Eulerian approach to the estimation of growth rates and population structure of jumbo squid (Dosidicus gigas) in the central gulf of California.
Article Type: Report
Subject: Squids (Physiological aspects)
Growth (Research)
Authors: Zavala, Cesar A. Salinas
Ferreri, Gaston A. Bazzino
Keyl, Friedemann
Pub Date: 08/01/2012
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: August, 2012 Source Volume: 31 Source Issue: 3
Topic: Event Code: 310 Science & research
Product: Product Code: 0912198 Squid NAICS Code: 114112 Shellfish Fishing SIC Code: 0913 Shellfish
Geographic: Geographic Scope: United States Geographic Code: 1USA United States
Accession Number: 303011405
Full Text: ABSTRACT An Eulerian approach was applied through a daily data set (n = 51) on mantle length frequencies of jumbo squid Dosidicus gigas derived from a small jigging fleet (5 vessels), which stayed fishing in the same area off Mulege, central Gulf of California. Data were corrected for observation bias introduced by the fishing gear (jigs) and were used to analyze population structure and growth-related parameters by modal progression analysis. Sexual maturity stages and size structure showed a predominance of medium-size immature specimens, both male and female. Mean size of jumbo squid showed a progressive increment throughout the fishing period that could be associated with growth or migration. Our estimations of growth rates were higher (3.15-3.85 mm/day) than those calculated previously for D. gigas with other methods in the same region (Gulf of California). This apparent overestimation of growth rates could he associated with a bias introduced by migration. In fact, our study area is part of some migratory routes known for this species and could be considered a transitory feeding ground for medium-size jumbo squid. The most possible explanation for the progressive increment of size (mantle length) during the fishing period considers a dynamic interaction between growth and migration.

KEY WORDS: Eulerian observations, growth rates, migratory behavior, jumbo squid, Dodidicus gigas, Gulf of California


The jumbo or Humboldt squid (Dosidicus gigas, D'Orbigny 1835) is endemic to the eastern Pacific Ocean, is considered one of the most important cephalopod species in world fisheries catches (approximately 800,000 t in recent years) (FAO 2011), and is, perhaps, the most abundant middle-size predator in the eastern Pacific Ocean (including the Gulf of California) (Markaida et al. 2007). During its life span, this fast-growing species can attain sizes of up to 50 kg in mass with a mantle length (ML) of 1.2 m (Nigmatullin et al. 2001).

The fishery of jumbo squid in the Gulf of California operates in different areas depending on the distribution and availability of the species. A seasonal pattern has been observed for D. gigas that occurs in the Santa Rosalia area during the summer (May to October) and in the Guaymas area during the winter (November to May) (Markaida & Sosa-Nishizaki 2001). Commercial catches of this species have reached 100,000 t in some years (; however, the strong interannual variability observed in the historical catch data series should not be disregarded (Fig. 1). Many authors suggest that the abundance of jumbo squid is related to migration, feeding, and reproduction patterns or recruitment success (Ehrhardt et al. 1983, Ehrhardt 1991). It was assumed that changes in environmental or oceanographic conditions, such as the occurrence of E1 Nino events or global climate change effects, are the origin of such variability in these endogenous processes (Zeidberg & Robison 2007, Keyl et al. 2008, Bazzino 2010).

A significant interannual variability was also observed in the population structure of jumbo squid in the Gulf of California (Markaida 2006, Nevarez-Martinez et al. 2006, Bazzino et al. 2007). Genetic and phenotypic plasticity have been mentioned as possible sources of differences in maximum size (Nesis 1983, Keyl et al. 2008). Based on statolith studies, its life span is generally assumed to be 1 y, and only the largest animals are thought to attain an age of 2 y (Nigmatullin et al. 2001). In this case, growth rates for different size groups must differ. Other studies have found that age is related to size (Arguelles et al. 2001), which in turn can be interpreted as equal or similar growth rates for all size classes. However, a tag-recapture study in the Gulf of California (Markaida et al. 2005) and a modal progression analysis in Peruvian waters (Keyl et al. 2011) suggest longer possible life spans.

