Growth, mortality, recruitment, and yield of the jumbo squid (Dosidicus gigas) off Guaymas, Mexico

Fisheries Research 79 (2006) 38–47

Growth, mortality, recruitment, and yield of the jumbo squid (Dosidicus gigas) off Guaymas, Mexico Manuel O. Nev´arez-Mart´ınez a,∗ , Francisco J. M´endez-Tenorio a , Celio Cervantes-Valle a , Juana L´opez-Mart´ınez b , Myrna L. Anguiano-Carrasco a b

a Instituto Nacional de la Pesca, CRIP Guaymas, Calle 20 Sur No. 605, Guaymas, Sonora, C.P. 85400, Mexico Centro de Investigaciones Biol´ogicas del Noroeste, S.C. Apartado Postal 349, Guaymas, Sonora, C.P. 85454, Mexico

Abstract This paper reports on the population dynamics of Dosidicus gigas from the Gulf of California over the period of the 1995–1996 to 2001–2002 fishing seasons. Data were collected on mantle length, individual weight, and total catch. The D. gigas catches varied, with the lowest landings (1970 t) in the 1997–1998 fishing season and the highest (41,330 t) in 2001–2002. Mantle length ranged from 16 to 96 cm. The mantle length–mass relationship for all seasons showed allometric growth. Growth and natural mortality of D. gigas varied between seasons. The analysis of cohorts showed high interannual variability in annual fishing mortality, annual exploitation rate, recruitment, and mean abundance. The Thompson–Bell predictive model indicated that in some seasons the maximum sustainable yield could have been obtained with 30–50% of the current fishing mortality. However for other seasons the maximum sustainable yield could have been obtained with a current or greater fishing mortality. The fishing mortality associated with the maximum sustainable yield, FMSY , did not necessarily coincide with the fishing mortality associated with a level of proportional escape of spawning biomass, F%BR . The variability observed in this study is typical of squid populations but impossible to anticipate using the Thompson–Bell model. Consequently, auxiliary information (i.e. from research cruises) reflecting such variability in recruitment is needed to make accurate predictions and efficiently manage these resources. Extreme care should be taken in using these methods alone to predict future yields of D. gigas. © 2006 Elsevier B.V. All rights reserved. Keywords: Dosidicus gigas; Growth; Natural mortality; Recruitment; Predictive model; MSY; F%BR

1. Introduction The jumbo squid Dosidicus gigas (d’Orbigny, 1835) is a true pelagic species widely distributed in the eastern Pacific Ocean between 40◦ N and 47◦ S and to 140◦ W at the equator (Nesis, 1983; Ehrhardt et al., 1983; Nigmatullin et al., 2001). The main habitats of D. gigas are the waters of the California and Peru currents and their derivatives, and their distribution is approximately coincident with the isoline of the average phosphate concentration of 0.8 mg P-PO4 3− /m2 in the 0–100 m layer (Nigmatullin et al., 2001; Tafur et al., 2001). This squid species is found off the continental shelf from the surface to at least 1200 m in depth, can reach a ∗

Corresponding author. Tel.: +52 622 2225925; fax: +52 622 2221021. E-mail address: [email protected] (M.O. Nev´arez-Mart´ınez). 0165-7836/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fishres.2006.02.011

mantle length of up to 120 cm, and can weigh up to 65 kg (Nigmatullin et al., 2001). Three groups have been distinguished on the basis of the mantle length of adult males and females; small (13–26 cm and 14–34 cm, respectively), medium-sized (24–42 cm and 28–60 cm, respectively), and large (>40–50 cm and 55–65 to 100–120 cm, respectively). The first group occurs in the near-equatorial area, the second over the whole species range, and the third at the northern and southern peripheries of the species range (Nigmatullin et al., 2001). Reproduction is year-round with a main peak between October and April. The size at first maturity is 25–45 cm for females and 18–51 cm for males (Ehrhardt et al., 1983; Morales-Boj´orquez et al., 2001; Tafur et al., 2001). Studies of age and growth, using analyses of mantle length frequency distributions and ageing analyses using statoliths, show D. gigas grows quickly and does not live for more than two years (Masuda et al., 1998; Hern´andez-

