Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue Crab (Callinectes sapidus, Rathbun 1896) of Laguna Madre, Tamaulipas, Mexico

Jorge Homero Rodriguez Castro, Sandra Edith Olmeda de la Fuente, Wanda Ortiz Baez, Alfonso Correa Sandoval and Jose Alberto Ramirez de León

#### Abstract

The fishery of the blue crab (Callinectes sapidus) in Laguna Madre (LM), Tamaulipas, Mexico, with an average annual catch of 3307 tons, is of great importance economically and socially. The objective of this research was to estimate the carrying capacity (K), the catchability coefficient (q), the maximum sustainable yield (MSY) (tons), and the optimal fishing effort ( fMSY) (traps). For this, a time series from 1998 to 2012 was used for the catch and number. The Fox (1970) and Schaefer (1954) models included in A Surplus-Production Model Incorporating Covariates (ASPIC) software were employed for this study. A set of statistical variability estimators and the Akaike's, Bayesian, and Hannan-Quinn information criteria were used for the selection of models. The results obtained by the fox model were K = 54,000, q = 0.00008798, MSY = 2567 and fMSY = 146,900 traps, whereas for the Schaefer model, the results were K = 28,370, q = 0.00002425, MSY = 2008, and fMSY = 58,390. The model with the best adjustment was that of Schaefer. It is concluded that the fishing resource has been overexploited during the period 2003–2011, with an average annual surplus of 670 tons and 25,000 traps. It is recommended to consider the MSY and fMSY values of the Schaefer model for the National Fishing Charter (NFC).

Keywords: Callinectes sapidus, blue crab, Laguna Madre, Mexico, maximum sustained yield, ASPIC

#### 1. Introduction

In 2017, a total of 48,602 tons of blue crab was captured in Mexico, 4033 of which came from the State of Tamaulipas. Such state capture allows the State to occupy the fifth place at a national scale, thus taking the fifth place among the nine main fisheries of the State, according to the definition of the Yearbook of Fishery and Aquaculture Statistics 2017 [1]. An estimate of 3307 tons from the capture the State of Tamaulipas comes from Laguna Madre (LM). This goes in accordance with the proportion of 0.82 that corresponds to LM from the total capture of the blue crab in Tamaulipas, according to Rodríguez-Castro et al. [2]. In economic terms the value (in Mexican pesos and its equivalent in US dollars) of the capture of the blue crab, corresponding to the year 2017, was 51.26 million pesos (2.44 million US dollars) for the Laguna Madre; 62.51 million pesos (2.98 million US dollars) for the State of Tamaulipas; and 753.33 million pesos (35.87 million US dollars) for the country.

theory, arose in parallel. The model selection based on the information theory is a relatively new paradigm in biological sciences and is very much different from the

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue…

can be employed to make decisions in the management of this resource.

Laguna Madre is located north of the State of Tamaulipas (23°480

Therefore, the objective of this research is to estimate fisheries reference points of the blue crab (Callinectes sapidus) of the Laguna Madre, Tamaulipas, Mexico, that

97°52' W) (Figure 1). The northern part of the lagoon is delimited by Río Bravo in the municipality of Matamoros and in the southern part by the Soto la Marina River in the municipality of Soto La Marina [30]. Its surface has an area of

, with an average depth of 0.7 m. It is separated from the Gulf of Mexico

25°30' N y 97°

classical method based on the null hypothesis test [26–29].

2.1 Study area: Laguna Madre, Mexico

DOI: http://dx.doi.org/10.5772/intechopen.90065

2. Methods

230

2000 km<sup>2</sup>

Figure 1.

93

Laguna Madre, State of Tamaulipas, Mexico.

The SEMARNAT [3] indicates that the blue crab fishery of LM forms part of the group of fisheries that concurs in the natural protected area, named as Área de Protección de Flora y Fauna Laguna Madre y Delta del Río Bravo, and thus is an important economic source in the zone. Furthermore, the SEMARNAT recognizes the need for generating biological reference points such as catch limits and optimal fishing effort (fMSY), among others, in order to manage the fisheries.

Nevertheless, and despite of the economic and social importance of this fishery resource, the normative of this is limited in terms of the specifications required in order to achieve its sustainable use. Certain regulatory guidelines specific for the Gulf of Mexico (e.g., National Fishing Charter (NFC)) are at disposal and used to administer its management [4]. However, the scope of the guidelines is limited given that these do not provide management specifications for the State of Tamaulipas. In part, this is due to the fact that the scientific reports for this fishery resource are scarce. Furthermore, those few reports are mainly focused on capture size analysis rather than management [5–7]. In sum, no scientific research has been made regarding the management of the blue crab in LM as a fishery resource. Particularly for the coast of the State of Tamaulipas, the NFC stablishes that the annual maximum catch limit is 2100 tons per year and that the maximum fishing effort consists of 47 permits, 11,802 hoops, 35,200 traps, and 641 vessels. The NFC also mentions that this fishery is "exploited to its sustainability maximum." This yearly allowed catch limit pertains to an average of the annual catch of the period from 2000 to 2007, and not to the maximum sustainable yield (MSY).

The estimation of the maximum sustainable yield from the surplus production models has been a popular goal in fisheries management even though it has been questioned regarding its supposed equilibrium [8–13]. On the other hand, the conceptualization of this reference point has transitioned from being a target goal into a target limit. Given the overexploitation status of the majority of fisheries in the world, in terms of fisheries management, the fisheries science seeks to minimize the probabilities of exceeding the limit of the MSY (fishery risk) or of the biomass declining beyond the level of natural renewal (stock risk) [14]. With this in mind, in the effort of minimizing probabilities, the precautionary approach in the fisheries management is implicitly included, represented by the fisheries biological reference points (e.g., MSY, maximum sustained effort or EMSY) or those based on the fishing mortality (e.g., FMRS, F0.1) [14, 15].

In the context of fisheries management, the line of research regarding the estimation of some fisheries reference points has currently resurfaced in the Middle East, primarily MSY and fRMS [16–24], by means of the adjustment of the Fox, Schaefer, and Pella-Tomlinson models, which are included in some computer packages such as A Surplus-Production Model Incorporating Covariates (ASPIC) [25], which in turn is a stock production model that incorporates the covariance of the parameters. On the other hand, on the topic of model selection, the flow of use of the information criteria (IC) reaching up to multimodel inference, within the framework of the information

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue… DOI: http://dx.doi.org/10.5772/intechopen.90065

theory, arose in parallel. The model selection based on the information theory is a relatively new paradigm in biological sciences and is very much different from the classical method based on the null hypothesis test [26–29].

Therefore, the objective of this research is to estimate fisheries reference points of the blue crab (Callinectes sapidus) of the Laguna Madre, Tamaulipas, Mexico, that can be employed to make decisions in the management of this resource.

#### 2. Methods

occupy the fifth place at a national scale, thus taking the fifth place among the nine main fisheries of the State, according to the definition of the Yearbook of Fishery and Aquaculture Statistics 2017 [1]. An estimate of 3307 tons from the capture the State of Tamaulipas comes from Laguna Madre (LM). This goes in accordance with the proportion of 0.82 that corresponds to LM from the total capture of the blue crab in Tamaulipas, according to Rodríguez-Castro et al. [2]. In economic terms the value (in Mexican pesos and its equivalent in US dollars) of the capture of the blue crab, corresponding to the year 2017, was 51.26 million pesos (2.44 million US dollars) for the Laguna Madre; 62.51 million pesos (2.98 million US dollars) for the State of Tamaulipas; and 753.33 million pesos (35.87 million US dollars) for the

The SEMARNAT [3] indicates that the blue crab fishery of LM forms part of the

Nevertheless, and despite of the economic and social importance of this fishery resource, the normative of this is limited in terms of the specifications required in order to achieve its sustainable use. Certain regulatory guidelines specific for the Gulf of Mexico (e.g., National Fishing Charter (NFC)) are at disposal and used to administer its management [4]. However, the scope of the guidelines is limited given that these do not provide management specifications for the State of Tamaulipas. In part, this is due to the fact that the scientific reports for this fishery resource are scarce. Furthermore, those few reports are mainly focused on capture size analysis rather than management [5–7]. In sum, no scientific research has been made regarding the management of the blue crab in LM as a fishery resource. Particularly for the coast of the State of Tamaulipas, the NFC stablishes that the annual maximum catch limit is 2100 tons per year and that the maximum fishing effort consists of 47 permits, 11,802 hoops, 35,200 traps, and 641 vessels. The NFC also mentions that this fishery is "exploited to its sustainability maximum." This yearly allowed catch limit pertains to an average of the annual catch of the period

group of fisheries that concurs in the natural protected area, named as Área de Protección de Flora y Fauna Laguna Madre y Delta del Río Bravo, and thus is an important economic source in the zone. Furthermore, the SEMARNAT recognizes the need for generating biological reference points such as catch limits and optimal

fishing effort (fMSY), among others, in order to manage the fisheries.

from 2000 to 2007, and not to the maximum sustainable yield (MSY).

mortality (e.g., FMRS, F0.1) [14, 15].