Previous growth studies on jumbo squid used different methodologies, including modal progression analysis (MPA) based on length frequency analysis (LFA), analysis of statolith rings, and tag-recapture experiments. The statolith analyses assumed that statolith rings are laid down daily, although the 1 mark/day assumption has never been tested for D. gigas (Keyl et al. 2011).

Daily growth rates of D. gigas show a wide range of values depending on the estimation method, the study area, and the size of the specimens:

* Southeastern Pacific Ocean (off Chile and Peru): 0.55-2.73 mm/day (200-995 mm/y) (Nesis 1970, Arguelles et al. 2001)

* Gulf of California: 2.00-2.65 mm/day (Markaida et al. 2004), 1.422.26 mm/day (Filauri 2005), and 1.0-1.5 mm/day (tag-recapture) (Markaida et al. 2005)

* Northeastern Pacific Ocean (off the Baja California peninsula): 0.99-2.10 mm/day (Mejia-Rebollo et al. 2008)

The objectives of this study were to analyze daily and weekly ML frequencies from a nontraditional fishing area in the Gulf of California to estimate growth-related parameters by MPA and to describe the population structure (sex ratio, sexual maturity, and size composition) of jumbo squid D. gigas in that area.



Fishing Operations

All fishing operations were performed between June 15, 2005, and August 4, 2005 (51 days), by 5 fishing vessels equipped with automatic jigging machines in a nontraditional fishing area near Mulege and Loreto (central Gulf of California; Fig. 2). During the entire period, the vessels remained anchored and fished in the same point. Biological sampling of jumbo squid was conducted on a daily basis. Stationary sampling results in an Eulerian approach for the analysis.

Jumbo squid were caught with small jigs--a size-selective fishing gear that introduces an observation bias on length frequencies (Keyl et al. 2011). Length selectivity of jigs follows a Gaussian distribution. They are deployed according to the size of the squid present in the area during fishing operations (Nesis 1983, Rathjen 1991).


Biological Sampling

Sex and ML (measured to the nearest centimeter) were recorded, and sexual maturity stages were assigned based on the classification proposed by Lipinski and Underhill (1995): I and II, immature; III, maturing; IV and V, mature; and VI, spent. The length-frequency data set contains 9,054 individuals; the sexual maturity data set contains a subsample (n = 614) of the total data.

Growth Parameters

MPA based on LFA was used for the estimation of growth parameters. The original data set on individual ML was integrated to obtain daily (n = 51) and weekly (n = 8) series of length frequencies grouped into 20- and 10-mm size classes, respectively. The raw length frequencies (daily or weekly) were standardized to 100 to increase comparability between time increments. A multiple-cohort model with Gaussian distribution and observation bias correction was used for the decomposition of the daily and weekly length-frequency distributions (from Keyl et al. 2011):


where parameters a-e determine the Gaussian functions that describe individual cohorts (second term) and the observation function (first term). The observation function corrects the assumed observation bias introduced by the size-selective jigs (for details see Keyl et al. (2011)). Models with and without observation bias were fitted to the data on a daily and weekly basis.

To obtain growth from the LFA, the progression of the size mode of specimens belonging to one similar-size cohort or group obtained during different sampling moments must be linked with a species-specific imminent growth function. Several growth functions have been used in previous studies on cephalopods (Markaida et al. 2004, Semmens et al. 2004, Filauri 2005, Miyahara et al. 2006, Mejia-Rebollo et al. 2008). In addition, the growth function depends on the ontogenic stage of specimens. For example, ommastrephid paralarvae show an exponential growth (Yatsu 2000) whereas for adult squid a nonasymptotic pseudolinear growth function has been proposed, captured in the basic general growth model proposed by Lipinski (2002). A previous MPA for Peruvian jumbo squid that did not take into account juvenile growth and senescence phase used a linear adult growth function (Keyl et al. 2011).

