Population dynamics of the jumbo squid (Dosidicus gigas) in the 2002–2008 fishing seasons off Guaymas, Mexico

Fisheries Research 106 (2010) 132–140

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Population dynamics of the jumbo squid (Dosidicus gigas) in the 2002–2008 fishing seasons off Guaymas, Mexico Manuel O. Nevárez-Martínez a,∗ , Enrique Morales-Bojórquez b , Celio Cervantes-Valle a , J. Pablo Santos-Molina a , Juana López-Martínez c a b c

Instituto Nacional de Pesca, CRIP Guaymas, Calle 20 Sur No. 605, C.P. 85400, Guaymas, Sonora, Mexico Centro de Investigaciones Biológicas del Noroeste, S.C. Mar Bermejo 195, Col. Playa Palo de Santa Rita, C.P. 23090, La Paz, Baja California Sur, Mexico Centro de Investigaciones Biológicas del Noroeste, S.C. Carretera a las Tinajas s/n, C.P. 85454, Guaymas, Sonora, Mexico

a r t i c l e

i n f o

Article history: Received 16 April 2010 Received in revised form 31 July 2010 Accepted 9 August 2010 Keywords: Dosidicus gigas Size structure Natural mortality Recruitment F%BR

a b s t r a c t We report on the population dynamics of Dosidicus gigas off Guaymas from the 2002–2003 to 2007–2008 fishing seasons. The study was supported by the catch-at-length data of the commercial fleets. The results showed a large variation in recruitment because during some fishing seasons the recruitment was poor. This condition in the population may also be impacted by migration, a new distribution of jumbo squid in the eastern North Pacific, or the changes in the California current. We identified a pattern in the variability ˜ conditions in the California current are coincident of recruitment. Warmer waters caused by the El Nino with low recruitment. Cooler waters identified with negative anomalies in the sea surface temperature ˜ were related to high recruitment. Our time-series showed a reduction in recruits and caused by La Nina a fall in the mean biomass. For the jumbo squid fishery off Guaymas, recruitment determines trends of biomass over time. Our results also showed that for all fishing seasons the proportional escapement was between 59% and 89%, which was higher than the target level of 40%. Consequently, the harvest of jumbo squid is less than the optimum level. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The variability in biomass of the stock of jumbo squid (Dosidicus gigas) in the central Gulf of California has been studied in the past (Hernández-Herrera et al., 1998; Morales-Bojórquez et al., 2001a; Nevárez-Martínez et al., 2000). However, those studies did not analyze time-series. The available information has been useful only on an annual basis, and cannot provide a comparative analysis over time. Thus the future stock and fishery of the jumbo squid remain uncertain and the main goal of this study is therefore is to obtain reliable estimates of the jumbo squid biomass and its trend over time. Nevárez-Martínez et al. (2006) published the first study that analyzed the variation of the biomass of jumbo squid over time, from the 1995–1996 to the 2001–2002 fishing seasons. An estimation procedure based on the length composition of the catch showed changes over time in recruitment, mean abundance, fishing mortality, and exploitation rate. The same procedure was applied to data for the 2002–2003 to 2007–2008 fishing seasons, extending the available time-series. The abundance and distribution of D. gigas in the Gulf of California were affected during the 1997–1998

∗ Corresponding author. Tel.: +52 622 222 5925; fax: +52 622 222 1021. E-mail address: [email protected] (M.O. Nevárez-Martínez). 0165-7836/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fishres.2010.08.003

˜ The catch during these years was less than 4000 t. In midEl Nino. 1998, the biomass was estimated at about 15,000 t and during 1998 the catch was less than 2000 t (Nevárez-Martínez et al., 2006). However, in the area of Bahía Magdalena, Baja California Sur (Pacific Ocean) there was a catch of about 20,000 t (Morales-Bojórquez et al., 2001a). During 1999, the squid population in the Gulf of California showed signs of recovery and the estimated biomass was almost 30,000 t (Nevárez-Martínez et al., 1999). During 1999 and 2000 the catch was about 50,000 t, increasing to about 86,000 t between 2001 and 2004. From 2005 to 2007 catches were reduced by 38%, but in 2008 they increased to 72,000 t. Beddington et al. (1990) and Rosenberg et al. (1990), established a management strategy based on a constant proportional escape, which allows a percentage of residual biomass to remain to spawn. For the jumbo squid fishery, Nevárez-Martínez and Morales-Bojórquez (1997) determined that a 40% residual biomass would be an adequate goal. This management strategy then relies on effort control, the success of which depends on an adequate knowledge of the population dynamics of the species. Catch-at-size analysis is a powerful tool in fisheries research for the estimation of historic stock abundance. It can be used with a limited time-series of data on the age-specific catch and the procedure does not depend on the knowledge of an effective fishing effort, catchability, or gear selectivity.