92

The estimation of the maximum sustainable yield from the surplus production models has been a popular goal in fisheries management even though it has been questioned regarding its supposed equilibrium [8–13]. On the other hand, the conceptualization of this reference point has transitioned from being a target goal into a target limit. Given the overexploitation status of the majority of fisheries in the world, in terms of fisheries management, the fisheries science seeks to minimize the probabilities of exceeding the limit of the MSY (fishery risk) or of the biomass declining beyond the level of natural renewal (stock risk) [14]. With this in mind, in the effort of minimizing probabilities, the precautionary approach in the fisheries management is implicitly included, represented by the fisheries biological reference points (e.g., MSY, maximum sustained effort or EMSY) or those based on the fishing

In the context of fisheries management, the line of research regarding the estimation of some fisheries reference points has currently resurfaced in the Middle East, primarily MSY and fRMS [16–24], by means of the adjustment of the Fox, Schaefer, and Pella-Tomlinson models, which are included in some computer packages such as A Surplus-Production Model Incorporating Covariates (ASPIC) [25], which in turn is a stock production model that incorporates the covariance of the parameters. On the other hand, on the topic of model selection, the flow of use of the information criteria (IC) reaching up to multimodel inference, within the framework of the information

country.

Crustacea

#### 2.1 Study area: Laguna Madre, Mexico

Laguna Madre is located north of the State of Tamaulipas (23°480 25°30' N y 97° 230 97°52' W) (Figure 1). The northern part of the lagoon is delimited by Río Bravo in the municipality of Matamoros and in the southern part by the Soto la Marina River in the municipality of Soto La Marina [30]. Its surface has an area of 2000 km<sup>2</sup> , with an average depth of 0.7 m. It is separated from the Gulf of Mexico

Figure 1. Laguna Madre, State of Tamaulipas, Mexico.

by a straight and uniform coastal barrier located windward and irregular towards the continental edge. The depression of the lagoon is partially filled by supply of the San Fernando River, thus being divided into two basins: northern and southern [31]. LM has a type BS1 (h') climate which is semiarid with rainfall in the summer though scarce throughout the year, with a winter precipitation between 5 and 10.2% [32]. The surface water of LM has a wide range of salinities, from 21.0 to 51.0 with euryhaline conditions during October (35.0–38.0 psu), poly-euhaline in January (21.0–36.0 psu), and eu-hyperhaline in May and July (33.0–46.0 and 36.0–51.0 psu, respectively) [30].

algorithms: dB

multiplicativeerror ¼

CI <sup>¼</sup> <sup>X</sup> � tn�<sup>1</sup> <sup>σ</sup>ffiffi

2.4 Model selection

(AICc <sup>¼</sup> AIC <sup>þ</sup> <sup>2</sup>k kð Þ <sup>þ</sup><sup>1</sup>

95

n p

dt <sup>¼</sup> rB Bð Þ <sup>∞</sup> � <sup>B</sup> [33] and dB

DOI: http://dx.doi.org/10.5772/intechopen.90065

variance were calculated using <sup>σ</sup>2, with additiveerror <sup>¼</sup>

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> ln <sup>y</sup> y^1 � � � � <sup>2</sup>

distribution with n � 1 = 14 degrees of freedom.

biomass of the stock, t is the time measured in years, B (K) is the carrying capacity, n is the inclination measure of the curve, and r is the intrinsic rate of population increase. In order to run these models, the ASPIC Version 5.0 computer package [25] was used. This software incorporates the values of the initial proportion, which correspond to the relative catch value of the first year of the time series, concerning the catch of the year with the highest catch value from the same time series. In addition to the variability estimators such as the coefficient of determination (r

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue…

and the coefficient of variation (CV), the outgoing parameters (management quantities) are the carrying capacity (K), the catchability coefficient (q), the maximum sustainable yield, and the optimal fishing effort (fMSY) (i.e., the maximum number of traps that the body of water can withstand without affecting the stock renewal). The management quantities were obtained by using two types of residual errors: the additive error and the multiplicative error. These types of errors of residual

estimated value, and n = number of data. Also, confidence intervals of the outgoing parameters were estimated at a confidence level of 95% (α = 0.05), according to Sparre and Venema [35]. This was carried out using the following algorithm:

t-distribution, σ = standard deviation, and n = number of data. In this study, tn�1= 2.5, as gathered from the t-distribution table. Given the confidence level of 95%, this percentile was searched in the table and used for the obtaining the t-

The information criteria were used for the selection of the model with the best adjustment. These were (a) the Akaike information criterion (AIC) [36], as in the corrected Aikake's information criterion (AICc) [37], given that n/k < 40 [26]

Once the values of the outgoing parameters and the IC were known, the statistical support was assessed, followed by the quantification of evidence from each model by estimating the differences (Δi) and the plausibility (i.e., the weight of the evidence in favor of the model i) of each (wi), according to the criterion set by Burnham and Anderson [26]. For the estimation of Δi, Δi = IC � ICmin was used, where IC = AICc, BIC, or HQIC and ICmin = model with the lowest value of AICc, BIC, or HQIC. According to Burnham and Anderson [26], the scale of Δ<sup>i</sup> is described as follows: if Δ<sup>i</sup> > 10, it shows that the candidate models lack statistical support and thus should not be taken into account; if Δ<sup>i</sup> < 2, the candidate models have high evidence as alternative functions; and if 4 < Δ<sup>i</sup> < 7, the candidate models can be taken into account, although they count with less statistical support than the

criterion (BIC) (BIC = �2σ^<sup>2</sup> <sup>+</sup> kn) [39]; and (c) the Hannan-Quinn information criterion (HQIC) (HQIC = �2σ^<sup>2</sup> + 2kn) [40]. From the shown equations, <sup>σ</sup>^<sup>2</sup> <sup>=</sup>

residual variance, k = number of parameters, and n = number of data.

previous ones. The wi were calculated using wi <sup>¼</sup> exp �<sup>1</sup>

BIC, or HQIC difference and K = number of parameters.

� �, where CI = confidence interval, tn�<sup>1</sup> = percentiles of Student'<sup>s</sup>

<sup>n</sup>�k�<sup>1</sup> , where AIC <sup>=</sup> <sup>n</sup>\*σ^<sup>2</sup> +2k) [39]; (b) the Bayesian information

2

ð Þ <sup>Δ</sup><sup>i</sup>

, where Δ<sup>i</sup> = AICc,

P

K <sup>K</sup>¼<sup>1</sup> exp �<sup>1</sup> <sup>2</sup> ð Þ <sup>Δ</sup><sup>i</sup>

dt ¼ rB lnB ð Þ <sup>∞</sup> � lnB [34], where B is the

P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> <sup>y</sup>1�b<sup>y</sup><sup>1</sup> � �<sup>2</sup>

<sup>n</sup> , where <sup>σ</sup><sup>2</sup> = variance, <sup>y</sup>1= observed value, <sup>y</sup>b<sup>1</sup> <sup>=</sup>

<sup>n</sup> , and σ2, with

2 )

#### 2.2 Data

The annual historical record of the catch measured in tons of the blue crab and the fishing effort (f), this last one represented by the number of traps (NT), were used for a time series of 14 years, corresponding to the period from 1998 to 2012 (Table 1). This information was provided in 2013 by the Fisheries Sub-delegation in Tampico, Tamaulipas, of the delegate of SAGARPA in Tamaulipas. The fishing effort was not standardized for the following reasons: (1) the blue crab fishery in LM is monospecific, (2) the extractive activity of this resource is carried out in a single zone during a single period of the year, and, (3) since the beginning of the fishery, the artisanal fishing fleet has remained technologically stable.

#### 2.3 Models

Both the Schaefer [33] and the Fox [34] models were the two surplus production models (or dynamic biomass models) employed in this study using the following


#### Table 1.

Catch, fishing effort, and catch per unit effort of the blue crab (Callinectes sapidus) in Laguna Madre, México, during the period 1998–2012.

