males during the spring and summer months of the 2001 to 2003 and 2007 to 2009 fishing seasons (chi-square, P < 0.05); the same pattern was observed during autumn of the 2000, 2002, and 2004 to 2006 fishing seasons (chi-square, P < 0.05). Males were more abundant than females during the spring months of 2006, 2008, and 2009 (Fig. 4). This pattern in the sex ratio showed that in the Santa Rosalia region, females are predominant in the population.

ML frequency distributions of jumbo squid in each fishing season showed that the size structure changes between 1 size group and 3 size groups in the population (Fig. 5, Table 3). Only 1 size group composed of adult individuals was identified during 2000 and 2006, whereas 3 size groups were found in 2003. In the remaining fishing seasons, 2 size groups were identified (Table 3), compared with only 1 size group during 2000 (ML = 73.2 cm) and 2006 (ML = 63.8 cm). These size groups were identified as individual adults in the population. Figure 6 shows the mean ML of the smallest size group of each fishing season. ANOVA showed significant differences in the ML of these size groups ([F.sub(9,7035)] = 1,258, P < 0.0001), and the post hoc test (P < 0.05) showed that the largest mean ML in the historical series occurred in the 2000 and 2006 fishing seasons.

[FIGURE 3 OMITTED]

The estimated MLc showed the influence of the number of size groups identified in the population. The highest MLc values were estimated during the 2000 (69 cm) and 2003 (71.3 cm) fishing seasons. During the first period, only 1 size group was observed (large). However, during the 2003 fishing season, 3 size groups were estimated--large, medium, and small--although the large group was the most abundant (Fig. 5). The variation of MLc, excluding the 2000 and 2003 fishing seasons, ranged from 42.8 (2009) 60.9 cm (2002; Table 4). According to the ML-frequency distribution and the dominant size group, the size at first capture depends on the number and abundance of size groups in the population, which could explain the changes in the MLc and ML of recruits in the fishery.

DISCUSSION

As is the case for many other squid species, because of their short life span the stock reduction method is commonly used for abundance estimation, which assumes one single cohort in the population (Morales-Bojorquez et al. 2001a). Thus, length-frequency analyses are valuable tools to gain insight into the population dynamics of exploited resources, and to identify problems such as inconsistent year-class strength, slow growth, and excessive mortality. Therefore, it is important to identify the link between size groups and the number of cohorts in the population. For jumbo squid from the Peruvian waters, between 1 cohort and 6 cohorts were determined by mode discrimination using ML frequency distribution (Keyl et al. 2011). The variability observed in the ML structure of the jumbo squid population in the central Gulf of California suggests that the number of cohorts varied interannually between 1 and 3, with the common presence of 2 cohorts. This variability could be attributable to 3 key factors: (1) variability in recruitment (Morales-Bojorquez et al. 2001a), (2) variability in individual growth (Markaida 2006), and (3) environmental influence such as an El Nino or La Nina events (Nevarez-Martinez et al. 2006).

[FIGURE 4 OMITTED]

Hernandez-Herrera et al. (1998) analyzed the annual ML-frequency for the fishing grounds off Guaymas and found evidence of only 1 cohort with annual recruitment. During fall and winter 1995, MLs between 60 cm and 80 cm were found, whereas a drastic change in the size composition was detected in spring 1996, with an ML between 20 cm and 40 cm. However, analysis of the catch-per-unit effort (CPUE) for the same fishing periods allowed 3 cohorts to be identified in the jumbo squid population, assuming that CPUE is an index of relative abundance (Morales-Boj6rquez et al. 2001b). If only 1 cohort supported the population of jumbo squid, then the expected trend of CPUE would show a constant decrease; however, the index of relative abundance showed recoveries, with 3 consistent peaks of catchability. The peaks occurred at 3 ML intervals: the first between 29 cm and 33 cm, the second between 53 cm and 57 cm, and the third between 65 cm and 71 cm. (Morales-Bojorquez et al. 2001b). Three different cohorts were also identified by Velazquez-Abunader et al. (2010) using ML-frequency distribution from research oceanographic cruises between 1997 and 2008. These discrepancies in the number of cohorts of the jumbo squid in the Gulf of California estimated from the ML composition of the commercial catch were reanalyzed by Morales-Bojorquez and Nevarez-Martinez (2002) and Morales-Bojorquez et al. (2008), who concluded that the jumbo squid population has several cohorts in its ML structure, and that the most abundant cohort will be identified as recruitment.