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in Guaymas, comprising commercial landings by both the artisanal and industrial fleets in the central zone of the Gulf of California, mainly off Guaymas. 2.1. Stock assessment Commercial squid fleet landings, recorded as mantle weights, were converted to number of squid. The power equation used to estimate the mantle length–mantle weight relationship was MW = aMLb , where MW is mantle weight (kg), ML is mantle length (cm), a is the y-axis intercept, and b is the slope. This equation, in conjunction with the total catch, was used to obtain the total number of D. gigas per length interval and used in the cohort analysis. The length at which 50% of the jumbo squid are captured (Lc ) was determined by fitting the logistic model (Pauly and Munro, 1984):

P=

Fig. 1. Gulf of California, Mexico. The shaded area shows the Dosidicus gigas fishing grounds.

Management of the jumbo squid fishery in the Gulf of California could be hampered by insufficient knowledge of the life-history of the species and the lack of total biomass estimates. In our study, we estimated the biomass and important biological parameters such as natural and total mortality, and parameters of individual growth from the 2002–2003 to 2007–2008 fishing seasons. We completed the analysis of the time-series from the 1995–1996 fishing season and discuss the high variability in abundance and catch of D. gigas associated with its recruitment off Guaymas, Mexico. 2. Materials and methods The period analyzed was from the 2002–2003 to the 2007–2008 fishing seasons. Biological data were collected on a weekly basis at the port of Guaymas, Sonora during each fishing season (Fig. 1). The fishing season is based on the availability of the resource to the fishery. The fleet consists of shrimp trawlers adapted with lights and jigs, operating from October every year, after the yield of the shrimp fishery falls. Random samples of the squid landed at the port of Guaymas, Sonora were selected, and the mantle length (cm) and mantle weight (kg) of all specimens recorded. The number of squid sampled each month and fishing season for six fishing seasons is shown in Table 1. Commercial catch data were obtained biweekly from the Subdelegación Federal de Pesca (Federal Fishing Office)

1 (1 − exp−r(L−L50) )

,

where P is the cumulative catch probability at mantle length, L is the midpoint of the mantle length interval, r is the intercept, and L50 is Lc (cm). We analyzed a mantle-length frequency distribution for monthly periods for each fishing season to obtain annual growth parameters by incorporating an oscillatory version of the von Bertalanffy model (Pitcher and Macdonald, 1973; Cloern and Nichols, 1978): Lt = L∞ (1 − e−[K(t−t0 )+C(K/2) sin 2(t−ts )] ), where Lt is the mantle length (cm) at time t, L∞ the asymptotic mantle length (cm), K the growth coefficient (per year), t0 is the time at zero length, C controls the magnitude of the oscillations, and ts is the starting time of the sine (ts – 0.5 is the winter point). Estimates of growth parameters for each season were obtained using ELEFAN I (Pauly and David, 1981; Pauly, 1987; Gayanilo et al., 1989). The growth performance index  (Munro and Pauly, 1983; Pauly and Munro, 1984; Sparre et al., 1989) was used to investigate if there were differences in the growth curve between years. The equation for each year is: y = log10 K + 2 log10 L∞ , where y is the year index. The  anomaly (anom) was calculated using:



i=n   i=1



anom =  y −

n



,

where  combined is the growth performance index, and n is the number of years.

Table 1 Number of squid sampled by month and fishing season at the port of Guaymas, Sonora, Mexico. Month

2002–2003

2003–2004

2004–2005

2005–2006

2006–2007

2007–2008

October November December January February March April May June July August September Total

179 876 800 260 1590 171 282 538 659 100 *

91 163 442 369 355 612 536 554 249 331 530 83 4315

426 591 390 357 418 290 117 267 269 83 * * 3208

* 521 83 383 98 58 122 374 394 319 322 66 2740

* 95 147 413 64 147 117 101 630 554 319 * 2587

377 687 930 3038 471 346 491 105 192 641 93 52 7423

5455

Note: Asterisks denote months when catch was not sampled and blank cells show an absence of catch.