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue… DOI: http://dx.doi.org/10.5772/intechopen.90065

algorithms: dB dt <sup>¼</sup> rB Bð Þ <sup>∞</sup> � <sup>B</sup> [33] and dB dt ¼ rB lnB ð Þ <sup>∞</sup> � lnB [34], where B is the biomass of the stock, t is the time measured in years, B (K) is the carrying capacity, n is the inclination measure of the curve, and r is the intrinsic rate of population increase. In order to run these models, the ASPIC Version 5.0 computer package [25] was used. This software incorporates the values of the initial proportion, which correspond to the relative catch value of the first year of the time series, concerning the catch of the year with the highest catch value from the same time series. In addition to the variability estimators such as the coefficient of determination (r 2 ) and the coefficient of variation (CV), the outgoing parameters (management quantities) are the carrying capacity (K), the catchability coefficient (q), the maximum sustainable yield, and the optimal fishing effort (fMSY) (i.e., the maximum number of traps that the body of water can withstand without affecting the stock renewal). The management quantities were obtained by using two types of residual errors: the additive error and the multiplicative error. These types of errors of residual

variance were calculated using <sup>σ</sup>2, with additiveerror <sup>¼</sup> P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> <sup>y</sup>1�b<sup>y</sup><sup>1</sup> � �<sup>2</sup> <sup>n</sup> , and σ2, with

multiplicativeerror ¼ P<sup>n</sup> <sup>i</sup>¼<sup>1</sup> ln <sup>y</sup> y^1 � � � � <sup>2</sup> <sup>n</sup> , where <sup>σ</sup><sup>2</sup> = variance, <sup>y</sup>1= observed value, <sup>y</sup>b<sup>1</sup> <sup>=</sup> estimated value, and n = number of data. Also, confidence intervals of the outgoing parameters were estimated at a confidence level of 95% (α = 0.05), according to Sparre and Venema [35]. This was carried out using the following algorithm: CI <sup>¼</sup> <sup>X</sup> � tn�<sup>1</sup> <sup>σ</sup>ffiffi n p � �, where CI = confidence interval, tn�<sup>1</sup> = percentiles of Student'<sup>s</sup> t-distribution, σ = standard deviation, and n = number of data. In this study, tn�1= 2.5, as gathered from the t-distribution table. Given the confidence level of 95%, this percentile was searched in the table and used for the obtaining the tdistribution with n � 1 = 14 degrees of freedom.

#### 2.4 Model selection

by a straight and uniform coastal barrier located windward and irregular towards the continental edge. The depression of the lagoon is partially filled by supply of the San Fernando River, thus being divided into two basins: northern and southern [31]. LM has a type BS1 (h') climate which is semiarid with rainfall in the summer though scarce throughout the year, with a winter precipitation between 5 and 10.2% [32]. The surface water of LM has a wide range of salinities, from 21.0 to 51.0 with euryhaline conditions during October (35.0–38.0 psu), poly-euhaline in January (21.0–36.0 psu), and eu-hyperhaline in May and July (33.0–46.0 and 36.0–51.0 psu,

The annual historical record of the catch measured in tons of the blue crab and the fishing effort (f), this last one represented by the number of traps (NT), were used for a time series of 14 years, corresponding to the period from 1998 to 2012 (Table 1). This information was provided in 2013 by the Fisheries Sub-delegation in Tampico, Tamaulipas, of the delegate of SAGARPA in Tamaulipas. The fishing effort was not standardized for the following reasons: (1) the blue crab fishery in LM is monospecific, (2) the extractive activity of this resource is carried out in a single zone during a single period of the year, and, (3) since the beginning of the

Both the Schaefer [33] and the Fox [34] models were the two surplus production models (or dynamic biomass models) employed in this study using the following

Years Catch (tons) Effort (number of traps) CPUE 2498 28,500 0.088 2302 45,600 0.05 1103 45,600 0.024 1318 45,600 0.029 1432 25,420 0.056 2699 25,420 0.106 2971 32,600 0.091 3462 32,600 0.106 2140 25,420 0.084 2097 83,450 0.025 2433 92,680 0.026 2362 92,680 0.025 2940 83,450 0.035 2967 73,836 0.04 1927 73,836 0.026

Catch, fishing effort, and catch per unit effort of the blue crab (Callinectes sapidus) in Laguna Madre,

fishery, the artisanal fishing fleet has remained technologically stable.

respectively) [30].

2.2 Data

Crustacea

2.3 Models

CPUE, Catch per unit effort.

México, during the period 1998–2012.

Table 1.

94

The information criteria were used for the selection of the model with the best adjustment. These were (a) the Akaike information criterion (AIC) [36], as in the corrected Aikake's information criterion (AICc) [37], given that n/k < 40 [26] (AICc <sup>¼</sup> AIC <sup>þ</sup> <sup>2</sup>k kð Þ <sup>þ</sup><sup>1</sup> <sup>n</sup>�k�<sup>1</sup> , where AIC <sup>=</sup> <sup>n</sup>\*σ^<sup>2</sup> +2k) [39]; (b) the Bayesian information criterion (BIC) (BIC = �2σ^<sup>2</sup> <sup>+</sup> kn) [39]; and (c) the Hannan-Quinn information criterion (HQIC) (HQIC = �2σ^<sup>2</sup> + 2kn) [40]. From the shown equations, <sup>σ</sup>^<sup>2</sup> <sup>=</sup> residual variance, k = number of parameters, and n = number of data.

Once the values of the outgoing parameters and the IC were known, the statistical support was assessed, followed by the quantification of evidence from each model by estimating the differences (Δi) and the plausibility (i.e., the weight of the evidence in favor of the model i) of each (wi), according to the criterion set by Burnham and Anderson [26]. For the estimation of Δi, Δi = IC � ICmin was used, where IC = AICc, BIC, or HQIC and ICmin = model with the lowest value of AICc, BIC, or HQIC. According to Burnham and Anderson [26], the scale of Δ<sup>i</sup> is described as follows: if Δ<sup>i</sup> > 10, it shows that the candidate models lack statistical support and thus should not be taken into account; if Δ<sup>i</sup> < 2, the candidate models have high evidence as alternative functions; and if 4 < Δ<sup>i</sup> < 7, the candidate models can be taken into account, although they count with less statistical support than the previous ones. The wi were calculated using wi <sup>¼</sup> exp �<sup>1</sup> 2 P ð Þ <sup>Δ</sup><sup>i</sup> K <sup>K</sup>¼<sup>1</sup> exp �<sup>1</sup> <sup>2</sup> ð Þ <sup>Δ</sup><sup>i</sup> , where Δ<sup>i</sup> = AICc, BIC, or HQIC difference and K = number of parameters.

#### 3. Results

#### 3.1 Maximum sustained yield according to the initial proportion

The values of K, q, MSY, fMSY, CV, and R2 of the Fox and the Schaefer models are presented in Table 2. Based on the results of the management quantities (B1/K, K, q, and MSY) of every IP value (from 0.1 to 0.9), the model with the best adjustment was the Fox model, according to r 2 , whereas the Schaefer model had the best adjustment, according to the CV (Table 2). However, considering the management quantities only for IP = 0.7 and based on the CV (Table 3), the regression estimator (r 2 ), the variability estimators (r 2 , CV, σ<sup>2</sup> , σ), and IC (AICc, BIC, and HQIC), the selected model was the Fox model (Table 4).

Parameters and confidence intervals Type of error of residual variance

DOI: http://dx.doi.org/10.5772/intechopen.90065

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue…

ILCI = inferior limit of the confidence interval, and SLCI = superior limit of the confidence interval.

Selection criteria Types of error

the residual variance.

Tamaulipas, Mexico.

Table 3.

r

σ2

Table 4.

97

Residual variance (σ<sup>2</sup>

multiplicative errors of the residual variance.

The initial values of the management quantities were estimated using the A Surplus-Production Model Incorporating Covariates (ASPIC) software with 0.7 as the initial proportion, considering the additive and multiplicative errors of

Average values and confidence intervals of the management quantities (K, q, MSY, and fmsy) generated by the Fox and logistic (Schaefer) models for the fishery of the blue crab (Callinectes sapidus) in Laguna Madre,

<sup>2</sup> 0.813 0.516 0.813 0.516

residual 665,217 2,132,349 0.1560 0.4148 σ 816 1460 0.3950 0.6441 k 3 3 33 AIC 9,978,258 31,985,238 8.34 12.22 AICc 9,978,256 31,985,235 5.94 9.82 BIC 9,978,297 31,985,277 47.34 51.22 HQIC 9,978,342 31,985,322 92.34 96.22 The initial values of the management quantities were estimated by means of the A Surplus-Production Model Incorporating Covariates (ASPIC) software with 0.7 as the initial proportion, considering the additive and

), standard deviation (σ), number of parameters (k), and the corrected Akaike's

information criterion (AICc) as well as the Bayesian (BIC) and the Hannan-Quinn (HQIC) information criteria for each model (Fox and logistic), of the management quantities (K, q, MSY, and fMSY), for the fishery

of the blue crab (Callinectes sapidus) in Laguna Madre, Tamaulipas, México.