The data only cover the summer season (from June to August) and provide no information on squid smaller than 24 cm in ML or larger than 76 cm in ML, so neither juvenile exponential nor asymptotic growth in the senescence phase can be identifiable from the data. Thus, to analyze the modal progression of a cohort, a simple linear regression corresponding to the adult growth phase of the basic general growth model Lipinski (2002) was applied to the identified maxima of the modes of a cohort. The mean modal progression of a cohort (i.e., the mean growth rate of all individuals of the cohort) is equal to the slope of the regression line resulting from the maxima of all modes belonging to that cohort (Keyl et al. 2011).

Fourier Analysis of Eulerian Observations

A spectral Fourier analysis was performed with daily mean size to explore cyclic patterns in the time series. The objective of such an analysis is to decompose the time series into sinusoidal functions representing possible periodicity in the arrival of new shoals to the fishing area and the consequent departure of older specimens to other areas in the Gulf as part of its migratory routes.

Daily time series was transformed into a 3-day running average to eliminate the high frequency variability. Total mean size and trend line were removed from the transformed data series.


Population Structure

The estimated sex ratios during the fishing period showed similar numbers of males and females. We did not observed significant deviations from the expected value of 1:1, except for week 1 and total data, in which males outnumbered the females significantly (Table 1).

Sexual maturity stages for males and females showed a clear predominance of immature specimens (stages I and II) and a lower proportion of maturing squid (III; Fig. 3). No mature (IV and V) or spent (VI) specimens were registered.

Size structure (ML) of males and females was similar, with presence of medium-size individuals of 24-76 cm in ML and the maximum mode located at an ML of 38-39 cm (Fig. 4). Mean size of jumbo squid showed a progressive increment during the fishing period (Fig. 5). We found significant differences between daily and weekly mean ML (Kruskal-Wallis, P < 0.05).

Growth Parameters: MPA (Daily and Weekly Pooled Data)

Daily Length Frequencies

Original and calculated length frequency data showed a good adjustment with linear growth function ([R.sup.2] [approximately equal to] 0.65). The increase of mean size present in the area during the fishing period (51 days) was 166 mm in ML, which implies a daily growth rate of 3.34 mm/day (Fig. 6). Assuming a constant growth rate during the adult stage (quasilinear growth function), the mean size of squid at 1 y would be larger than 1,200 mm, and therefore considerably larger than any growth rate published until now (Keyl et al. 2011).

Weekly Length Frequencies

Original data also showed an excellent adjustment with linear growth function ([R.sup.2] [approximately equal to] 0.94). The increase in cohort size was 197 mm in ML, resulting in a daily growth rate of 3.85 mm/day and a mean size of 1,278 mm in ML after 1 y. Calculated length frequency data also showed an excellent adjustment with linear growth function ([R.sup.2] ~ 0.95) reflecting an increase of 161 mm in ML in cohort size during the 8 wk the fishing period, and a daily growth rate of 3.15 mm/day (mean size at 1 y, 1,045 mm in ML; Fig. 6).

Fourier Series Analysis

The results of the Fourier analysis showed that the higher value of the periodogram and the higher spectral density corresponded to a period between 7 days and 8 days (Fig. 7), which could indicate the periodicity of arrival of new specimens to the fishing area.



Population Structure

The sex ratio obtained for the entire fishing period showed an apparent dominance of D. gigas males over females, which is the opposite of what has been reported in previous studies from the Gulf of California (Markaida & Sosa-Nishizaki 2001, Bazzino et al. 2007) and Peruvian waters (Tafur et al. 2001, Tafur et al. 2010). This condition could be the product of the selective effect of the jigs when specimens are immature or the product of spatial segregation and migration between sexes in the study area.