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The natural mortality (M) was estimated using two empirical methods, the Pauly method (Pauly, 1980, 1987): ln Mp = −0.0152 − 0.279 × ln L∞ + 0.6543 × ln K + 0.463 × ln T, where L∞ is the asymptotic mantle length (cm), K is the growth coefficient (per year), and T is the average annual temperature of the habitat in ◦ C; the Jensen method (Jensen, 1996): Mj = 1.5 × K. The length-dependent fishing mortality (F per year), exploitation rate (E per year), recruitment (R, in number), and stock abundance (N, in number) were estimated by a length-based virtual-population analysis (Jones, 1984). This requires a length composition of the total catch and values of L∞ , K, M, a, and b. The equation for cohort analysis (Pope, 1972) converted to length (Jones, 1984) is: Nsize1 = (Nsize2 × Xsize1 ,size2 + Csize1 ,size2 ) × Xsize1 ,size2 , where Nsize1 and Nsize2 are the abundance (number) at the beginning (L1 ) and ending (L2 ) length interval i, Csize1 ,size2 is the catch (number) for the length interval i, and Xsize1 ,size2 is the natural mortality factor for the length interval i. Xsize1 ,size2 is defined by Jones (1984) as: Xsize1 ,size2 =

 L − L M/2K ∞ 1 L∞ − L2

.

The equation that allows the estimation of abundance (number) for the length interval (Nlargest size1 ) comprising the largest animals is (Jones, 1984): Nlargest size1 =

F × Clargest size1 ,size2 . Z

We assumed, a value of 0.5 for the exploitation rate (F/Z) of the largest animals according to the convergence analysis (Pope, 1972; Jones, 1984). The Z parameter is defined as total mortality. Because Csize1 ,size2 , the catch (number) by length interval, and the abundance of the largest animals are known, it is possible to calculate backward for the abundance (number) for the rest of the successively smaller length intervals (Jones, 1984). In this method the abundance estimated for the smallest length interval is the magnitude of the recruitment (R, in number). In marine fisheries, biologists usually refer to recruitment as the first age when fishing occurs (Hilborn and Walters, 1992; Quinn and Deriso, 1999; Haddon, 2001; Myers, 2002). We defined recruitment as the number of individuals at some age or stage added to the exploitable stock in each fishing season because of growth and/or migration into the fishing area (Boyle and Rodhouse, 2005). According to Jones (1984), the exploitation rate Ei , was estimated for each length interval as: Ei =

Csize1 , size2 Nsize1 − Nsize2

.

as: Ei . 1 − Ei

To estimate the average abundance (Nmi , in number) in a length interval at any particular time, the abundance to length interval i should be adjusted by the time (t) that the animals spend in each ¯ y ) is obtained length interval. So, the average annual abundance (N by the equation (Jones, 1984): ¯y = N



Nmi t =

F¯ y =

 Fi × Ni  , Ni

where Ni is the number of survivors to length interval i and y is the year index. The value of the average annual exploitation rate was obtained by: E¯ y =

F¯ y F¯ y + My

.

The variations of the future yields defined as Y (t) and average annual biomass defined as B (t) of the population as a function of changes in the fishing mortality (F) were explored with the predictive length-based Thompson–Bell model (Sparre et al., 1989). The Thompson and Bell method consists of two main stages, (1) essential inputs and (2) the calculation of outputs in the form of predictions of future yields and biomass levels (Sparre et al., 1989). The main input is an array of fishing mortality (F) values per length interval. It is customary to use a fishing mortality array that has been obtained from a cohort analysis. Another important input parameter is the number of recruits (R) and Xsize1 ,size2 , which must be the same as that used in the cohort analysis (Sparre et al., 1989). The model further requires the mantle weight of per mantle-length interval. The output of the model is in the form of predictions of the number at the lower limit of the length interval, Nsize1 , catch in numbers, the total number of deaths, the yield at time t, and the biomass at time t, all by length interval and related to values of F for each length interval. Finally, the total catch (numbers), mean biomass at time t, and yield at time t were obtained (Sparre et al., 1989). The equations are slightly different and are derived from those used for the Jones length-based cohort analysis (Sparre et al., 1989) as:



Nsize2 = Nsize1 ×

1/(Xsize1 ,size2 − (Fsize1 ,size2 /(Fsize1 ,size2 + M))) Xsize1 ,size2 − (Fsize1 ,size2 /(Fsize1 ,size2 + M))



,

where Xsize1 ,size2 is the same natural mortality factor as used in the Jones length-based cohort analysis. To calculate the yield at time t by length interval, the catch, Csize1 ,size2 (numbers) has to be multiplied by the mean weight of the mantle-length interval, MLsize1 ,size2 , which is obtained from:



MLsize1 , size2 = a ×

(MLsize1 )b + (MLsize2 )b 2



,

where a and b are the parameters of the mantle length–mantle weight relationship (Sparre et al., 1989). The yield (t) of this length interval is then given by: Ysize1 ,size2 = Csize1 ,size2 × MLsize1 ,size2 .

The fishing mortality (Fi ) for each length interval was estimated

Fi = M ×

Once values for Fi and Ni were estimated, we estimated the average annual fishing mortality (F¯ y ) as:

 Nsize − Nsize 1 2 Z

.

During the time that it takes a cohort to grow from size1 to size2 (t), the number of survivors decreases from Nsize1 to Nsize2 . The mean number of survivors of that length interval is calculated as (Sparre et al., 1989): Nmi t =

Nsize1 − Nsize2 Zsize1 ,size2

.

The corresponding mean biomass (t) by length interval is: Bmi t = Nmi t × MLsize1 ,size2 . The annual yield (t) is simply the sum of the yield of all length intervals Y = Yi . The estimate of the annual average biomass dur-

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Fig. 2. Annual Dosidicus gigas catch landings in Guaymas, Mexico from fishing seasons 2002–2003 to 2007–2008.

ing the life span of a cohort, or of all cohorts during a year, were expressed as: B¯ =



B¯ i ti .

The index i refers here to the length interval (sizei , sizei+1 ). New values of fishing mortality were obtained by multiplying the reference array of fishing mortality (F) values as a whole by a factor, noted as fc (Sparre et al., 1989). Finally we estimate the maximum sustainable yield (MSY), FMSY , and F%BR (the value of the fishing mortality that corresponds to a proportional escapement of the spawning biomass, in percent) for all seasons. In this fishery, a target value of 40% has been used as a reference point for the exploitation of D. gigas in the Gulf of California (NevárezMartínez and Morales-Bojórquez, 1997; Hernández-Herrera et al., 1998; Morales-Bojórquez et al., 2001b). 3. Results From the 2002–2003 to the 2005–2006 fishing seasons, we observed a fall in the catch of D. gigas, decreasing from 36,200 t to 11,450 t. During the 2006–2007 and 2007–2008 fishing seasons, the catch was 15,000–20,000 t (Fig. 2). The mantle-length frequency distribution varied among the six fishing seasons (Fig. 3). Mean mantle length (Lm ) and the mantle length at first capture (Lc ) varied between 56.6 and 68.1 cm (Table 2). The time-series of mantle-length frequency distribution showed that recruitment was absent or moderately weak in some fishing seasons. During the 2002–2003, 2003–2004 and 2006–2007 fishing seasons, there was a mode in the 26–46 cm ML size-class (recruitment) and a second mode in the 58–70 ML size-class (Fig. 3). During the 2004–2005, 2005–2006, and 2007–2008 fishing seasons, recruits (22–38 cm ML) were absent in the catch-at-length (Fig. 3). The mantle length–mantle weight relationship for all fishing seasons showed positive allometric growth (b significantly different from 3. Student’s t-test, P < 0.01) (Fig. 4, Table 2). The parameters of the oscillatory von Bertalanffy growth function for each fishing season are summarized in Table 2. In all cases C (the parameter that defines the magnitude of the oscillation) was 0. When C = 0 the equation reduces to the ordinary von Bertalanffy equation because C = 0 implies there is no seasonality in growth rate (Fig. 5). Growth in jumbo squid presented interannual variations with values of the coefficient of growth, K/year, from 1.05 to 1.38, asymptotic mantle length (L∞ ) from 93 to 98 cm, and the growth performance index ( ) from 4.373 to 4.504 (differences between years were significantly different, P < 0.05) (Table 2, Fig. 6). Estimates of the natural mortality rate using the Pauly (1980, 1987) and Jensen (1996) empirical methods were 1.07 ≥ Mp ≥ 1.31 and 1.58 ≥ Mj ≥ 2.1 (Table 2). Both estimates showed a similar pattern