Additive models Multiplicative models Fox Schaefer Fox Schaefer

K 54,000 28,370 54,000 28,370 ILCI (P < 0.05) 53,547 27,559 53,781 28,012 SLCI (P < 0.05) 54,453 29,181 54,219 28,728 q 0.00008798 0.00002425 0.00008798 0.00002425 ILCI (P < 0.05) 0.00008753 0.00002344 0.00008776 0.00002389 SLCI (P < 0.05) 0.00008843 0.00002506 0.00008820 0.00002461 RMS 2567 2008 2567 2008 ILCI (P < 0.05) 2114 1197 2348 1650 SLCI (P < 0.05) 3020 2819 2786 2366 fRMS 146,900 58,390 146,900 58,390 ILCI (P < 0.05) 142,370 57,579 144,710 58,032 SLCI (P < 0.05) 151,430 59,201 149,090 58,748 K = carrying capacity, q = catchability coefficient, MSY = maximum sustained yield, fMSY = optimal fishing effort,

Additive Multiplicative Models Models Fox Schaefer Fox Schaefer

Table 3 shows the punctual estimations and the confidence intervals of the management quantities (K, q, MSY, and fMSY) calculated by both models, Fox and Schaefer, according to the type of error in the residual variance and based on the IP = 0.7. Based on the standard deviation, the sizes of confidence intervals are in the following ascending order: Fox (multiplicative), Schaefer (multiplicative), Fox (additive), and Schaefer (additive), respectively. The punctual values of the management measures varied between models, but not between types of error of residual variance.


IP = initial proportion, B1/K = initial biomass divided by carrying capacity, K = carrying capacity, q = catchability coefficient, MSY = maximum sustained yield, fMSY = optimal effort, CV = coefficient of variation, and r2 = coefficient of determination.

#### Table 2.

Management quantities (B1/K, K, q, and MSY) and variability estimators (CV and r<sup>2</sup> ) according to the Fox and the Schaefer models, in function with the initial proportion of the biomass (IP), of the fishery of the blue crab (Callinectes sapidus) in Laguna Madre, Mexico, during the period of 1998–2012.

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue… DOI: http://dx.doi.org/10.5772/intechopen.90065


K = carrying capacity, q = catchability coefficient, MSY = maximum sustained yield, fMSY = optimal fishing effort, ILCI = inferior limit of the confidence interval, and SLCI = superior limit of the confidence interval. The initial values of the management quantities were estimated using the A Surplus-Production Model Incorporating Covariates (ASPIC) software with 0.7 as the initial proportion, considering the additive and multiplicative errors of the residual variance.

#### Table 3.

3. Results

Crustacea

(r 2

ual variance.

of determination.

Table 2.

96

was the Fox model, according to r

), the variability estimators (r

selected model was the Fox model (Table 4).

3.1 Maximum sustained yield according to the initial proportion

2

2 , CV, σ<sup>2</sup>

The values of K, q, MSY, fMSY, CV, and R2 of the Fox and the Schaefer models are presented in Table 2. Based on the results of the management quantities (B1/K, K, q, and MSY) of every IP value (from 0.1 to 0.9), the model with the best adjustment

adjustment, according to the CV (Table 2). However, considering the management quantities only for IP = 0.7 and based on the CV (Table 3), the regression estimator

Table 3 shows the punctual estimations and the confidence intervals of the management quantities (K, q, MSY, and fMSY) calculated by both models, Fox and Schaefer, according to the type of error in the residual variance and based on the IP = 0.7. Based on the standard deviation, the sizes of confidence intervals are in the following ascending order: Fox (multiplicative), Schaefer (multiplicative), Fox (additive), and Schaefer (additive), respectively. The punctual values of the management measures varied between models, but not between types of error of resid-

Model IP B1/K K q MSY fMSY CV r<sup>2</sup> Fox 0.1 0.1337 53,990 0.00008798 2567 146,900 0.3318 0.803

Logistic (Schaefer) 0.1 1.098 26,850 0.00002528 2006 58,960 0.235 0.517

IP = initial proportion, B1/K = initial biomass divided by carrying capacity, K = carrying capacity, q = catchability coefficient, MSY = maximum sustained yield, fMSY = optimal effort, CV = coefficient of variation, and r2 = coefficient

and the Schaefer models, in function with the initial proportion of the biomass (IP), of the fishery of the blue

Management quantities (B1/K, K, q, and MSY) and variability estimators (CV and r<sup>2</sup>

crab (Callinectes sapidus) in Laguna Madre, Mexico, during the period of 1998–2012.

0.2 0.1337 53,990 0.00008798 2567 146,900 0.3175 0.803 0.3 0.1337 53,990 0.00008798 2567 146,900 0.342 0.803 0.4 0.1337 53,990 0.00008798 2567 146,900 0.3166 0.803 0.5 0.1337 53,990 0.00008798 2567 146,900 0.337 0.803 0.6 0.1337 54,000 0.00008798 2567 146,900 0.3186 0.803 0.7 0.1337 54,000 0.00008798 2567 146,900 0.3472 0.803 0.8 0.1337 53,990 0.00008798 2567 146,900 0.3272 0.803 0.9 0.1337 54,000 0.00008798 2567 146,900 0.3329 0.803

0.2 1.098 27,440 0.00002488 2006 58,760 0.205 0.517 0.3 1.098 27,850 0.00002459 2007 58,610 0.2099 0.516 0.4 1.098 28,060 0.00002444 2007 58,520 0.2585 0.516 0.5 1.098 28,200 0.00002435 2008 58,470 0.2079 0.516 0.6 1.098 28,300 0.00002429 2008 58,430 0.2345 0.516 0.7 1.098 28,370 0.00002425 2008 58,390 0.2117 0.516 0.8 1.098 28,420 0.00002422 2009 58,370 0.2273 0.515 0.9 1.098 28,460 0.0000242 2009 58,350 0.2074 0.515

) according to the Fox

, whereas the Schaefer model had the best

, σ), and IC (AICc, BIC, and HQIC), the

Average values and confidence intervals of the management quantities (K, q, MSY, and fmsy) generated by the Fox and logistic (Schaefer) models for the fishery of the blue crab (Callinectes sapidus) in Laguna Madre, Tamaulipas, Mexico.


The initial values of the management quantities were estimated by means of the A Surplus-Production Model Incorporating Covariates (ASPIC) software with 0.7 as the initial proportion, considering the additive and multiplicative errors of the residual variance.

#### Table 4.

Residual variance (σ<sup>2</sup> ), standard deviation (σ), number of parameters (k), and the corrected Akaike's information criterion (AICc) as well as the Bayesian (BIC) and the Hannan-Quinn (HQIC) information criteria for each model (Fox and logistic), of the management quantities (K, q, MSY, and fMSY), for the fishery of the blue crab (Callinectes sapidus) in Laguna Madre, Tamaulipas, México.

#### 3.2 Model selection

The values of the parameters r 2 , CV, σ<sup>2</sup> , σ, and those of the IC (AICc, BIC, and HQIC), which correspond to the Fox and Schaefer models and according to the type of error of residual variance, are presented in Table 4. The lowest values of those estimators pertain to the Fox model in both types of errors. Nevertheless, the values of the management measures obtained from this model (Fox) are far from reality, particularly the optimal fishing effort (number of traps).

4. Discussion

(HQIC).

4.1 Management quantities

DOI: http://dx.doi.org/10.5772/intechopen.90065

be used to generate management measures.

sustainability of the fishery resource.

4.2 Fishing effort measure

99

delivered adjustment was the Fox model, according to r

This is the first time that management quantities have been estimated for the fishery of the blue crab (Callinectes sapidus) in Laguna Madre, Tamaulipas, Mexico. Furthermore, this is the first work carried out for aquatic organisms on the coast of Tamaulipas, Mexico, in which the information theory is applied with the purpose of selecting models by means of the IC, using the corrected Akaike's information criterion [41] (AICc) (which is used for small samples), the Schwarz or Bayesian information criterion [39] (BIC) and the Hannan-Quinn information criterion

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue…

Fisheries research investigations that deliver fishery management measures through application software programs such as ASPIC and CEDA (catch effort data analysis) to mention some, which include the adjustment of the Fox, Schaefer, and Pella-Tomlinson models, have recently resurfaced [16–24]. However, in this resurgence, there has been an underutilization of the management measures delivered by these software programs given that these only give even more emphasis to the MSY and the fMSY, thus leaving both K and q unused. Both K and q are parameters relative to the initial biomass and the catchability of the fishing gear and, hence, can

The results presented in this study for the two main reference points were MSY = 2567 tons and fMSY = 146,900 traps, from the Fox model, and MSY = 2008 tons and fMSY = 58,390 traps, from the Schaefer model. The model with the best

criteria. As for the MSY, the Schaefer model presented a result (2008 tons) that was a little more conservative than the one delivered by the Fox model (2567 tons). The difference between both results was of 22%. However, the values of the management measures obtained from this model (Fox model) were far from reality, for the optimal fishing effort (number of traps) particularly. By accepting this model could mean allowing an increase of more than 170% of the fishing effort (number of traps) which in turn could imply an increase of overfishing risk in the short term, whereas, to accept the Schaefer model (fRMS = 58,390), which is a more conservative proposal, could imply the sustainability fortification of this fishery resource. With the Schaefer model, and in relation with the average number of traps from the last 6 years of the time series, the use of about 25 traps (the equivalent of a 30%) would be restricted. This also means a lower social impact without affecting the