M.O. Nev´arez-Mart´ınez et al. / Fisheries Research 79 (2006) 38–47

Herrera et al., 1998; Arg¨uelles et al., 2001; Nigmatullin et al., 2001). The world squid catch has increased substantially over the last two decades and there is evidence to suggest that overfishing groundfish stocks has had a positive impact on D. gigas productivity (Rodhouse, 2001). D. gigas supports an important fishery in the eastern Pacific Ocean, mostly off the Peruvian coast in the southern hemisphere and in the Gulf of California in the northern hemisphere (Yamashiro et al., 1998; Morales-Boj´orquez et al., 2001), where the total catch reached about 140,000 t in the Gulf of California during 1996 and 1997, and 190,000 t off Peru in 1994. The fishery for D. gigas has been developed in the Gulf of California and comprises three fleets: an artisanal fleet (small boats with outboard motors, called pangas) based in Santa Rosal´ıa, Baja California Sur, and an artisanal fleet and a vessel fleet (shrimp trawler) adapted to take six to ten fishermen at Guaymas, Sonora (Fig. 1). In all three fleets the fishing gear is hand jigs with four to six rings of barbless hooks (Nev´arez-Mart´ınez et al., 2000; Morales-Boj´orquez et al., 2001). Fishing occurs between April and September in Santa Rosal´ıa and between October and July in Guaymas (Hern´andez-Herrera et al., 1998; Morales-Boj´orquez et al., 2001). Occasionally D. gigas are caught along the western coast of the Baja California peninsula, Mexico (Ehrhardt et al., 1983; Morales-Boj´orquez et al., 2001; Nev´arez-Mart´ınez et al., 2000). A high abundance of D. gigas during 1994 led to the increased development of the commercial fishery, which has since shown a high level of interannual catch variabil-

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ity (Morales-Boj´orquez et al., 2001). D. gigas is a resource that has periods of high catch and greatly decreased catch (Nev´arez-Mart´ınez et al., 2000; Morales-Boj´orquez et al., 2001). These fluctuations, in addition to the occasional presence of large volumes of D. gigas along the western coast of the Baja California peninsula (Morales-Boj´orquez et al., 2001), have lead some researchers to propose that the D. gigas population may leave the Gulf of California when environmental conditions are not favourable, particularly during an El Ni˜no event (Ehrhardt et al., 1983; Klett, 1996). This would imply that the D. gigas catch in the Gulf of California, like in other regions, is largely determined by the effects of environmental variability on the abundance and/or the availability of this resource to the fishing fleet (Rodhouse, 2001). Another cause of interannual variability in the catch can be changes in biomass caused by interannual changes in the population characteristics: growth, natural mortality, and recruitment. This paper describes interannual variability in these characteristics and discusses the effects of this variability on the yield of the D. gigas fishery off Guaymas, Mexico. The paper also discusses the use of auxiliary information (i.e. research cruises) in managing the fishery.

2. Methods Data were analyzed for the 1995–1996 to 2001–2002 fishing seasons. Biological data were collected on a weekly basis

Fig. 1. Gulf of California, Mexico, showing Dosidicus gigas fishing grounds.

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at the port of Guaymas during each of the seven fishing seasons. First, a random sample of 50–100 specimens of D. gigas was taken and the mantle length of each individual was measured. A subsample of 20–25 specimens was then taken and the mantle length and individual mantle mass was recorded. Catch data were obtained once every 2 weeks from the Subdelegacion Federal de Pesca (Federal Fishing Office) in Guaymas. This information corresponded to commercial landings by the artisanal fleet and vessel fleet fishing in the central part of the Gulf of California, mainly off Guaymas. The power equation used to estimate the mantle length–mass relationship was M = aMLb where M is the mass (in kg), ML the mantle length (in cm), a the y-axis intercept, and b is the slope. This equation, in conjunction with the total catch, is used later 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 of Pauly (1984) P=