Fig. 3. Mantle-length frequency distributions for D. gigas in commercial landings at Guaymas, Mexico for fishing seasons 2002–2003 to 2007–2008.

of interannual variation, although they were higher by the Pauly method than by the Jensen method (Fig. 7). In this study, we completed the time-series of recruitment with data reported by Nevárez-Martínez et al. (2006). The analysis of cohorts indicated that recruitment (number of individuals) had a large variation. Recruitment strongly declined during the 1997–1998 and the 2004–2005 fishing seasons, both coincident ˜ years 1997 (Hayward, 2000; Lea and Rosenblatt, 2000) with El Nino and 2004 (Goericke et al., 2005). From 2002–2003 to 2004–2005, there was a decline from 37 million to 7.4 million, followed by a recovery to 28 million during 2006–2007 (Fig. 8a). The same pattern was evident for mean abundance (Fig. 8b). Annual fishing mortality also exhibited high interannual variability (0.11/year < F < 0.53/year – Fig. 8c), whereas the average exploitation rate showed a peak of 0.25/year during 2005–2006, varying between 0.06/year and 0.25/year (Fig. 8d). The Thompson–Bell predictive model indicated that for all seasons the maximum sustainable yield (MSY) could have been obtained with the highest levels of fishing mortality (Fig. 9). The same pattern was observed in the fishing mortality associated with a level of proportional escape (F%BR ) (when first defined it was shown as F%BR , in this case %BR = 40%), and FMSY did not coincide

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Table 2 Parameters of: mantle length–mass relationship (a, b), von Bertalanffy growth model (L∞ , K, t0 ), growth performance index ( ), average mantle length (Lm ), mantle length at first capture (Lc ) and natural mortality (by the Jensen (Mj ) and Pauly (Mp ) methods) for D. gigas sampled at Guaymas, Mexico. Standard error (SE) in parenthesis. Parameter

2002–2003

2003–2004

2004–2005

2005–2006

2006–2007

2007–2008

Lm (cm) Lc (cm) a

62.0 (0.18) 59.5 (0.29) 1.11 × 10−5 (2.00 × 10−6 ) 3.2147 (0.0408) 95.0 1.20 −0.0873 4.478 1.80 1.19

58.4 (0.21) 56.6 (0.33) 1.73 × 10−5 (1.00 × 10−6 ) 3.1007 (0.0156) 93.0 1.38 −0.076 4.521 2.07 1.31

64.8 (0.17) 63.1 (0.11) 1.06 × 10−5 (3.00 × 10−6 ) 3.2253 (0.0700) 94.5 1.28 −0.0818 4.502 1.92 1.23

63.3 (0.18) 61.8 (0.18) 0.54 × 10−5 (2.20 × 10−6 ) 3.2857 (0.0658) 98.0 1.05 −0.0995 4.447 1.58 1.07

67.3 (0.32) 66.9 (0.67) 0.85 × 10−5 (1.94 × 10−6 ) 3.1882 (0.0382) 96.0 1.10 −0.0953 4.450 1.65 1.12

68.8 (0.11) 67.0 (0.09) 0.30 × 10−5 (1.36 × 10−6 ) 3.4482 (0.0589) 96.0 1.25 −0.0835 4.505 1.88 1.20

b L∞ (cm) K (year−1 ) t0 (years)  Mj (year−1 ) Mp (year−1 )

Fig. 4. Mantle length–mantle weight relationship for D. gigas in commercial landings at Guaymas, Mexico.

with F%BR , the latter being greater, except during the 2003–2004 fishing season (Fig. 9). 4. Discussion In the Gulf of California the early development of the jumbo squid fishery occurred in the absence of fishery information. Several years of fishery data were needed before a time-series of biological and ecological information was available. This study showed that from the 2002–2003 to 2007–2008 fishing season, the stock of jumbo squid off Guaymas was mainly composed of one annual cohort. In contrast in the Gulf of California and in the western waters of the California peninsula (Pacific Ocean) there appears to be a complex intrapopulation structure with multiple intra-annual cohorts (Morales-Bojórquez et al., 2001c), as evidenced by the variability in catchability of the different cohorts in the population. Díaz-Uribe et al. (2006) showed, by histological analysis of ovaries of D. gigas, a pattern of asynchronous maturity in oocytes, and ovary tissues. Markaida and Sosa-Nishizaki (2001) found that the jumbo squid reproduction in the Gulf of California occurs throughout the year, with no apparent peaks, and they assumed that it probably takes place in different zones around the study area. Consequently, when the distribution of hatching dates of jumbo squid