The definition of the fishing effort measure always represents a challenge for fisheries research, given the need for seeking the measure that can best explain the variability of fisheries catch. In this study, the number of traps was used as the measure of fishing effort, assuming that this measure of fishing effort delivers better adjustments to the models than the number of fishermen and vessels can do. Yet, it remains the assessment of the best adjustment of these management measure units for this fishery. A better measure would probably be the time length on which a trap remains underwater; this will also be a pending challenge. The same situation is presented by the shrimp fishery in the Gulf of California, where the approach of using engine power (horsepower) as a measure to normalize fishing power has been

2

, CV, and the information

Figure 2A shows how the fishing catch developed through time as well as the obtained MSY from the models (Schaefer and Fox). It can be observed that, according to the Schaefer model, during the period beginning from 2003 up to 2011, the fishery resource of the blue crab in LM became overexploited. During this period, approximately 24,000 tons of blue crab were captured, with a surplus of 6000 tons as defined by the function based on the difference in tons of catch with the MSY (2008 tons). Regarding the number of traps (f), the fMSY was exceeded from 2007 to 2012 (Figure 2B). During this mentioned period (2007–2012), approximately 500,000 traps were registered, with a surplus of 150,000 traps.

As for the Fox model, the results indicate that the resource was overexploited during only 5 (2003, 2004, 2005, 2010, and 2011) out of the 14 years that make up the time series of this study. During these years of overexploitation, the catch should have not exceeded 12,835 tons; but 15,039 tons were gathered instead. This shows a surplus of 2204 tons. In this period of overexploitation, 132, 404, 895, 373, and 400 tons were overfished in the years 2003, 2004, 2005, 2010, and 2011, respectively. This is the equivalent of an overfished resource by 5%, 14%, 26%, 13%, and 13%, respectively. In terms of fishing effort (number of traps), the fMSY was surpassed (14,690 traps) by 40 up to 85% within the whole time series, according to the Fox model.

#### Figure 2.

Fishing catch development through time of blue crab from 1998 to 2012 in Laguna Madre,Tamaulipas, Mexico, with the maximum sustained yield (A) and the number of traps and the optimal number of traps (optimal fishing effort) during this period (B).

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue… DOI: http://dx.doi.org/10.5772/intechopen.90065

#### 4. Discussion

3.2 Model selection

Crustacea

the Fox model.

Figure 2.

98

(optimal fishing effort) during this period (B).

The values of the parameters r

2 , CV, σ<sup>2</sup>

particularly the optimal fishing effort (number of traps).

HQIC), which correspond to the Fox and Schaefer models and according to the type of error of residual variance, are presented in Table 4. The lowest values of those estimators pertain to the Fox model in both types of errors. Nevertheless, the values of the management measures obtained from this model (Fox) are far from reality,

Figure 2A shows how the fishing catch developed through time as well as the

according to the Schaefer model, during the period beginning from 2003 up to 2011, the fishery resource of the blue crab in LM became overexploited. During this period, approximately 24,000 tons of blue crab were captured, with a surplus of 6000 tons as defined by the function based on the difference in tons of catch with the MSY (2008 tons). Regarding the number of traps (f), the fMSY was exceeded from 2007 to 2012 (Figure 2B). During this mentioned period (2007–2012), approximately 500,000 traps were registered, with a surplus of 150,000 traps. As for the Fox model, the results indicate that the resource was overexploited during only 5 (2003, 2004, 2005, 2010, and 2011) out of the 14 years that make up the time series of this study. During these years of overexploitation, the catch should have not exceeded 12,835 tons; but 15,039 tons were gathered instead. This shows a surplus of 2204 tons. In this period of overexploitation, 132, 404, 895, 373, and 400 tons were overfished in the years 2003, 2004, 2005, 2010, and 2011, respectively. This is the equivalent of an overfished resource by 5%, 14%, 26%, 13%, and 13%, respectively. In terms of fishing effort (number of traps), the fMSY was surpassed (14,690 traps) by 40 up to 85% within the whole time series, according to

obtained MSY from the models (Schaefer and Fox). It can be observed that,

Fishing catch development through time of blue crab from 1998 to 2012 in Laguna Madre,Tamaulipas, Mexico, with the maximum sustained yield (A) and the number of traps and the optimal number of traps

, σ, and those of the IC (AICc, BIC, and

This is the first time that management quantities have been estimated for the fishery of the blue crab (Callinectes sapidus) in Laguna Madre, Tamaulipas, Mexico. Furthermore, this is the first work carried out for aquatic organisms on the coast of Tamaulipas, Mexico, in which the information theory is applied with the purpose of selecting models by means of the IC, using the corrected Akaike's information criterion [41] (AICc) (which is used for small samples), the Schwarz or Bayesian information criterion [39] (BIC) and the Hannan-Quinn information criterion (HQIC).

#### 4.1 Management quantities

Fisheries research investigations that deliver fishery management measures through application software programs such as ASPIC and CEDA (catch effort data analysis) to mention some, which include the adjustment of the Fox, Schaefer, and Pella-Tomlinson models, have recently resurfaced [16–24]. However, in this resurgence, there has been an underutilization of the management measures delivered by these software programs given that these only give even more emphasis to the MSY and the fMSY, thus leaving both K and q unused. Both K and q are parameters relative to the initial biomass and the catchability of the fishing gear and, hence, can be used to generate management measures.

The results presented in this study for the two main reference points were MSY = 2567 tons and fMSY = 146,900 traps, from the Fox model, and MSY = 2008 tons and fMSY = 58,390 traps, from the Schaefer model. The model with the best delivered adjustment was the Fox model, according to r 2 , CV, and the information criteria. As for the MSY, the Schaefer model presented a result (2008 tons) that was a little more conservative than the one delivered by the Fox model (2567 tons). The difference between both results was of 22%. However, the values of the management measures obtained from this model (Fox model) were far from reality, for the optimal fishing effort (number of traps) particularly. By accepting this model could mean allowing an increase of more than 170% of the fishing effort (number of traps) which in turn could imply an increase of overfishing risk in the short term, whereas, to accept the Schaefer model (fRMS = 58,390), which is a more conservative proposal, could imply the sustainability fortification of this fishery resource. With the Schaefer model, and in relation with the average number of traps from the last 6 years of the time series, the use of about 25 traps (the equivalent of a 30%) would be restricted. This also means a lower social impact without affecting the sustainability of the fishery resource.

#### 4.2 Fishing effort measure

The definition of the fishing effort measure always represents a challenge for fisheries research, given the need for seeking the measure that can best explain the variability of fisheries catch. In this study, the number of traps was used as the measure of fishing effort, assuming that this measure of fishing effort delivers better adjustments to the models than the number of fishermen and vessels can do. Yet, it remains the assessment of the best adjustment of these management measure units for this fishery. A better measure would probably be the time length on which a trap remains underwater; this will also be a pending challenge. The same situation is presented by the shrimp fishery in the Gulf of California, where the approach of using engine power (horsepower) as a measure to normalize fishing power has been attempted [42]. Nevertheless, it has been considered that this measure does not properly represent the variation of the applied fishing effort since trawls use a speed of 3 knots for efficient fishing [43]. Instead, Morales-Bojórquez et al. [43] suggest that the best measure for this crustacean is the drag time; also, they indicate that the number of vessels is a good measure of fishing effort, which Altran and Loesch suggest as well [44].

determination, standard deviation, and the IC used (AICc, BIC, and HQIC) delivered the same results with respect to the selection of the model with the best adjustment. However, it has been shown that the criteria based on the information theory in the adjustment of the models are those that deliver values with greater certainty for their particular properties according to Burnham and Anderson [26].