1 1 − e−r(L−L50)

where P is the catch probability at mantle length L, L the midpoint of the length interval, r the intercept, L50 the Lc (in cm), and e is the exponential function. The mantle length frequency distribution was analyzed for monthly periods for each fishing season to obtain annual growth parameters, incorporating an oscillatory function in the von Bertalanffy model (Cloern and Nichols, 1978) Lt = L∞ (1 − e−[K(t−t0 )+C(K/2π) sin 2π(t−ts )] ) where Lt is the mantle length (in cm) at time t, L∞ the asymptotic mantle length (in cm), K the growth coefficient (per year), t0 the time at zero length, C the control of 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). The phi-prime index φ (Sparre et al., 1989) was used to investigate whether there were differences in the D. gigas growth curve between years. The equation is φ = log10 K + 2 log10 L∞ where L∞ is the asymptotic mantle length and K is the growth coefficient (per year). The φ anomaly (anom) was calculated using 
 i=n   i=1 φ anom = φy − n

where φ is the growth performance index, n the number of years, and y is the year index. Natural mortality (M) was estimated using two empirical methods; the Pauly (1980, 1987) equation ln Mp = −0.0152 − 0.279 ln L∞ + 0.6543 ln K+0.463 ln T where L∞ is the asymptotic mantle length (in cm), K the growth coefficient (per year), and T is the average annual temperature of the habitat in ◦ C, and the Jensen (1996) formula Mj = 1.5K 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 length-based virtualpopulation analysis (length-VPA) following Jones (1984). This required a length composition of the total catch, and needed values of L∞ , K, M, a, and b. The equation of cohort analysis (Pope, 1972) converted to length (size) (Jones, 1984) is Nsize1 = (Nsize2 Xsize1 ,size2 + Csize1 ,size2 )Xsize1 ,size2 where Nsize1 and Nsize2 are the abundance (in number) for the beginning (L1 ) and ending (L2 ) length interval i, Csize1 ,size2 is the catch (in number) for the length interval i, and Xsize1 ,size2 is the natural mortality factor for the length interval i. Xsize1 ,size2 was defined by Jones (1984) as  Xsize1 ,size2 =

L∞ − L1 L∞ − L 2

M/2K

The equation that allows the estimation of the abundance (in number) of the D. gigas for the largest length interval (Nlargestsize1 ) is (Jones, 1984) Nlargestsize1 =

F Clargestsize1 ,size2 Z

To begin the calculations, it was necessary to assign, or to assume, a value of exploitation rate (F/Z) for the largest length interval, which was taken as 0.5 (according to the convergence analysis (Pope, 1972; Jones, 1984)). Because Csize1 ,size2 , the catch (in number) by length interval, and the abundance for the largest length interval are known, it is possible to calculate backward for the abundance (in number) for the rest of the successively smaller length intervals (Jones, 1984). In this method the abundance estimated for the smallest length inteval is the magnitude of the recruitment (R, in number). The exploitation rate, Ei , was estimated for each length interval after Jones (1984) as Ei =

Csize1 ,size2 Nsize1 − Nsize2

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The fishing mortality (Fi ) for each length interval was given by Jones (1984) as   Ei Fi = M 1 − Ei To estimate the average abundance (Nmi , in number) present in a length interval at any particular moment, the abundance to length interval i should be adjusted by the time (t) that the animals spend in each length interval. So, the average ¯ y ) was obtained using the equation of annual abundance (N Jones (1984) ¯y = N



Nmi t =

 Nsize − Nsize 1 2 Z

Once values for Fi and Ni were estimated, the average annual fishing mortality (F¯ y ) was estimated as  F i Ni F¯ y =  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 ¯y = E

F¯ y ¯ Fy + M y

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where Xsize1 ,size2 is the same natural mortality factor as used in the Jones length-based cohort analysis. To calculate the yield (catch in t) by length interval, the catch, Csize1 ,size2 (in numbers), must be multiplied by the mean mass of the mantle length interval, Msize1 ,size2 , which is obtained from (Sparre et al., 1989)   size1 + size2 b Msize1 ,size2 = a 2 where a and b are the parameters of the mantle length–mass relationship. The yield (in t) of this length interval is then given by Ysize1 ,size2 = Csize1 ,size2 Msize1 ,size2 During the time t that it takes a cohort to grow from size1 to size2 , 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 (in t) by length interval is Bmi t = Nmi tMsize1 ,size2