Fig. 5. Growth of the mantle of D. gigas off Guaymas, estimated using the von Bertalanffy model for each fishing season.

was analyzed, the presence of a complex population structure with multiple intra-annual cohorts was observed (Markaida et al., 2004). The same intrapopulation structure was reported off the western coast of the Baja California Peninsula (Mejía-Rebollo et al., 2008). However, off Guaymas, Hernández-Herrera et al. (1998) found evidence of only one cohort with an annual recruitment in May at

Fig. 6. Interannual variability in the growth of D. gigas off Guaymas, Mexico.

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Fig. 7. Annual estimate of natural mortality for D. gigas off Guaymas, Mexico, using the methods of Jensen (Mj ) and Pauly (Mp ) equations.

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6 months of age. Markaida et al. (2004) reported the age of recruitment to the fishery of jumbo squid to be between 155 and 180 days old. Hernández-Herrera et al. (1998) assumed that the recruitment during this month is the most important and sustains the squid fishery during the fishing season. At least a second cohort, not targeted by the fleets off Guaymas, is characterized by a low abundance and yield of large individuals. This cohort has low abundance and yield and is not a target of the fleets off Guaymas. The recruitment in this zone of the Gulf of California could be the result of spawning at another time and area, which was proposed by Markaida and Sosa-Nishizaki (2001). In our data, the fishing seasons of 2003–2004 and 2006–2007 showed the presence of more than one cohort. However, the common pattern is the presence of only one cohort. Nevárez-Martínez

¯ y , in numbers), annual average fishing mortality (F¯ y ), and annual average exploitation rate (E) Fig. 8. Annual recruitment magnitude (R, in numbers), average abundance (N for D. gigas off Guaymas, Mexico. Data for the fishing seasons of 1995–1996 to 2001–2002 from Nevárez-Martínez et al. (2006).

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Fig. 9. Yield [Y (t)] and mean biomass [B (t)] as a function of fishing mortality (F) of D. gigas population off Guaymas, Mexico. FMSY is the value associated to the maximum sustainable yield (MSY); F%BR is the value of the fishing mortality that corresponds to a proportional escapement of 40% of the spawning biomass.

et al. (2006) reported the same after analyzing seven fishing seasons of which only two had multiple cohorts (1995–1996 and 1996–1997). During the 13 fishing seasons from 1995–1996 to 2007–2008, four fishing seasons had more than one cohort. This information has been inferred from a mantle-length frequency analysis. Markaida et al. (2004) suggested that jumbo squid of the large group (males >40 to 50 cm ML and females >55 to 65 cm ML) in the Gulf of California inhabit upwelling areas, thereby resulting in a larger, late maturing form, perhaps coupled with higher growth rates. Jumbo squid of the medium group mature earlier at small sizes (males >24 to 42 cm ML and females >28 to 60 cm ML) and may inhabit areas or seasons not subject to upwelling, presumably with warmer waters and less availability of food. In the Gulf of California wind-driven upwelling occurs off the eastern coast between November and May and off Baja California between June

and October. We showed evidence that the jumbo squid population off Guaymas is represented by only one cohort. The change in the intrapopulation structure to multiple cohorts matches favorable conditions, as predicted by Cushing’s Match-Mismatch hypothesis (Cushing, 1982). However, according to Markaida et al. (2004) this plausible relationship between growth, reproductive activity, multiple cohorts, and peaks of productivity must be confirmed with data. Our data off Guaymas showed evidence for large individuals with a mantle length of 86 cm. According to the growth model this mantle length represents an age near 1.5 years. We did measure individuals with a mantle length between 88 and 94 cm, but the frequency of these sizes was <3%. The presence of these individuals must be associated to with an age >1.5 years old. Markaida et al. (2004) analyzed the daily rhythm of statolith deposition of