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue…

a. Despite the economic and social importance of the crab fishery from Mexico, and in particular the blue crab (Callinectes sapidus) on the coast of the Gulf of Mexico, specifically in the Laguna Madre, Tamaulipas, the official measures

corresponding to unofficial scientists are nonexistent. On the Pacific Ocean side, several species of the genus Callinectes concur for which certain regulations (Official Mexican Standard) and planning (Regional Fisheries Management Plan) applicable to fisheries regulation are available. In the specific case of Laguna Madre, Tamaulipas, there is currently no specific regulation or regional fisheries planning; this is the first work that delivers some fisheries management measures such as MSY and fMSY, mainly and specifically for the fishing resource of the blue crab Callinectes sapidus in the Laguna Madre, Tamaulipas. Consequently, the comparative analysis of fishery management measures of this species is only carried out between those officially indicated and those thrown by this study, and in particular,

b. The scientific publications on the blue crab Callinectes sapidus of the Laguna Madre, Tamaulipas, and the State of Tamaulipas are scarce; the existing ones deal mainly with growth issues and are located in gray literature, with little access. On the contrary, for this same species, in other regions of the Atlantic, such as the Chesapeake Bay, USA, and Lake Maracaibo in Venezuela, there is research on the estimation of fishery management measures, located both in gray literature as in published literature, but infrequent and outdated.

c. According to the results presented in this study, and considering the period analyzed (1998–2012), the fishery resource of the blue crab (Callinectes sapidus) of the Laguna Madre, Tamaulipas, was under-exploited for the first 5 years, and subsequently, the last 10 years, an overexploitation is recorded

d. It is recommended to use the fishery management measures thrown in this study for blue crab (Callinectes sapidus), in particular those corresponding to MSY and fMSY (MSY = 2.008 ton and fMSY = 58.390 traps), specifically for the Laguna Madre, Tamaulipas. It is necessary to incorporate these measures into the applicable regulations in force or add them to the NFC, as well as include them in the Fisheries Management Plan that is being prepared for this purpose. These actions would be in order to contribute to fisheries regulation,

and, consequently, to the conservation of the fishery resource.

e. The use of the information criteria (Akaike, Bayesian, and Hannan and Quinn) is proposed to select, according to the best fit, the dynamic biomass models of Schaefer and Fox, since they increase the certainty during the

of fishing management are insufficient and outdated, while those

5. Conclusions and recommendations

DOI: http://dx.doi.org/10.5772/intechopen.90065

these measures are only the MSY and fMSY.

according to the RMS obtained in this same study.

selection process.

101

The fishing effort (number of traps) in this study is expressed in absolute values and was not normalized by any technique, given that (1) the fishery of the blue crab in Laguna Madre is monospecific, (2) the fishing season is the same throughout LM during the year, and (3) the fishing gear has remained technologically stable since the beginning of the fishery. It is important to properly identify the need for normalizing the fishing effort, or not, given that the results may vary according to the unit of the measure of fishing effort and that the results of some measures could be less realistic. Morales-Bojórquez et al. [43] standardized the number of vessels for the yellowleg or brown shrimp (Farfantepenaeus californiensis) fishery in the Gulf of California considering methods of using average efforts. However, the results were not successful [43]. Using average efforts can lead to poor results [45].

#### 4.3 Model selection

In a large number of research publications, the values of the coefficient of determination (r 2 ) and the coefficient of variation (CV) are established as selection criteria between different candidate models of individual growth [46]. The selection criterion consists of the process of identifying the candidate model with both an r <sup>2</sup> value closest to 1 and the lowest CV. According to Burnham and Anderson [26], r <sup>2</sup> is a measure of the description and variation of the adjustment of the model to fit the data. Regardless of this, it is not a useful criterion to select models that compete to describe the observed data [26]. Because of this, the use of the information criteria is recommended to align with the theory of information [26].

The AICc, BIC, and HQIC have as their foundation the Kullback–Leibler distance, which measures the approximation of the calculated model with the real data; this way, the best candidate model is selected [27, 47]. The information criteria rank the models according to the lower values of these information criteria, so that the models with the lower values of AICc, BIC, and HQIC will be considered as the best models [48–50]. The most important premise on the IC method is to penalize the number of parameters from each model based on the principle of parsimony [46]. In other words, there is a criterion based on the goodness of fit (adjustment) of the model to the data defined by the objective function of maximum likelihood or residual sum of squares (RSS) [46]. At the same time, there is a penalization associated with the total amount of parameters of the model [46].

The NFC establishes that capture over 2100 tons per year should not be allowed. Additionally, it indicates that this fishery is in a state of "exploited to its sustainable maximum." In this study, the model with the best adjustment, according to both the scientific criteria and reality, was the Schaefer model (MSY = 2008 tons per year). Following this criterion, the maximum catch recommended by the NFC represents the overexploitation of the blue crab as a fishery resource, given a surplus of 90 tons per year on average.

#### 4.4 Decision criteria

The model selection based on the information theory is a relatively new paradigm in the biological sciences and is very different from the classic method based on null hypothesis testing [26–29]. In this study, the estimators of the coefficient of Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue… DOI: http://dx.doi.org/10.5772/intechopen.90065

determination, standard deviation, and the IC used (AICc, BIC, and HQIC) delivered the same results with respect to the selection of the model with the best adjustment. However, it has been shown that the criteria based on the information theory in the adjustment of the models are those that deliver values with greater certainty for their particular properties according to Burnham and Anderson [26].

#### 5. Conclusions and recommendations

attempted [42]. Nevertheless, it has been considered that this measure does not properly represent the variation of the applied fishing effort since trawls use a speed of 3 knots for efficient fishing [43]. Instead, Morales-Bojórquez et al. [43] suggest that the best measure for this crustacean is the drag time; also, they indicate that the number of vessels is a good measure of fishing effort, which Altran and Loesch

The fishing effort (number of traps) in this study is expressed in absolute values and was not normalized by any technique, given that (1) the fishery of the blue crab in Laguna Madre is monospecific, (2) the fishing season is the same throughout LM during the year, and (3) the fishing gear has remained technologically stable since the beginning of the fishery. It is important to properly identify the need for normalizing the fishing effort, or not, given that the results may vary according to the unit of the measure of fishing effort and that the results of some measures could be less realistic. Morales-Bojórquez et al. [43] standardized the number of vessels for the yellowleg or brown shrimp (Farfantepenaeus californiensis) fishery in the Gulf of California considering methods of using average efforts. However, the results were not successful [43]. Using average efforts can lead to poor results [45].

In a large number of research publications, the values of the coefficient of

criteria between different candidate models of individual growth [46]. The selection criterion consists of the process of identifying the candidate model with both

to fit the data. Regardless of this, it is not a useful criterion to select models that compete to describe the observed data [26]. Because of this, the use of the information criteria is recommended to align with the theory of information [26]. The AICc, BIC, and HQIC have as their foundation the Kullback–Leibler distance, which measures the approximation of the calculated model with the real data; this way, the best candidate model is selected [27, 47]. The information criteria rank the models according to the lower values of these information criteria, so that the models with the lower values of AICc, BIC, and HQIC will be considered as the best models [48–50]. The most important premise on the IC method is to penalize the number of parameters from each model based on the principle of parsimony [46]. In other words, there is a criterion based on the goodness of fit (adjustment) of the model to the data defined by the objective function of maximum likelihood or residual sum of squares (RSS) [46]. At the same time, there is a penalization associated with the total amount of parameters of the model [46].

<sup>2</sup> value closest to 1 and the lowest CV. According to Burnham and Anderson

<sup>2</sup> is a measure of the description and variation of the adjustment of the model

The NFC establishes that capture over 2100 tons per year should not be allowed. Additionally, it indicates that this fishery is in a state of "exploited to its sustainable maximum." In this study, the model with the best adjustment, according to both the scientific criteria and reality, was the Schaefer model (MSY = 2008 tons per year). Following this criterion, the maximum catch recommended by the NFC represents the overexploitation of the blue crab as a fishery resource, given a surplus of 90 tons

The model selection based on the information theory is a relatively new paradigm in the biological sciences and is very different from the classic method based on null hypothesis testing [26–29]. In this study, the estimators of the coefficient of

) and the coefficient of variation (CV) are established as selection

suggest as well [44].

Crustacea

4.3 Model selection

2

determination (r

per year on average.

4.4 Decision criteria

100

an r

[26], r


#### Author details

Jorge Homero Rodriguez Castro<sup>1</sup> \*, Sandra Edith Olmeda de la Fuente<sup>1</sup> , Wanda Ortiz Baez<sup>2</sup> , Alfonso Correa Sandoval<sup>1</sup> and Jose Alberto Ramirez de León<sup>3</sup> References

[1] Comisión Nacional de Pesca y Acuacultura (CONAPESCA). Anuario Estadístico de Acuacultura y Pesca. México: SAGARPA; 2017. Available at: https://www.conapesca.gob.mx/work/ sites/cona/dgppe/2017/ANUARIO\_ ESTADISTICO\_2017.pdf [Last consultation: November 17, 2018]

DOI: http://dx.doi.org/10.5772/intechopen.90065

sapidus) en la región norte de la Laguna Madre, Tamaulipas. In: Memorias del III Foro Científico de Pesca Ribereña. 3–5 de Octubre del 2006. Trabajo 075: Cartel. Puerto Vallarta, Jal. 2006. pp. 153-154. Retrieved from http:// www.inapesca.gob.mx/portal/docume ntos/publicaciones/15III%20foro%20pe

sca%20riberena2006.pdf

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gob.mx/portal/documentos/

[8] Ricker WE. Computation and interpretation of biological statistics of fish populations. Bulletin of the Fisheries Research Board of Canada.