Sexual maturity stages and size structure showed that the majority of the jumbo squid population was composed of medium-size immature specimens both male and female. This suggests that the study area could be a transitory feeding ground where the squid are growing and possibly migrating from and to other feeding areas or reproductive grounds, perhaps northward to Santa Rosalia, following the migration schemes of Ehrhardt et al. (1983), Ehrhardt (1991), and Markaida and Sosa-Nishizaki (2001). It seems that we are looking at a short-term detail of the overall picture regarding the life cycle of jumbo squid connected to the Gulf of California.

Progressive Increment of Size: Growth or Migration?

The application of MPA based on LFA for the estimation of growth parameters in cephalopod populations has been rejected before, but the results presented by Keyl et al. (2011) suggest that a modified approach is appropriate if it can correct the observation bias introduced by the size-selective fishing gear. The progressive increment of size (ML) during the fishing period could be explained as a consequence of (1) growth process; (2) migratory behavior, in which increasingly larger specimens arrive to the study area day after day; or (3) a mixture of both factors (growth and migration).


The approach of the current study was to conduct an MPA with length frequency data from a relatively short period but with high temporal resolution (daily and weekly). A quasilinear growth function was used to calculate the growth parameters of the cohorts identified, following Keyl et al. (2011). Our estimations of growth rates were higher (3.15-3.85 mm/day) than those reported for D. gigas in the same region (Gulf of California): 2.00-2.65 mm/day (Markaida et al. 2004) and 1.47-2.26 mm/day (Filauri 2005). In fact, it is higher than any growth rate reported for D. gigas until now. The most direct, and therefore supposedly most accurate, method to evaluate growth rates--tag--recapture experiments--obtained 1.0-1.5 mm/day (Markaida et al. 2005), roughly a third of our calculated growth rates. This apparent overestimation of growth rates, which is contrary to the error made when using uncorrected LFA in MPA (Keyl et al. 2011), is assumed to be associated with a bias introduced by migration (Hatfield & Rodhouse 1994). To avoid such bias, the study area must be large enough to include almost all large-scale movement patterns of the species.

If the migratory behavior of D. gigas is the explanation for the progressive increment in size frequency with time, then the following question arises: Why do the specimens or groups arrive in the study area with increasing size? One possible reason for this pattern is related to the fact that jumbo squid seem to migrate in schools or shoals. Although schools of jumbo squid may be independently mobile, a common behavioral trend regarding horizontal movement was observed in previous migratory studies (Bazzino et al. 2010). We propose that this pattern represents the sustained arrival of jumbo squid schools, one after the other, from their respective feeding grounds to the study area.


Based on this, it is necessary to explain why the squid arrive in an area that is supposedly a transition area. The specimens or groups that usually consist of very similar-size individuals (Nigmatullin et al. 2001) migrate to new feeding areas according to size, with the larger squid consecutively following the smaller ones. The reason for such behavior could be the fact that large specimens have a considerably higher energy demand that, with reduced food availability, may not be satisfied anymore in a specific area of origin. The smaller squid in this scenario might escape larger ones during periods of food scarcity to avoid the resulting increased cannibalistic pressure (Ibanez & Keyl 2010). Accordingly, based on our Fourier analysis, the periodicity of arrival of new specimens or groups to the study area could be between 7 days and 8 days.


A second question that arises is related to the origin of the specimens that arrive to the study area: Where do they come from? According to the migration scheme proposed by Ehrhardt et al. (1983) for D. gigas in the Gulf of California, the observed specimens in the study area at the time of our sampling (June to August) should be dwelling in the central Gulf and moving southward to exit the Gulf later in the year. This scheme also shows a northward migration through the study area in January and February (Ehrhardt et al. 1983). More recent studies on the migratory behavior of D. gigas support and contradict this scheme in part. A conventional tag--recapture study demonstrated a seasonal and reciprocal migration between major traditional fishing centers in Santa Rosalia and Guaymas (Markaida et al. 2005). Moreover, pop-up satellite tagging experiments revealed sustained movements of at least 30 km/day within the Gulf of California for up to 1 wk (Gilly et al. 2006b, Gilly 2007). Some of the squid tagged in Santa Rosalia in October and November migrated southward to other areas of the Gulf that are currently not subject to commercial fishing. Other squid migrated northeast toward the San Pedro Martir Basin, an area which has been reported to be a mating and spawning location (Gilly et al. 2006a). In a similar study in the Pacific Ocean off the Baja California peninsula, 4 specimens of D. gigas where tagged with pop-up satellite devices outside Magdalena Bay in June and moved southward toward the tip of the Baja California peninsula (Bazzino et al. 2010). It must be stated that variability clearly exists with respect to exact direction and timing of migration pathways.