The annual yield (in t) is simply the sum of the yield of all length intervals The variations of the future yields (Y, in t) and average annual  biomass (Bm , in t) of the D. gigas population as a function Y= Yi of changes in the fishing mortality (F) were explored using the predictive length-based Thompson–Bell model (Sparre and the estimate of the annual average biomass (in t) during et al., 1989). The Thompson–Bell method involves two main the life span of a cohort, or of all cohorts during a year is stages: (1) essential inputs and (2) the calculation of outputs  in the form of predictions of future yields and biomass levels ¯ = ¯ i ti B B (Sparre et al., 1989). The main input is an array of fishing mortality (F) values The index i refers here to the length interval (sizei , sizei+1 ). per length intervals. It is customary to use a fishing mortality New values of fishing mortality can be obtained by mularray that has been obtained from a cohort analysis. Another tiplying the reference array of fishing mortality (F) values as important input parameter is the number of recruits (R) and a whole by a certain factor, noted as fc (Sparre et al., 1989). the Xsize1 ,size2 , the natural mortality factor for the length interBy making a whole series of calculations with different valval i, which must be the same as the one used in the cohort ues for fc (from 0 to 3, changing each by 0.1), graphs can analysis (Sparre et al., 1989). The model also requires the be drawn that illustrate clearly the effects of changes in F mantle mass of D. gigas per mantle length interval. on the yield (in t) and the average biomass (in t). Finally, The output of the model is in the form of predictions of the maximum sustainable yield (MSY), the fishing mortality the number at the lower limit of the length interval, Nsize1 , associated with the maximum sustainable yield FMSY , and catch in numbers, the total number of deaths, the yield (Y, F%SB (the value of the fishing mortality that corresponds to in t), and the biomass (Bm , in t), all per length interval, and a proportional escape of the spawning biomass, in percent) related to values of F for each length interval. Finally, the are estimated for all seasons. In this fishery, a target value of total catch (in numbers), mean biomass (in t), and yield (in t) 40% has been used as a reference point for the exploitation are obtained (Sparre et al., 1989). of D. gigas in the Gulf of California (Nev´arez-Mart´ınez and The formulae are slightly different and are derived from Morales-Boj´orquez, 1997; Hern´andez-Herrera et al., 1998; those used for the Jones length-based cohort analysis (Sparre Morales-Boj´orquez et al., 2001). et al., 1989)   1/(Xsize1 ,size2 − (Fsize1 ,size2 /(Fsize1 ,size2 + M))) Nsize2 = Nsize1 Xsize1 ,size2 − (Fsize1 ,size2 /(Fsize1 ,size2 + M))

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Fig. 2. Annual D. gigas landings in Guaymas, Mexico, for the 1995–1996 to 2001–2002 fishing seasons.

3. Results Catches of D. gigas varied from 1970 t (1998–1999) to 41,330 t (2001–2002) (Fig. 2). The mantle length frequency distribution varied for the seven fishing seasons, each having one or two modes per year. The intervals of mantle length in the catches were 24–88 cm for 1995–1996, 16–88 cm for 1996–1997, 16–92 cm for 1997–1998, 16–76 cm for 1998–1999, 28–88 cm for 1999–2000, 24–92 cm for 2000–2001, and 26–96 cm for 2001–2002 (Fig. 3). The mean mantle length (Lm ) and the mantle length at first capture (Lc ) was 36–63 cm (Table 1). The length–mass relationship for almost all seasons showed positive allometric growth (b significantly different from 3, Student’s t-test P < 0.01) (Fig. 4 and Table 1). For the 1996–1997 season the jumbo squid showed a negative allometry (P < 0.01). The parameters adjusted for the von Bertalanffy growth function for each season are summarized in Table 1. In all cases C (the parameter that defines the magnitude of the oscillation) was 0, and when C = 0 the equation reduces to the ordinary von Bertalanffy equation, for C = 0 implies there is no seasonality in the growth rate of D. gigas (Fig. 5). The growth in D. gigas had interannual variations with values of coefficient of growth, K per year, from 1.05 to 1.30, asymp-

