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Geoduck species are in the genus Panopea (family Hiatellidae), and they are distributed around the world. The genus comprises many species, including but not limited to Panopea abbreviata (Valenciennes, 1839), endemic to the southwestern Atlantic; Panopea zelandica (Quoy & Gaimard, 1835), found in the southwestern Pacific; Panopea globosa (Dall, 1898), found primarily in the Gulf of California; and Panopea generosa (Gould, 1850), which ranges from Alaska to Baja California (Mexico). The spatial distributions and proper name of the last two species have generated debate. The discussion regarding whether P. globosa inhabits only the Gulf of California was resolved when it was determined that this species is also harvested in Bahia Magdalena and Baja California Sur, Mexico, on the Pacific Coast (Suarez-Moo et al. 2013). The fishing areas for P. globosa include both the coast (eastern and western) in the northern part of the Gulf of California and the eastern coast in the central Gulf of California. This species is also fished on the Pacific Coast of the Baja California Peninsula. There was a dispute as to whether P. generosa was synonymous with Panopea abrupta (Conrad, 1849), but Vadopalas et al. (2010) determined that the correct name for the geoduck clam fished from Alaska to Baja California, Mexico, was P. generosa.

Species with broad spatial distributions are ideal to study the effects of environmental versus biological traits such as growth parameter variations. The three-parameter von Bertalanffy growth model (VBGM) is frequently used to apply management strategies for resources in commercial fisheries as the VBGM requires estimating biomass and targeting mortality based on the output of an age-structured equilibrium yield model (Bradbury & Tagart 2000). Hoffmann et al. (2000) conducted a study in four regions in the state of Washington and found that Panopea generosa growth parameters differed among regions and among sites within regions. Similar studies were performed by Campbell and Ming (2003) in locations throughout British Columbia, and similar results were obtained. In addition, Campbell et al. (2004) and Zhang and Hand (2006) found that the key parameters required to estimate biomass and productivity differed among regions. Most recently, Wood et al. (2018) concluded that the growth parameters of P. generosa were good indicators that this species has larger sizes in zones with colder water and higher primary productivity than in other regions. They studied six populations from Dungeness West, WA, to San Quintin, Baja California, Mexico. Wood et al. (2018) included very different climatological regions.

Body growth is used as a parameter in ecological studies because it provides insight into species population dynamics, such as natural mortality rates and other parameters that are commonly used in life history studies. Although there are many mathematical equations used to describe individual growth parameters for populations, the VBGM is the most popular for fisheries because its parameters, such as the yield per recruit, are used to evaluate other fishery models (Kimura 1980). This fact suggests that any comparison of growth performance for Panopea globosa throughout fishing areas should be performed using VBGM. For P. globosa, the VBGM has been used to estimate growth in four different regions (by three different authors) with similar results, although the parameters of the VBGM were different among the locations. Similar studies were performed for Panopea zelandica (Breen et al. 1991, Gribben & Creese 2005) and Panopea abbreviata (Morsan et al. 2010). Based on those results, among the various species, and specifically among four fishing zones in northwestern Mexico, it appears that populations living in the northern Gulf of California possess greater asymptotic lengths than populations inhabiting the central Gulf of California. Several growth studies of P. globosa have been published; these include fishing locations in the Gulf of California (Cortez-Lucero et al. 2011, Cruz-Vasquez et al. 2012, Perez-Valencia & Aragon-Noriega 2013, Aragon-Noriega et al. 2015) and on the Pacific Coast (Gonzalez-Pelaez et al. 2015), but no one has assessed a statistical comparison of growth curves between sites. Thus, the objective of this study was to compare the growth curves for P. globosa at four locations with different climatological patterns.



Sea surface temperature (SST) data were obtained from the Comprehensive Oceanic and Atmospheric Data Set generated and provided by the National Oceanographic and Atmospheric Administration--Cooperative Institute for Research in Environmental Science Climate Diagnostics Center. The optimum interpolation SST analysis based on a one-degree grid is produced weekly. This analysis uses in situ and satellite SST estimates in addition to SST estimates simulated by sea-ice cover. The optimum interpolation v2 analysis is described by Reynolds et al. (2002). An area of northwestern Mexico was selected to cover the four fishing zones. Data from these rectangular areas were monthly averages from January 1983 to December 2017. The average of the entire period for each zone was compared, and the regional climatology was calculated by averaging the monthly SSTs of all the years in the study period.