Despite the evidence retrieved from fishing data and tagging experiments, details of migratory routes and rates of migration remain poorly understood. However, on the basis of the current study, together with the results presented by Markaida et al. (2005), Gilly et al. (2006b) and Bazzino et al. (2010), a possible migration route of D. gigas could be from the Pacific Ocean (off the Baja California peninsula) in June via the study area off Mulege (June to August) to the central Gulf of California between Santa Rosalia and Guaymas (October to April). This route, compared with the scheme of Ehrhardt et al. (1983), either does not match temporally by around half a year or does not match in direction. Another possibility is that D. gigas completes its entire life cycle in the Gulf of California, which is contrary to the idea of a permanent exchange between jumbo squid populations inside and outside the Gulf. Long-term movements into the Pacific Ocean could be associated exclusively with atypical years, such as those that include El Nino or La Nina events. The idea of the entire life cycle in the Gulf of California is supported by evidence presented in previous studies of this species. For example, the presence of putative mating adults, paralarvae, and juveniles of D. gigas in the San Pedro Martir Basin was confirmed (Gilly et al. 2006a). Besides, it is common to find subadults and adults in the central Gulf of California during alternate fishing seasons between Santa Rosalia (May to October) and Guaymas (November to May) (Markaida & Sosa-Nishizaki 2001, Bazzino et al. 2007). The existence of several cohorts of D. gigas cohabiting in the Gulf is obvious and implies a spatial overlapping of different ontogenic stages.


In summary, we cannot fully accept or reject any of the hypotheses postulated to explain the progressive increment of size (ML) during the fishing period. The most real possibility considers a dynamic interaction between growth and migration. The highest growth rates ever reported for D. gigas suggest an apparent overestimation associated with a bias introduced by migration. In this context, we need further research on early life stages as well as distribution and migration of jumbo squid.


We express our gratitude to the group of observers onboard the fishing fleet coordinated by the Centro de Investigaciones Biologicas del Noroeste (CIBNOR). We also thank the owner of the fishing company and the crew of each fishing vessel (Miriam III, Miriam IV, Miriam V, Catalina I, and Carmelita G).


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(1) Centro de Investigaciones Biologicas del Noroeste (CIBNOR), Mar Bermejo 195, Colonia Playa Palo de Santa Rita, La Paz, BCS 23090, Mexico; (2) Johann Heinrich von Thunen-Institut, Federal Research Institute for Rural Areas, Forestry and Fisheries, Palmaille 9, 22767 Hamburg, Germany

* Corresponding author. E-mail:

DOI: 10.2983/035.031.0326
Numbers of females and males examined per week during the
fishing period.

Week     Females   Males   Total   Sex Ratio      Test      P Value

1             16      33      49     0.48            5.90   <0.02 *
2             27      29      56     0.93            0.07   <0.79
3             59      61     120     0.97            0.03   <0.86
4             68      71     139     0.96            0.06   <0.80
5             40      50      90     0.80            1.11   <0.29
6             45      55     100     0.82            1.00   <0.32
7             26      34      60     0.76            1.07   <0.30
Total        281     333     614     0.84            4.40   <0.04 *

* Significant differences (P < 0.05).

Sex ratio values and the results of the chi-square test with
the probability (P) associated are shown.
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