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jumbo squid in the Gulf of California and they assumed that larger squid (>75-cm ML) are older than 1 year, and maximum sizes could even attain a longevity of 1.5–2 years. Mejía-Rebollo et al. (2008) commented that previous studies on jumbo squid aging through readings of statoliths showed that jumbo squid could live between 1 and 2 years. Mejía-Rebollo et al. (2008) and Markaida et al. (2004), found the age of squid (males and females) to be between 12 and 15 months old along the west coast of the Baja California Peninsula and the Gulf of California. Hernández-Herrera et al. (1998) analyzed mantle-length frequency-distribution data, and their individual growth model assumed that jumbo squid live longer than 2 years, something that was not observed in the field. Individuals with this age have not been sampled or identified off Guaymas. Nigmatullin et al. (2001) grouped three categories of mantle length or interspecies groups; small males from 13 to 26 cm ML and females 14 to 34 cm ML, medium-sized males from 24 to 42 cm ML and females 28 to 60 cm ML, and large males >40 to 50 cm ML and females from 55 to 65 cm ML; in this last group there are squid 100 cm ML and larger. The life span of all three groups is approximately 1 year, with the largest individuals of the large group probably living 2 years of age. The intrusion of the warmer waters of the California current ˜ events coincides with low recruitment periods. The during El Nino recovery in recruitment began during the 2000–2001 fishing season and continued to the 2002–2003 fishing season. The year 2000 was characterized by negative anomalies in sea surface tempera˜ year (Durazo et al., 2001) and may ture an indication of a La Nina have triggered the recovery of the subsequent seasons. These patterns appear to show a causal relationship between sea surface temperature and recruitment of D. gigas. Fishing activity can negatively impact habitat complexity and in turn affect the species composition and diversity of an area. However our estimates of biological reference points showed that the estimates of F%BR and FMSY were greater than our reference of 40% of proportional escapement. Consequently, fishing mortality and exploitation rates could be increased without detrimental effects to the population. Although the FMSY from the production model is traditionally calculated using equilibrium analysis and serves as a threshold harvest-rate level in this case, it should not be used as the target harvest-rate The observed variability in the abundance, recruitment, and environment for the jumbo squid fishery are challenging for fishery managers, and may require inventive and innovative approaches to stock assessment and fishery management. We showed the first time-series of recruitment and average abundance of D. gigas off Guaymas. We believe that this study provides information about the variability in recruitment and the exploitation rate corresponding to an optimal yield. The methodology we used can provide be estimates of an important biological reference point (%BR) for the management of the jumbo squid fishery in the central Gulf of California. We have provided a possible explanation for the decline of recruitment in the fishing seasons of 1997–1998, 1998–1999, 2004–2005, and 2005–2006. We believe that research cruise data or estimates of relative abundance of this species can improve our estimates. It must be noted that these results are only valid for the jumbo squid population of Guaymas. In the Gulf of California and the Mexican Pacific Ocean jumbo squid show different dynamics and specific management strategies may be required for each region. Finally, we recognize that length-based virtual-population analysis can be biased (Hilborn and Walters, 1992). However, because no age information on the jumbo squid population is necessary, this approach can be applied to populations for which ageing is impractical (e.g. no validated ageing methods, substantial ageing errors). The bias on parameters estimates could be corrected if auxiliary information is employed as a means