[9] Pitcher TJ, Hart PJ. Fisheries Ecology. London: Chapman and Hall;

[10] Hilborn R, Walters CJ. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. New York: Chapman and Hall; 1992. 570 pp.

[11] Prager MH. A suite of extensions to a nonequilibrium surplusproduction model. Fishery Bulletin. 1994;92:

[12] Quinn TJ II, Deriso RB. Quantitative Fish Dynamics. New York, USA: Oxford

University Press; 1992. 542 pp

[13] Maunder MN, Sibert JR,

Fonteneau A, Hampton J, Kleiber P, Harley SJ. Interpreting catch per unit

1975;191:382

1982

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[7] Leo-Peredo AS, Conde-Galaviz E. Algunos aspectos de la pesquería de la jaiba azul (Callinectes sapidus) en la parte norte de la Laguna Madre, Tamaulipas. In: Memorias del IV Foro Científico de Pesca Ribereña. 9–11 de Septiembre 2008. Trabajo 046: Cartel. Acapulco, Gro. 2008. pp. 153-154. Retrieved from http://www.inapesca.

[2] Rodríguez-Castro JH. Sustentabilidad Pesquera de la Jaiba Azul Callinectes sapidus (Rathbun, 1896) en Tamaulipas, México: Un análisis de la Incertidumbre en los parámetros de Crecimiento y en los Puntos de Referencia Para el Manejo de la pesquería [Tesis de Doctorado].

Universidad Autónoma de Tamaulipas;

[3] Secretaria de Medio Ambiente y Recursos Naturales (SEMARNAT). Acuerdo por el que se da a conocer el Resumen del Programa de Manejo del Área de Protección de Flora y Fauna Laguna Madre y Delta del Río Bravo. México, D.F.: Diario Oficial de la

[4] Diario Oficial de la Federación (DOF). del 25 de agosto del 2006. Carta Nacional Pesquera. SAGARPA, CONAPESCA. 2006. Segunda Sección. Gobierno Constitucional de los Estados Unidos Mexicanos México; 2006

[5] Medellín-Avila M, Arzate-Aguilar E, Gómez-Ortíz MA, González-Cruz A. La pesquería ribereña de la jaiba (Callinectes sapidus) en la Laguna, Madre, Tam., durante 2001 y 2002. In: Memorias del II Foro Científico de Pesca Ribereña. 20–22 de Octubre del 2003; Ciudad de Colima, Col. 93–94. 2003. Retrieved from http://www.inapesca. gob.mx/portal/documentos/publicacione s/14II+foro+pesca+riberena2003.pdf

[6] Leo-Peredo AS, Conde-Galaviz E. Estudio pesquero de la jaiba (Callinectes

103

Ciudad Victoria, Tamaulipas:

Federación. DOF; 2015

2017

1 División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México, Instituto Tecnológico de Cd. Victoria, Ciudad Victoria, Tamaulipas, Mexico

2 Universidad de Puerto Rico-Recinto, Universitario de Mayagüez, Mayagüez, Puerto Rico

3 Dirección General de Innovación Tecnológica, Universidad Autónoma de Tamaulipas, Centro Universitario, Mexico

\*Address all correspondence to: rodriguezjh@hotmail.com; jorgehomero2000@gmail.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue… DOI: http://dx.doi.org/10.5772/intechopen.90065

#### References

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Author details

Crustacea

Wanda Ortiz Baez<sup>2</sup>

Puerto Rico

102

Jorge Homero Rodriguez Castro<sup>1</sup>

Tamaulipas, Centro Universitario, Mexico

provided the original work is properly cited.

jorgehomero2000@gmail.com

\*Address all correspondence to: rodriguezjh@hotmail.com;

\*, Sandra Edith Olmeda de la Fuente<sup>1</sup>

, Alfonso Correa Sandoval<sup>1</sup> and Jose Alberto Ramirez de León<sup>3</sup>

1 División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México, Instituto Tecnológico de Cd. Victoria, Ciudad Victoria, Tamaulipas, Mexico

2 Universidad de Puerto Rico-Recinto, Universitario de Mayagüez, Mayagüez,

3 Dirección General de Innovación Tecnológica, Universidad Autónoma de

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

,

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[18] Kalhoro MA, Liu Q, Memon KH, Chang MS, Jatt AN. Estimation of maximum sustainable yield of Bombay Duck, Harpadon nehereus fishery in Pakistan using the CEDA and ASPIC packages. Pakistan Journal Zoology. 2013;45(6):1757-1764

[19] Kalhoro MA, Liu Q, Memon KH, Waryani B, Soomro SH. Maximum sustainable yield of Greater lizardfish Saurida tumbil fishery in Pakistan using the CEDA and ASPIC packages. Acta Oceanologica Sinica. 2015;34(2):68-73. DOI: 10.1007/s13131-014-0463-0

[20] Siyal FK, Li Y, Tianxiang G, Liu Q. Maximum sustainable yield estimates of silver pomfret, Pampus argenteus (family: Strometidae) fishery in Pakistan. Pakistan Journal of Zoology. 2013;45:447-452

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[31] Yánez A, Schlaepfer CJ. Composición y distribución de los sedimentos recientes de la Laguna Madre, Tamaulipas. Boletín del Instituto de Geología. UNAM. 1968;84:5-34

[32] Secretaría de Programación y Presupuesto (SPP). Atlas Nacional del Medio Físico. México. 1981. pp. 80–97

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[34] Fox WW. An exponential surplus yield model for optimizing exploited fish populations. Transactions American

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tropicales. In: Parte 1. Manual. Valparaíso: Food and Agriculture Organization of the United Nations FAO; 1995. 420 pp

Fisheries Society. 1970;99:80-88

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Biometrika. 1973;60(2):255-265

autoregressive moving average models.

identification of Gaussian

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1954;1(2):23-56

Abundancia y distribución de juveniles de Farfantepenaeus aztecus (Ives 1891), F. duorarum (Burkenroad 1939) y Litopenaeus setiferus (Linnaeus 1767) en la Laguna Madre, Tamaulipas, México. Hidrobiológica. 2008;18(3):199-208

2014;22(1):6-7

Katsanevakis S. Strengthening statistical usage in marine ecology. Journal of Experimental Marine Biology and Ecology. 2012;426-427:97-108

DOI: http://dx.doi.org/10.5772/intechopen.90065

[37] Sugiura N. Further analysis of the data by Akaike's information criterion

Communications in Statistics, Theory and Methods. 1978;A7:13-26. DOI: 10.1080/03610927808827599

[38] Burnham KP, Anderson DR. Multimodel inference understanding AIC and BIC in model selection. Sociological Methods and Research.

[39] Schwarz G. Estimating the dimension of a model. Annals of Statistics. 1978;6:461-464

[40] Hannan EJ, Quinn BG. The determination of the order of an autoregression. Journal of the Royal Statistical Society. 1979;41B:190-195

[41] Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control.

[42] Díaz de Leon-Corral JA.

Exploitation and Management of the Shrimp Fishery from Sinaloa, México [PhD dissertation]. London: Imperial

[43] Morales-Bojórquez E, López-Martínez J, Hernández-Vázquez S. Modelo dinámico de captura y esfuerzo para el camarón café Farfantepenaeus californiensis (Holmes) del Golfo de California, México. Ciencias Marinas.

[44] Altran SM, Loesch JG. An analysis of weekly fluctuations in catchability coefficients. Fishery Bulletin. 1995;93:

[45] Polacheck T, Hilborn R, Punt AE. Fitting surplus production models: Comparing methods and measuring uncertainty. Canadian Journal of Fisheries and Aquatic Sciences. 1993;

1974;19(6):716-723

College; 1993. 256 p

2001;27(1):105-124

50(12):2597-2607

562-567

and the finite corrections.