totic mantle length (L∞ ) from 90 to 98 cm, and the growth performance index (φ ) from 4.373 to 4.504 (Table 1 and Fig. 6). The estimates of natural mortality rate using the Pauly (1980, 1987) and Jensen (1996) empirical methods were 1.02 ≥ Mp ≥ 1.27 and 1.57 ≥ Mj ≥ 1.95 (Table 1), and showed a similar pattern of interannual variation (Fig. 7). The analysis of cohorts indicated that recruitment of D. gigas (in number) had important variations, being estimated at 25.4 million for 1995–1996, 2.6 million for 1997–1998, and 37.8 million for 2001–2002 (Fig. 8(a)). The same pattern is shown for mean abundance (Fig. 8(b)). The annual average fishing mortality had a high interannual variability, 0.44 per year < F < 3.6 per year (Fig. 8(c)), and the average exploitation rate peaked (at 0.7 per year) in 1998–1999, with the minimum values (0.24 and 0.22 per year) observed in the seasons immediately before and after (Fig. 8(d)). The Thompson–Bell predictive model indicated that for the 1995–1996, 1996–1997, and 1998–1999 seasons the maximum sustainable yield (MSY) could have been obtained with 30–50% of the fishing mortality used (Fig. 9). However, although the MSY in the 1999–2000 season could have been obtained with a higher fishing mortality level, in the 2000–2001 and 2001–2002 fishing seasons the MSY could be obtained with the current fishing levels (Fig. 9). The same pattern was observed in the fishing mortality associated with a level of proportional escape (F%BR ), in this case %BR = 40%. This study found that FMSY did not necessarily coincide with F%BR , with F%BR sometimes higher than FMSY and vice versa (Fig. 9).

4. Discussion The catch of D. gigas observed between 1995–1996 and 2001–2002 showed a high variability, a characteristic that has been observed in this species off Peru (Yamashiro et al., 1998; Taipe et al., 2001) and also in other cephalopod species and in fish and crustaceans (Sakurai et al., 2000; Anderson and Rodhouse, 2001; Nev´arez-Mart´ınez et al., 2001; L´opezMart´ınez et al., 2003). The decrease in the catch in the 1997–1998 and 1998–1999 seasons was probably related to

Table 1 Parameters of the mantle length–mass relationship (a, b), von Bertalanffy model (L∞ , K, t0 ), growth performance index (φ ), average mantle length (Lm ), mantle length at first capture (Lc ), and natural mortality (Jensen, Mj , and Pauly, Mp , equation) for D. gigas sampled at Guaymas, Mexico Parameter

1995–1996

1996–1997

1997–1998

1998–1999

1999–2000

2000–2001

2001–2002

Lm (cm) Lc (cm) a b L∞ (cm) K per year t0 (years) φ Mj per year Mp per year

58.7 57.8 0.6 × 10−5 3.2913 94.0 1.10 −0.091 4.431 1.65 1.11

55.8 53.7 5.0 × 10−5 2.7806 95.0 1.10 −0.091 4.441 1.65 1.12

62.1 59.9 0.3 × 10−5 3.4508 94.0 1.30 −0.077 4.504 1.95 1.27

38.9 35.7 0.4 × 10−5 3.3438 90.0 1.05 −0.097 4.373 1.57 1.03

58.6 56.3 0.21 × 10−5 3.5019 92.0 1.05 −0.096 4.392 1.57 1.02

62.7 61.0 0.1 × 10−5 3.646 95.4 1.09 −0.092 4.440 1.63 1.05

63.1 61.2 0.82 × 10−5 3.1582 98.0 1.11 −0.089 4.471 1.66 1.05

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

Fig. 5. Fitted von Bertalanffy model to growth in mantle length of D. gigas off Guaymas, Mexico.

try for the 1996–1997 season (b < 3) and positive allometry (b > 3) for the others. Such an allometric relationship has been observed in other cephalopod species (Gonz´alez et al., 1996; Gabr et al., 1999; Quetglas et al., 2001). This implies that the growth pattern for D. gigas differed between seasons, thus

Fig. 3. Mantle length frequency distributions of D. gigas in commercial landings at Guaymas, Mexico for the 1995–1996 to 2001–2002 fishing seasons.

the environmental variability associated with the 1997–1998 El Ni˜no and 1998–1999 La Ni˜na events (Nev´arez-Mart´ınez et al., 1999; Lluch-Cota et al., 1999), because there were significant catches in those years in the Pacific Ocean off the coast at Bahia Magdalena, Baja California Sur, Mexico (MoralesBoj´orquez et al., 2001). For the D. gigas fishery along the Sonora coast, the relationship between mantle length and mass was allometric and varied between fishing seasons; with negative allome-

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

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

indicating that D. gigas had different weights at the same mantle length. This could be related to variations in feeding and the reproductive strategy, as has been suggested for other species (Mangold et al., 1993; Gabr et al., 1999).