Considering recruitment as a key process in a dynamic population, and that recruits can be defined as the first size interval subject to fishing pressure (Myers 2002), then the variability in size composition of the jumbo squid can be used as a good indicator of recruitment. In the current study, during the 2000 and 2006 fishing seasons, there was only 1 medium-to-large size group. The absence of the small size group commonly caught by the fishery in these years probably indicates a failure in the recruitment of this group. In the Gulf of California, the 3 groups described by Nigmatullin et al. (2001) on the basis of ML, the small size group, a medium size group, and a third group with larger individuals, have been observed previously at Guaymas (Nevarez-Martinez et al. 2006, Nevarez-Martinez et al. 2010).

Despite its mathematical simplicity, the weight-length relationship represents a complex interaction of different factors, such as food availability, feeding rate, gonad development, and spawning period (Bagenal & Tesch 1978, Anderson & Gutreuter 1983). Isometric growth is defined when [beta] = 3, which means that any length increment is related to a proportional increment in weight. If [beta] [not equal to] 3, an allometric growth is observed. So the positive allometric growth ([beta] > 3) estimated for giant squid, means that the growth in weight is proportionately greater than the growth in length. This growth pattern was also found by Nevarez-Martinez et al. (2006, 2010) at Guaymas along the Sonora coast between 1996 and 2008. The relationship between ML and MW was allometric and varied between fishing seasons, with negative allometry for the 1996 to 1997 fishing season ([beta] < 3) and positive allometry ([beta] > 3) for the others. Ehrhardt et al. (1983) reported 13 = 2.9, close to isometric or a slightly negative allometric growth, and Hernandez-Herrera et al. (1998) estimated [beta] = 3.4 by 1995 to 1996. Consequently, positive allometry seems to be the growth pattern of jumbo squid in the central Gulf of California. Given the fast growth and massive early reproduction strategy, positive allometry is congruent with the fife history of jumbo squid (Nigmatullin et al. 2001).

[FIGURE 5 OMITTED]

The importance of environmental variability for the recruitment strength among cephalopod populations is well known; however, there is no general agreement on criteria for the recognition of recruits. Typically, recruits are defined simply by their body size. Despite the apparently simple life cycle of most fished cephalopod species, analysis of size- or age-frequency of the catch usually results in a series of multiple size or age groups, presumably representing successive subannual waves of recruitment. The reasons for this phenomenon are not clear, but perhaps it is mainly caused by the presence of more than 1 seasonal cohort (Boyle & Rodhouse 2005). Nevarez-Martinez et al. (2010) identified a pattern in the variability of recruitment according to environmental variability. Warmer waters caused by El Nino conditions in the California Current were coincident with low recruitment. Cooler waters identified with negative anomalies in the sea surface temperature caused by La Nina conditions were related to high recruitment. Markaida (2006) explained that in the Gulf of California, the response of the jumbo squid to changes in environmental conditions presented a certain degree of delay. The abundance of squid decreased even well after El Nino had ended and during the subsequent transition to La Nina in 1998 to 2001. This could be caused by a failure in squid recruitment during the previous year. The great abundance of medium-size jumbo squid in the Gulf of California in early 1999 followed the development of the mature La Nina conditions more closely.

Markaida (2006) analyzed MLs of 157 jumbo squid between May 10, 1998, and October 29, 2000, to assess environmental factors and their impact on the size composition of jumbo squid in the Gulf of California. The locations in the Gulf of California were Isla Tortuga, Loreto, Topolobampo, and Santa Rosalia. The most important fishing ground in the Gulf of California off Guaymas, Sonora, was not sampled (Morales-Bojorquez et al. 2001b). Markaida (2006) showed that the size composition changed among locations, and the abundance of males and females varied. Our results also showed that females dominated the sex ratio at Santa Rosalia, principally during spring and summer months, and occasionally during autumn months. The abundance and sizes of females could explain the changes in the ML structure. In our study, MLc varied from 42.8-71.3 cm; however, the interval estimated at Guaymas varied from 35.7-61 cm during 1995 to 2002, and from 56.6-67 cm during 2003 to 2008. The variation of MLc between locations could suggest segregation by size group in the central Gulf of California.