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of increasing precision of parameters in the model. The auxiliary information could be hydroacoustic estimation of population size, or survey data on recruitment, the statistical procedure for to use auxiliary information in the catch-at-length analysis was provided by Sullivan et al. (1990). The biomass of jumbo squid in the Gulf of California is commonly estimated from survey data, and catch-per-unit effort data (Morales-Bojórquez et al., 2001a). This alternative approach from catch-at-length data showed similar trends in biomass and recruitment in comparison with alternative models and data, and the method estimated relevant biological information. Despite, successful management of D. gigas fishery requires the identification of an appropriate suite of methods to best meet the needs of the fishery in the region. Acknowledgements We thank the Centro Regional de Investigación Pesquera de Guaymas for support in obtaining biological and statistical data on jumbo squid. We thank Ellis Glazier for editing the Englishlanguage text. One anonymous reviewer and Chinguis Nigmatullin provided helpful comments on the draft, for which we are grateful. This research was supported by grants from the Instituto Nacional de Pesca (INAPESCA). References Beddington, J.R., Rosenberg, A.A., Crombie, J.A., Kirkwood, G.P., 1990. Stock assessment and the provision of management advice for the short fin squid fishery in Falkland Island waters. Fish. Res. 8, 351–365. Boyle, P.R., Rodhouse, P.G., 2005. Cephalopods: Ecology and Fisheries. Blackwell, Oxford. Cloern, J.E., Nichols, F.H., 1978. A von Bertalanffy growth with a seasonally varying coefficient. J. Fish. Res. Board Can. 35, 1478–1482. Cushing, D.H., 1982. Climate and Fisheries. Academia Press, London. Díaz-Uribe, J.G., Hernández-Herrera, A., Morales-Bojórquez, E., Martínez, S., Suárez, C., Hernández, A., 2006. Histological validation of the gonadal maturation stages of female jumbo squid (Dosidicus gigas) in the Gulf of California, Mexico. Cienc. Mar. 32, 23–31. Durazo, R., Baumgartner, T., Bograd, S., Collins, C., de la Campa, S., García, J., GaxiolaCastro, G., Huyer, A., Hyrenbach, D., Loya, D., Lynn, R., Schwing, F., Smith, R., Sydeman, W., Wheeler, P., 2001. The state of the California current 2000–2001: ˜ year. CalCOFI Rep. 42, 29–60. a third straight La Nina Gayanilo, F.C., Soriano, M., Pauly, D., 1989. A draft guide to the Compleat ELEFAN. ICLARM Software 2, 70 pp. Goericke, R., Venrick, E., Mantyla, A., Bograd, S., Schwing, F., Huyer, A., Smith, R., Wheeler, P., Hoof, R., Peterson, W., Chavez, F., Curtis, C., Marinovic, B., Lo, N., Gaxiola-Castro, G., Durazo, R., Hyrenbach, K.D., Sydeman, W., 2005. State of the California Current, 2004–2005: still cool? CalCOFI Rep. 46, 32–71. Haddon, M., 2001. Modeling and Quantitative Methods in Fisheries. Chapman-Hall, Florida. ˜ 1997–98 in the coastal waters of southern California: a Hayward, T.L., 2000. El Nino timeline of events. CalCOFI Rep. 41, 98–116. Hernández-Herrera, A., Morales-Bojórquez, E., Cisneros-Mata, M.A., NevárezMartínez, M.O., Rivera-Parra, G.I., 1998. Management strategy for the giant squid (Dosidicus gigas) fishery in the Gulf of California, Mexico. CalCOFI Rep. 39, 212–218. Hilborn, R., Walters, C., 1992. Quantitative Fisheries Stock Assessment. Choice, Dynamics and Uncertainty. Chapman-Hall, New York. Jensen, A.L., 1996. Beverton and Holt life history invariants result from optimal tradeoff of reproduction and survival. Can. J. Fish. Aquat. Sci. 53, 820–822. Jones, R., 1984. Assessing the effects in exploitation pattern using length composition data (with notes on VPA and cohort analysis). FAO Fish. Tech. Pap. 256, 118. Lea, R.N., Rosenblatt, R.H., 2000. Observations on fishes associated with the 1997–98 ˜ off California. CalCOFI Rep. 41, 117–129. El Nino ˜ Markaida, U., Quinónez-Velázquez, C., Sosa-Nishizaki, O., 2004. Age, growth and maturation of jumbo squid Dosidicus gigas (Cephalopoda: Ommastrephidae) from the Gulf of California, Mexico. Fish. Res. 66, 31–47. Markaida, U., Sosa-Nishizaki, O., 2001. Reproductive biology of jumbo squid Dosidicus gigas in the Gulf of California, 1995–1996. Fish. Res. 54, 63–82. ˜ Mejía-Rebollo, A., Quinonez-Velázquez, C., Salinas-Zavala, C., Markaida, U., 2008. Age, growth and maturity of jumbo squid (Dosidicus gigas D’Orbigny, 1835) off the western coast of the Baja California Peninsula. CalCOFI Rep. 49, 256–262. Morales-Bojórquez, E., Cisneros-Mata, M.A., Nevárez-Martínez, M.O., HernándezHerrera, A., 2001a. Review of stock assessment and fishery research for Dosidicus gigas in the Gulf of California, Mexico. Fish. Res. 54, 393–404. Morales-Bojórquez, E., Hernández-Herrera, A., Nevárez-Martínez, M.O., CisnerosMata, M.A., Guerrero-Escobedo, F., 2001b. Population size and exploitation of

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