Fig. 9. Yield and mean biomass, as a function of fishing mortality (F), for the D. gigas population off Guaymas, Mexico.

Fig. 8. Annual recruitment magnitude (R, in numbers), average abundance ¯ y , in numbers), annual average fishing mortality (F¯ y ), and annual average (N exploitation rate (E) for D. gigas off Guaymas, Mexico.

The range in mantle length observed in the catches between 1995–1996 and 2001–2002 was similar to that described in other studies of D. gigas (Nesis, 1970; Nigmatullin et al., 2001). The 1997–1998 catch contained only the large-sized D. gigas, while these were poorly represented in the 1998–1999 season, with a higher proportion of small-sized squid caught at this time. The variability in the mantle length structure for this period can possibly be attributed to the El Ni˜no and La Ni˜na events occurring at that time, during which large D. gigas were found in coastal areas outside the Gulf of California (Morales-Boj´orquez et al., 2001). Studies of age and growth in D. gigas have used two different methods: mantle length frequency distributions (Nesis, 1970, 1983; Ehrhardt et al., 1983; Hern´andez-Herrera et al., 1998) and ageing analysis using statolith and gladii (Masuda

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et al., 1998; Arg¨uelles et al., 2001). Using the assumption that modal size groups represented year-classes, Nesis (1970, 1983) estimated that D. gigas grow to 20–35 cm in the first year in Peruvian waters, while Ehrhardt et al. (1983), working with samples from the Gulf of California, described five cohorts and growth curves fitted by a linear function or the von Bertalanffy function, and concluded that D. gigas grow rapidly, could attain 70 cm during their first year, and do not live for more than 2 years. Hern´andez-Herrera et al. (1998) found that D. gigas can grow to 52 cm in the first year. Statolith-ageing studies (Masuda et al., 1998; Arg¨uelles et al., 2001) confirmed the high growth rates of D. gigas revealed by a mantle length frequency distribution analysis, with D. gigas able to reach large mantle lengths in less than a year, but that some very large individuals (>75 cm) can live for 18 months to 2 years (Nigmatullin et al., 2001). Although the ‘one increment-one day’ hypothesis is generally accepted, the statolith growth increments have not yet been validated for D. gigas (Nigmatullin et al., 2001). The growth model used in the present study described growth adequately between the smaller and larger mantle lengths observed in each fishing season, and indicated an almost linear growth rate, with asymptotic lengths and weights far beyond the observed maxima. Dunn (1999) stated that this could be expected where mortality is abrupt, but could also be a consequence of sizespecific migrations, or errors or bias in the samples. In the present study the mantle lengths achieved at age, and the growth rates, are greater than those described by Hern´andezHerrera et al. (1998), and similar to those described by Ehrhardt et al. (1983) for the Gulf of California. They are also similar to those reported by Masuda et al. (1998), Arg¨uelles et al. (2001), and Nigmatullin et al. (2001) for Peru. Despite potential errors caused by sampling (Martinez-Garmendia, 1997), it is likely that the interannual variability found in D. gigas growth rates is a real effect. The causes of the variability may include biotic factors (food, reproduction, predators) and abiotic factors (temperature, light, salinity) (Forsythe and Van Heukelem, 1987). As Dunn (1999) stated, the important implications are that published growth parameters cannot be used for describing separate stocks, and that calculated weights at-age from 1 year cannot be used to infer numbers at-age from catch data for another year. Interannual variability in the natural mortality of D. gigas was high considering the range in values obtained (1.57–1.95 per year). These changes reflect population dynamics and the effects of environmental variability on stock dynamics and can affect estimates of population abundance and fishing mortality rate (and also exploitation rate) when not taken into account in stock assessment models (Anderson and Rodhouse, 2001; Rodhouse, 2001). Variability in the exploitation pattern by size shows the D. gigas population response to prevailing conditions in the Gulf of California, where interannual variability in the environment is the main source of variation in the ecosystem (Lavin et al., 1997), affecting resident populations (Lluch-Cota et al., 1999) such as D. gigas and other biotic components such as