[FIGURE 6 OMITTED]

We conclude that the ML structure of jumbo squid at Santa Rosalia fluctuated between 1 and 3 cohorts from 2000 to 2009. In the study zone, the presence of 2 cohorts is common, defined as the medium size group (ML, 28-60 cm) and the large size group (ML, 50-120 cm). The species shows positive allometric growth, and the females are more abundant than the males in the region. MLc is larger than those caught at Guaymas. Last, the comparison between the most important fishing grounds in the central Gulf of California (Santa Rosalia and Guaymas) showed similar patterns in the number of cohorts, sex ratios, growth pattern, and migration pattern identified between both coasts (Markaida et al. 2005, Gilly et al. 2006). We believe that this could be evidence of a single population that is widely distributed in the central Gulf of California.

ACKNOWLEDGMENTS

We thank the Centro Regional de Investigacion Pesquera de La Paz, and CICIMAR for support in obtaining biological and statistical data of jumbo squid. AHH received support from COFAA-IPN and is an EDI-IPN fellow.

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JOSE IVAN VELAZQUEZ-ABUNADER, (1) * AGUSTIN HERNANDEZ-HERRERA, (2) SUSANA MARTINEZ-AGUILAR, (3) JUAN GABRIEL DIAZ-URIBE (3) AND ENRIQUE MORALES-BOJORQUEZ (4)

(1) Centro de Investigaciones y de Estudios Avanzados del Instituto Politecnico Nacional, Unidad Merida, Antigua carretera a Progreso km 6, CP 97310, Merida, Yucatan, Mexico; (2) Centro Interdisciplinario de Ciencias Marinas, Instituto Politecnico Nacional, Av. IPN. s/n. Colonia Playa Palo de Santa Rita, CP 23000, La Paz, Baja California Sur, Mexico; (3) Instituto Nacional de Pesca, Centro Regional de Investigacion Pesquera La Paz, Carretera a Pichilingue s/n km 1, CP 23020, La Paz, Baja California Sur, Mexico; (4) Centro de Investigaciones Biologicas del Noroeste SC (CIBNOR), Mar Bermejo 195, Col. Playa Palo de Santa Rita, CP 23090, La Paz, Baja California Sur, Mexico

* Corresponding author. E-mail: jvelazqueza@ipn.mx

DOI: 10.2983/035.031.0116
TABLE 1.
Number of squid sampled per fishing season at the port of
Santa Rosalia, Baja California Sur, Mexico.

                                  Year

Month        2000   2001   2002   2003   2004   2005   2006

March                                    100            91
April
May                 292    215     73    336            96
June                279     92    107    273    246    213
July         140    269    178     94    256    254    213
August       141    145    265           247    236    100
September    257           136           138    200    231
October      298     31    153           123    112     83
November     121    177                  118

                    Year

Month        2007   2008   2009

March                      223
April        101    153    247
May          146    204    235
June         206    210    250
July         224    235    243
August       227    101    252
September    184    188
October             206    250
November            215

TABLE 2.
Mantle length-mantle weight relationship ([alpha], [beta])
parameters.