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue…

2004;33(2):261-304

[21] Wang Y, Liu Q. Application of CEDA and ASPIC computer packages to the hairtail (Trichiurus japonicus) fishery in the East China Sea. Chinese Journal of Oceanology and Limnology. 2013;31(1): 92-96

[22] Memon KH, Liu Q, Kalhoro MA, Nabi A, Kui Z. Maximum sustainable yield estimates of barramundi Lates calcarifer fishery from Pakistani waters. Indian Journal of Geo-Marine Sciences. 2015;44(6):825-832

[23] Liao B, Liu Q, Zhang K, Wang X. Verifier of the maximum sustainable yield estimates of the southern Atlantic albacore,Thunnus alalunga, stock. Fisheries Management and Ecology. 2016;23(2):161-168

[24] Liao B, Liu Q, Zhang K, Baset A, Memon AM, Memon KH, et al. A continuous time delay-difference type model (CTDDM) applied to stock assessment of the southern Atlantic albacore and Thunnus alalunga. Chinese Journal of Oceanology and Limnology. 2016;34(5):977-984

[25] Prager MH. A Stock-Production Model Incorporating Covariates (version 5) and auxiliary programs. Beaufort Laboratory Document. CCFHR (NOAA) Miami Laboratory Document MIA-92/93–55, 2005. BL-2004-01

[26] Burnham KP, Anderson DR. Model Selection and Multimodel Inference: A Practical Information Theoretic Approach. 2nd ed. New York: Springer; 2002. 488 p

[27] Katsanevakis S.Modelling fish growth: Model selection, multi-model inference and model selection uncertainty. Fisheries Research. 2006;81(2–3):229-235

Estimation of the Maximum Sustainable Yield and the Optimal Fishing Effort of the Blue… DOI: http://dx.doi.org/10.5772/intechopen.90065

[28] Beninger PG, Boldina I, Katsanevakis S. Strengthening statistical usage in marine ecology. Journal of Experimental Marine Biology and Ecology. 2012;426-427:97-108

effort data to assess the status of individual stocks and communities. ICES Journal of Marine Science: Journal du Conseil. 2006;63(8):1373-1385

silver pomfret, Pampus argenteus (family: Strometidae) fishery in Pakistan. Pakistan Journal of Zoology.

[21] Wang Y, Liu Q. Application of CEDA and ASPIC computer packages to the hairtail (Trichiurus japonicus) fishery in the East China Sea. Chinese Journal of Oceanology and Limnology. 2013;31(1):

[22] Memon KH, Liu Q, Kalhoro MA, Nabi A, Kui Z. Maximum sustainable yield estimates of barramundi Lates calcarifer fishery from Pakistani waters. Indian Journal of Geo-Marine Sciences.

[23] Liao B, Liu Q, Zhang K, Wang X. Verifier of the maximum sustainable yield estimates of the southern Atlantic albacore,Thunnus alalunga, stock. Fisheries Management and Ecology.

[24] Liao B, Liu Q, Zhang K, Baset A, Memon AM, Memon KH, et al. A continuous time delay-difference type model (CTDDM) applied to stock assessment of the southern Atlantic albacore and Thunnus alalunga. Chinese Journal of Oceanology and Limnology.

[25] Prager MH. A Stock-Production Model Incorporating Covariates (version 5) and auxiliary programs. Beaufort Laboratory Document. CCFHR (NOAA) Miami Laboratory Document MIA-92/93–55, 2005. BL-2004-01

[26] Burnham KP, Anderson DR. Model Selection and Multimodel Inference: A Practical Information Theoretic Approach. 2nd ed. New York: Springer;

[27] Katsanevakis S.Modelling fish growth: Model selection, multi-model inference and model selection uncertainty. Fisheries

Research. 2006;81(2–3):229-235

2013;45:447-452

2015;44(6):825-832

2016;23(2):161-168

2016;34(5):977-984

2002. 488 p

92-96

[14] Mace PM. Relationships between common biological reference points used as thresholds and targets of fisheries management strategies. Canadian Journal of Fisheries and Aquatic Sciences. 1994;51(1):110-122

[15] FAO. Reference points for fishery

management: Their potential application to straddling and highly migratory resources. In: FAO Fisheries Circular 864. Food and Agriculture Organization of the United Nations;

[16] Panhwar SK, Liu Q, Khan F, Siddiqui PJ. Maximum sustainable yield estimates of Ladypees, Sillago sihama (Forsskål), fishery in Pakistan using the ASPIC and CEDA packages. Journal of Ocean University of China. 2012;11(1):

[17] Panhwar SK, Liu Q, Khan F, Waryani B. Maximum sustainable yield estimates of spiny lobster fishery in Pakistan using non-equilibrium CEDA package. Russian Journal of Marine Biology. 2012;38(6):448-453. DOI: 10.1134/S1063074012060077

[18] Kalhoro MA, Liu Q, Memon KH, Chang MS, Jatt AN. Estimation of maximum sustainable yield of Bombay Duck, Harpadon nehereus fishery in Pakistan using the CEDA and ASPIC packages. Pakistan Journal Zoology.

[19] Kalhoro MA, Liu Q, Memon KH, Waryani B, Soomro SH. Maximum sustainable yield of Greater lizardfish Saurida tumbil fishery in Pakistan using the CEDA and ASPIC packages. Acta Oceanologica Sinica. 2015;34(2):68-73. DOI: 10.1007/s13131-014-0463-0

[20] Siyal FK, Li Y, Tianxiang G, Liu Q. Maximum sustainable yield estimates of

2013;45(6):1757-1764

104

1993. 52 pp.

Crustacea

93-98

[29] Katsanevakis S. Multi-model inference and model selection in Mexican fisheries. Ciencia Pesquera. 2014;22(1):6-7

[30] Ocaña-Luna A, Hernández-Batún G, Sánchez-Ramírez M. Abundancia y distribución de juveniles de Farfantepenaeus aztecus (Ives 1891), F. duorarum (Burkenroad 1939) y Litopenaeus setiferus (Linnaeus 1767) en la Laguna Madre, Tamaulipas, México. Hidrobiológica. 2008;18(3):199-208

[31] Yánez A, Schlaepfer CJ. Composición y distribución de los sedimentos recientes de la Laguna Madre, Tamaulipas. Boletín del Instituto de Geología. UNAM. 1968;84:5-34

[32] Secretaría de Programación y Presupuesto (SPP). Atlas Nacional del Medio Físico. México. 1981. pp. 80–97

[33] Schaefer M. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Bulletin Inter-American Tropical Tuna Commission. 1954;1(2):23-56

[34] Fox WW. An exponential surplus yield model for optimizing exploited fish populations. Transactions American Fisheries Society. 1970;99:80-88

[35] Sparre P, Venema S. Introducción a la evaluación de recursos pesqueros tropicales. In: Parte 1. Manual. Valparaíso: Food and Agriculture Organization of the United Nations FAO; 1995. 420 pp

[36] Akaike H. Maximum likelihood identification of Gaussian autoregressive moving average models. Biometrika. 1973;60(2):255-265

[37] Sugiura N. Further analysis of the data by Akaike's information criterion and the finite corrections. Communications in Statistics, Theory and Methods. 1978;A7:13-26. DOI: 10.1080/03610927808827599

[38] Burnham KP, Anderson DR. Multimodel inference understanding AIC and BIC in model selection. Sociological Methods and Research. 2004;33(2):261-304

[39] Schwarz G. Estimating the dimension of a model. Annals of Statistics. 1978;6:461-464

[40] Hannan EJ, Quinn BG. The determination of the order of an autoregression. Journal of the Royal Statistical Society. 1979;41B:190-195

[41] Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control. 1974;19(6):716-723

[42] Díaz de Leon-Corral JA. Exploitation and Management of the Shrimp Fishery from Sinaloa, México [PhD dissertation]. London: Imperial College; 1993. 256 p

[43] Morales-Bojórquez E, López-Martínez J, Hernández-Vázquez S. Modelo dinámico de captura y esfuerzo para el camarón café Farfantepenaeus californiensis (Holmes) del Golfo de California, México. Ciencias Marinas. 2001;27(1):105-124

[44] Altran SM, Loesch JG. An analysis of weekly fluctuations in catchability coefficients. Fishery Bulletin. 1995;93: 562-567

[45] Polacheck T, Hilborn R, Punt AE. Fitting surplus production models: Comparing methods and measuring uncertainty. Canadian Journal of Fisheries and Aquatic Sciences. 1993; 50(12):2597-2607

[46] Guzmán-Castellanos AB, Morales-Bojórquez E, Balart EF. Estimación del crecimiento individual en elasmobranquios: la inferencia con modelos múltiples. Hidrobiológica. 2014;24(2):137-150

[47] Katsanevakis S, Maravelias CD. Modelling fish growth: Multi-model inference as a better alternative to a priori using von Bertalanffy equation. Fish and Fisheries. 2008;9(2):178-187

[48] Cailliet GM, Smith WD, Mollet HF, Goldman KJ. Age and growth studies of chondrichthyan fishes: The need for consistency in terminology, verification, validation, and growth function fitting. Environmental Biology of Fishes. 2006; 77:211-228

[49] Romine JG, Grübbs RD, Müsick JA. Age and growth of the sandbar shark, Carcharhinus plumbeus, in Hawaiian waters through vertebral analysis. Environmental Biology of Fishes. 2006; 77:229-239

[50] Griffiths SP, Fry GC, Manson FJ, Loü DC. Age and growth of long tail tuna (Thunnus tonggol) in tropical and temperate waters of the central indo-Pacific. International Council for the Exploration of the Sea. Journal of Marine Science. 2010;67(1):125-134

**107**

Section 3

Genetics

Section 3