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the small pelagic fish that represent an important part of the diets (Ehrhardt, 1991). This interannual variability is most obvious during years in which El Ni˜no (and La Ni˜na) events occur and is reflected in the mantle length structure present in the catch. The annual average fishing mortality and exploitation rate for D. gigas showed high interannual variability, with greater variation between 1997–1998 and 1999–2000, coincident with the pattern for fishing mortality estimated by RiveraParra (2001) for this species in the Gulf of California. This contrasts with the situation for mean abundance and recruitment, which could be interpreted as a consequence of fishing effort used. However, the important point is that with low values of mean abundance and recruitment in the 1997–1998 and 1998–1999 fishing seasons, D. gigas later showed the highest values in mean abundance and recruitment. This surprising fact has been reported for other aquatic species in other regions of the world (Sheridan, 1996; Atkinson et al., 1997; Nev´arez-Mart´ınez et al., 2001). There was a considerable decrease in mean abundance and recruitment in the year of the strongest El Ni˜no event of the twentieth century and the following La Ni˜na event, which has been suggested to have had important repercussions in the D. gigas fishery and for other species in the Gulf of California (Nev´arez-Mart´ınez et al., 1999; Lluch-Cota et al., 1999) and other places in the world (Waluda et al., 1999; Anderson and Rodhouse, 2001; Rodhouse, 2001). The results presented here highlight factors important in terms of fishing management. Under the fundamental assumption of the stock assessment model – constant recruitment and natural mortality (Jones, 1984; Sparre et al., 1989) – the size of the population in the period 1997–1999 would not have been greater than 8000 t (a value represented by the virgin biomass, when F = 0). In spite of a high level of exploitation (E > 0.6 per year), the recruitment increased in such a way that it supported a growing catch in the period 1999–2002. The assumption of constant recruitment and natural mortality was not achieved. In the event of management measures taken on the basis of the results obtained in 1997–1999 (or 1995–1997), the recommendation had been to maintain the catch at a lesser level than the actual or optimum level. In fact very important favourable (or adverse) changes were occurring in recruitment levels and mean biomass, promoted by environmental conditions within the Gulf of California. Evidence of environmental change within the Gulf of California, starting in late 1997, was first the presence of warmer surface water temperatures and then colder surface water temperatures, caused by the El Ni˜no and La Ni˜na events (Lluch-Cota et al., 1999). Before and after that period the surface temperature had average values. Exploratory fishing indicated that D. gigas abundance was higher in 1996 than at any time in 1998 (Nev´arez-Mart´ınez, Unpublished data), and was also higher in 2002 (Nev´arez-Mart´ınez, Unpublished data). Because cruise information showed low D. gigas abundance throughout 1998 (Nev´arez-Martinez, Unpublished data), the present authors advised not allowing more fish-

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ing permits for the first half of 1998 and the first half of 1999. Based on abundance estimated from cruise data in May 1999 (Nev´arez-Martinez, Unpublished data) the present authors advised allowing more fishing permits from the start of the second half of 1999. The average yield observed in the 1999–2000 and 2000–2001 fishing seasons was 13,500 t. The catch continued to grow (40,000 t in 2001–2002) and cruise data showed the state of the D. gigas population to be good. Predictions using the Thompson–Bell method are not reliable for populations which exhibit large, unpredictable interannual fluctuations in abundance and recruitment, such as is the case for D. gigas (Anderson and Rodhouse, 2001), particularly in periods of transition when the stability assumed by the model is not achieved. Consequently, auxiliary information is needed (such as from research cruises) to describe abundance and recruitment variability and so enable accurate predictions and efficient management of these resources. The outcome of this study emphasises that much care must be taken in applying these methods in the D. gigas fishery, an issue that has been identified in relation to other fishing resources (Nev´arez-Mart´ınez et al., 1997).

Acknowledgements We thank Ellis Glazier who edited the English-language manuscript. We thank Claire Waluda for her comments and suggestions on this paper and two anonymous reviewers who provided helpful comments on the manuscript. This research was supported by grants from the Centro Regional de Investigacion Pesquera de Guaymas, Instituto Nacional de la Pesca (INP).

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