               Mantle Length (cm)

Year     n     Minimum   Maximum

2000     957    35         89

2001   1,193    31         93

2002   1,039    37         90

2003     274    26.2      100.9

2004   1,591    27.4       84.9

2005   1,048    36         82.9

2006   1,088    29.8       87

2007   1,700    30         93.6


2008   1,512    27.6       97.8

2009   1,700    24.9       82.1

       Parameters

Year   [alpha]                                [beta]        [R.sup.2]

2000      4 x [10.sup.-6]                      3.35           0.88
         (2 x [10.sup.-5] -5 x [10.sup.-6])   (3.27-3.42)

2001      4 x [10.sup.-6]                      3.32           0.94
         (3 x [10.sup.-6] -5 x [10.sup.-6])   (3.27-3.37)

2002    1.8 x [10.sup.-6]                      3.53           0.96
       (1.9 x [10.sup.-6] -2 x [10.sup.-5])   (3.49-3.57)

2003      4 x [10.sup.-6]                      3.30           0.94
         (2 x [10.sup.-6] -6 x [10.sup.-6])   (3.21-3.40)

2004      3 x [10.sup.-6]                      3.35           0.93
         (2 x [10.sup.-6] -4 x [10.sup.-6])   (3.30-3.39)

2005    1.4 x [10.sup.-6]                      3.59           0.93
       (1.1 x [10.sup.-6] -1.8 x              (3.53-3.64)
         [10.sup.-6])

2006      3 x [10.sup.-6]                      3.36           0.90
         (2 x [10.sup.-6] -5 x [10.sup.-6])   (3.29-3.42)

2007    4.8 x [10.sup.-6]                      3.30           0.96
       (4.1 x [10.sup.-6] -5.6 x              (3.26-3.34)
         [10.sup.-6])
2008    2.6 x [10.sup.-6]                      3.45           0.95
       (2.6 x [10.sup.-6] -3 x [10.sup.-6])   (3.31-3.49)

2009      6 x [10.sup.-6]                      3.31           0.91
         (5 x [10.sup.-6] -7 x [10.sup.-6])   (3.26-3.35)

Sample size (n), mantle length interval (minimum and maximum),
and the coefficient of determination ([R.sup.2]) are shown.
Confidence intervals are presented in parentheses.

TABLE 3.
Number of cohorts estimated based on mantle-length
frequency distributions for Dosidicus gigas at Santa Rosalia,
Baja California Sur, Mexico.

                   No. of Cohorts

Year    1             2             3

2000                  73.2#
                      (72.8-73.5)
2001    56.8#         74.8#
        (56.3-57.3)   (74.3-75.2)
2002    49.5#         69.9#
        (49.2-49.8)   (69.5-70.4)
2003    50.9#         70.2#         86.4#
        (50.1-51.8)   (69.4-71.0)   (85.8-87.0)
2004    47.5#         62.8#
        (47.1-47.8)   (62.4-63.2)
2005    45.6#         59.3#
        (45.4-15.8)   (58.8-59.8)
2006                  63.8#
                      (63.3-64.3)
2007    44.1#         67.3#
        (43.8-44.4)   (66.8-67.7)
2008    52.4#         70.9#
        (52.0-52.8)   (70.5-71.2)
2009    41.8#         64#
        (41.5-42.1)   (63.7-64.4)

The mean value estimated by cohort is shown in bold type. Confidence
intervals for each cohort are shown in parentheses.

Note: Number in bold type indicated with #.

TABLE 4.
Estimates of the mantle at which 50% of the jumbo squid are
captured (MLc), the r parameter, and residuals (SSQ).

Year       r             MLc             SSQ

2000       0.22          69.09           0.008
           (0.20-0.24)   (68.52-69.41)
2001       0.13          60.31           0.005
           (0.12-0.14)   (59.83-60.73)
2002       0.13          60.90           0.017
           (0.11-0.14)   (60.01-61.81)
2003       0.10          71.35           0.033
           (0.09-0.11)   (69.98-72.72)
2004       0.15          52.98           0.005
           (0.14-0.16)   (52.50-53.45)
2005       0.19          56.61           0.001
           (0.18-0.20)   (56.37-56.86)
2006       0.17          58.21           0.002
           (0.16-0.18)   (57.94-58.48)
2007       0.12          59.08           0.032
           (0.10-0.14)   (57.85-60.32)
2008       0.14          56.40           0.012
           (0.12-0.15)   (55.68-57.13)
2009       0.16          42.89           0.026
           (0.13-0.18)   (41.91-43.88)

The confidence intervals for MLc and r are shown in parentheses.
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