The growth data have been presented in previous individual studies (Cruz-Vasquez et al. 2012, Aragon-Noriega et al. 2015, Gonzalez-Pelaez et al. 2015), so this study is a reanalysis of existing information on growth. Sampling was conducted (Fig. 1) at two locations in the northern part of the Gulf of California eastern coast (Puerto Penasco 31[degrees] 30' N, 113[degrees] 23' W) and western coast (San Felipe 31[degrees] 09' N, 114[degrees] 53' W), a location in the central Gulf of California (Guaymas 27[degrees] 53' N, 110[degrees] 43' W) and the western coast of the Baja California Peninsula on the eastern Pacific Coast (Bahia Magdalena 24[degrees] 38' N, 112[degrees] 00' W). Hookah divers harvested one clam at a time using a stinger (a high-flow hydraulic tool used to uncover buried clams) at a depth of 10-30 m. Collection was restricted to soft-bottom areas because geoduck clams can only be found in this type of substratum. This clam lives completely buried in the sediment (Feldman et al. 2004) and can only be detected by a circular characteristic pattern in the substrate left by the siphon.

Growth Model Tested

The curves were generated using the VBGM because it is a model that was used in most of the previous studies (Cruz-Vasquez et al. 2012, Aragon-Noriega et al. 2015, Gonzalez-Pelaez et al. 2015) and is compatible with the Akaike information criterion among other models tested in those studies, mainly because VBGM is the most commonly used model in growth studies of Panopea species worldwide.

VBGM is given by

[mathematical expression not reproducible]

where L(t) is the length at age t, t is the age at size L(t), [L.sub.[infinity]] is the asymptotic length, k determines how quickly [L.sub.[infinity]] is reached (curvature parameter), and to is the hypothetical age at which the organism has zero length (initial condition parameter). The VBGM parameters for any location and for fitting a global model were fitted by the residual sum of squares (RSS), which was necessary for applying Kimura's likelihood ratio test (Kimura 1980).

Test for Curve Comparison

Kimura's likelihood ratio test provides a general method for the statistical comparison of growth curves. Kimura's likelihood ratio test can be used for multisample problems comparing growth curves generated by VBGMs in different populations, when it is desirable to test whether a sample came from a population with known values for any or all of the parameters. This test finds the best-fitting curves for each data set separately; then, the total RSS from the base case is sequentially compared by adding various constraints. When likelihood ratios are calculated, a difference between the curves is indicated by a comparison with the global model under the assumption of the same curve fitting both data sets. Because Kimura's likelihood ratio test is based on statistics having an asymptotic [[chi].sup.2.sub.i] distribution, the validity of this test is dependent on the sample size. For multisample problems, a linear constraint takes the form of fitting von Bertalanffy curves so that any or all parameters are equal in any or all of the i populations. In this case, the degrees of freedom for [[chi].sup.2.sub.i] are equal to the number of parameters in the model. This method tests the hypothesis that all curves are coincident. If this hypothesis is not rejected, then the analysis ends; however, if the hypothesis is proven false, then it is necessary to make subsequent pairwise comparisons between individual growth curves to find which curve is different. The Kimura's likelihood ratio test (Kimura 1980) is based on the following equation:

[X.sup.2.sub.k] = Nx Ln([RRS.sub.[OMEGA]]/[RRS.sub.[omega]])

where k is the degrees of freedom (equal to the number of constraints placed upon the fit), N is the total number of observations from both curves combined, [RRS.sub.[omega]] is the total sum of squared residuals derived from fitting both curves separately (the minimum sum of squared residuals from each curve added together), and [RRS.sub.[omega]] is the total sum of squared residuals derived from fitting the curves with one of the hypothesized constraints.


In the four fishing zones, minimum temperatures occur in February (winter) and maximum temperatures occur in August--September (summer). There is marked seasonal variability (Fig. 2). The maximum SSTs in August and September are the same in the Gulf of California (Guaymas, Puerto Penasco, and San Felipe, 31[degrees]C), but the SST is 27[degrees]C on the Pacific Coast (Bahia Magdalena); however, the minimum SST is 17[degrees]C in the upper Gulf of California (Puerto Penasco and San Felipe), 18[degrees]C in the central Gulf of California (Guaymas), and 20[degrees]C on the Pacific Coast (Fig. 2). Temperatures were warmer (above 25[degrees]C) for a longer period in Guaymas than in any other location.

The length-at-age data used for each location were averaged before fitting the model (Table 1). Table 2 contains the estimates of the [L.sub.[infinity]] K, and [t.sub.0] parameters for each location used to graph each growth curve (Fig. 3). From the graphed curves, there appear to be differences between one location (Guaymas) and the other three fishing zones. The remaining three locations (San Felipe, Puerto Penasco, and Bahia Magdalena) appear very similar. The Kimura's likelihood ratio test results (Table 3) show significant or nonsignificant differences in growth curves. Comparing the central Gulf of California populations demonstrates the smallest length-at-age considered in this study, which is the smallest of the four analyzed here.

The size and age structure (Figs. 4 and 5) among the four fishing zones are notable. Among the four studied locations, in Guaymas, the results are consistent with growth results in that the Guaymas geoducks are the "youngest" and "shortest." The discrepancies appear among the other three zones; geoducks from Puerto Penasco are younger and larger than geoducks from San Felipe (Figs. 4 and 5). Geoducks from Bahia Magdalena were found to have nonsignificant differences in age with geoducks from San Felipe, but geoducks from Bahia Magdalena were significantly larger than geoducks from San Felipe. Of the studied locations, geoducks from Bahia Magdalena were the largest average size fished.


Geoducks are the largest burrowing clams in the world, and species in the genus Panopea can attain shell lengths greater than 200 mm. To date, growth parameters have been described for four Panopea species worldwide. Growth parameters are different among regions and among sites within regions in the studies on each species. Because the range of asymptotic lengths is wide for each of these species, it could be stated that there are no differences in the growth curves between the species or that the differences among their growth parameters are qualitative; however, in this study, a quantitative analysis was performed to compare the growth curves generated by VBGMs for Panopea globosa in four locations in northwestern Mexico. The findings provided evidence, suggesting that the northern gulf populations are the largest inside the Gulf of California; notably, no differences were found between the two populations of this region and the populations inhabiting the Pacific Coast in Bahia Magdalena. By contrast, the central Gulf of California populations are the smallest of the studied populations, and there were significant differences between them.

When a difference in growth for the same species is found, a popular hypothesis attributes this difference to differences in genetic structure among populations. Munguia-Vega et al. (2015) reported the genetic diversity in Panopea globosa populations for the same four locations selected in the present study to perform a growth revision. Munguia-Vega et al. (2015) found that geoducks from Bahia Magdalena are distinct morphologically and genetically from populations in the Gulf of California. The largest differences were observed between Bahia Magdalena and San Felipe and Puerto Penasco. In the present growth study, no differences in growth curves were found among these three locations. This result was unexpected given the geographic isolation and genetic findings of Munguia-Vega et al. (2015). The explanations for this must be that the environmental stimuli rather than genetics drive the results. The SST was used to find the environmental factors to explain why differences in growth were present. The most notable differences were between the minimum and maximum SST at each location; on the Pacific Coast (Bahia Magadalena), there are only 7[degrees]C temperature spans, whereas in the Gulf, there are 13[degrees]C and 14[degrees]C spans for the central and upper parts of the Gulf, respectively. This scenario could be the reason why among the four sites, Bahia Magdalena presented the largest asymptotic length; however, the question remains as to why the differences in growth rates exist between the central and upper gulf populations. The possible explanation is that temperatures are warmer (above 25[degrees]C) for a longer period in Guaymas than in any other location (see Fig. 2). The congeners of P. globosa are distributed in temperate waters, and the population inside the Gulf of California is the only one located in tropical and subtropical waters. Wood et al. (2018) reported larger sizes of Panopea generosa in colder water; they studied the growth performance (among other morphological traits) of this species through a von Bertalanffy model in six locations from Washington to Baja California, Mexico. If P. globosa responds as P. generosa does, then the aforementioned explanation is the most plausible, in that the largest size is found in colder waters, with less SST variability between winter and summer.

The Bahia Magdalena population is distributed in the eastern Pacific Ocean and is particularly influenced by the California Current, which is an area with some of the world's richest ecosystems in terms of productivity (Lluch-Cota et al. 2007). The northern Gulf is also recognized as a high productivity area because of the mixed water triggered by the high velocity of tidal currents. The central Gulf of California is less productive, and the variations in primary productivity between the fishing locations rather than genetic factors may be responsible for differences in growth rates. These findings are consistent with those of Kahru et al. (2004), who used satellite data to obtain time series of surface chlorophyll a concentrations and phytoplankton net primary production for 12 subareas within the Gulf of California. These time series showed variability at many scales, including a dominant annual cycle in all subareas. Notably, the upper Gulf of California exhibited higher primary production per unit area than that of the central Gulf of California. Morsan et al. (2010) observed different growth patterns between two southern geoduck populations (Panopea abbreviata) and concluded that the difference in asymptotic sizes between the patterns were derived from two water masses: the warmer and saltier waters in the northern section and the colder and less salty water in the south. In addition, Wood et al. (2018) reported larger sizes of Panopea generosa in zones with higher primary productivity.

One of the caveats of this study is that the original data set does not contain enough small individuals to obtain an unbiased length-at-age t = 0 or t = 1. According to the average VBGM, a population from Guaymas attains a shell length of 58 mm at 2 y old, whereas the combined data demonstrate a shell length of 35.67 mm at 1 y old; however, the growth curves generated by VBGM for each location are in the acceptable range.

The growth curve comparisons in this study were performed by comparing VB growth equations that can easily be repeated using the data from Table 1. Although there are many other ways to compare growth curves, such as those proposed by Wang and Milton (2000) and Haddon (2001), Kimura's likelihood ratio test (Kimura 1980) is appropriate for the purposes of this study.

Finally, notably, three of the four populations analyzed inhabit the Gulf of California, one lives in the eastern Pacific Ocean, and the smallest of the geoduck clam populations was found in the Gulf of California. Because the fishing management strategy for this species uses the minimum legal size, minimum legal size should vary regionally to promote sustainable use.


Autonomous University of Nayarit and CONACYT (scholarship 248931) supported R.C.V. Fishing cooperatives in the studied areas kindly provided logistical and diving team support for this project.


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(1) Centro de Investigaciones Biologicas del Noroeste, Unidad Sonora, Km 2.35 Camino al Tular, Estero Bacochibampo, Guaymas, Sonora 85454, Mexico; (2) Posgrado en Ciencias Biologico Agropecuarias, Universidad Autonoma de Nayarit, Carretera Tepic-Compostela, Km 9 Xalisco, Nayarit 63780, Mexico, (3) Universidad Autonoma de Sinaloa, Facultad de Ciencias del Mar, Paseo Claussen S/N, Col. Los Pinitos, Mazatlan, Sinaloa 82000, Mexico

(*) Corresponding author. E-mail:

DOI: 10.2983/035.038.0208
Average length at different estimated ages of Panopea globosa at four
locations in northwestern Mexico.

  Age          Total shell length (mm)
(years)  Guaymas  Puerto    San     Bahia
                  Penasco  Felipe  Magdalena

   2      65       102     -       -
   3      71       107     -       100
   4      82       131     -       -
   5      96       -       -       -
   6      97       126     -       120
   7     110       138     124     -
   8     114       135     147     146
   9     118       154     -       150
  10     138       148     -       145
  11     117       154     133     163
  12     115       154     -       160
  13     118       153     135     153
  14     119       155     155     168
  15     120       161     165     123
  16     123       146     -       161
  17     111       161     -       161
  18     101       162     138     164
  19     128       156     136     165
  20     133       169     138     168
  21      76       159     144     161
  22     109       157     144     171
  23      97       -       155     170
  24     107       -       150     190
  25     -         -       153     160
  26     -         -       -       -
  27     112       -       -       180
  33     -         -       170     -
  34     -         169     -       -
  36     -         -       177     -
  40     -         -       165     180
  44     -         -       170
  46     -         -       -       180
  47     -         -       -       160
  50     -         -       184     -
  56     -         -       166     -
  60     -         -       179     -

Estimated parameters of the VBGM for Panopea globosa at four locations,
based on the data in Table 1 (latitudes in parentheses).

       Locations                   [L.sub.[infinity]]    K   [t.sub.0]

Bahia Magdalena (24.65[degrees]N)      168.39          0.258  0.00
Guaymas (27[degrees]N)                 114.37          0.408  0.26
San Felipe (31[degrees]N)              161.48          0.18   0.00
Puerto Penasco (31[degrees]N)          156.60          0.392  0.00
Global model                           150.62          0.287  0.00

Kimura's likelihood ratio test comparing VBGM curves estimated for the
four fishing locations of Panopea globosa.

       Source         RSSi    RSSb    n   [X.sup.2.sub.i]  P value

All locations         12,130  44,397  90     116.77        0.0000   ***
Guaymas-Puerto         5,144  23,239  45      67.86        0.0000   ***
Guaymas-San Felipe     7,618  23,196  45      50.10        0.0000   ***
Guaymas-Bahia          6,814  32,590  48      75.12        0.0000   ***
San Felipe-Bahia       6,986   8,633  45       9.53        0.0492   *
San Felipe Puerto      5,316   6,461  42       8.19        0.0848   NS
Puerto Penasco-Bahia   4,512   5,468  45       8.65        0.0704   NS
Guaymas                3,723   -      24       -           -        -
Puerto Penasco         1,421   -      21       -           -        -
San Felipe             3,895   -      21       -           -        -
Bahia Magdalena        3,090   -      24       -           -        -

RSSi, residual squared sum as individual; RSSb, residual squared sum as
base model; NS, nonsignificant.
(*) P < 0.05.
(***) P < 0.001.
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Article Details
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Author:Aragon-Noriega, Eugenio Alberto; Alcantara-Razo, Edgar; Cruz-Vasquez, Rolando; Castillo-Vargasmachuc
Publication:Journal of Shellfish Research
Article Type:Report
Geographic Code:1USA
Date:Aug 1, 2019

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