Estimation of catchability for the Heterocarpus reedi AND Cervimunida johni fisheries in northern Chile, using different 

catch per unit of area estimators

Eduardo P. Pérez E. and Omar Defeo

Eduardo P. Pérez E. Marine Biologist, Universidad Católica del Norte (UCN), Chile. M.Sc. and Ph.D., Centro de Investigación y Estudios Avanzados (CINVESTAV-IPN), Mexico. Professor, Department of Marine Biology, UCN, Chile and Researcher, Centro de Estudios Avanzados en Zonas Áridas, Coquimbo, Chile. Address: Casilla 117, Coquimbo, Chile, e-mail: eperez@ucn.cl

Omar Defeo. Ph.D., CINVESTAV-IPN, Mexico. Professor, CINVESTAV-IPN,Unidad Mérida. Ardes: A.P. 73 Cordemex C.P. 97310, Mérida, Yucatán, Mexico.

Resumen

Se estimaron los coeficientes de capturabilidad (q) para la pesquería de Heterocarpus reedi y Cervimunidia johni en el Norte de Chile. Anteriormente, se reportó una relación inversa entre q y CPUE (captura por unidad de esfuerzo) para H. reedi. Sin embargo, altas varianzas asociadas a este tipo de estimaciones no permiten rechazar la utilidad de estimaciones basadas en un q estático. No existen antecedentes para el caso de C. johni. Dada la alta variabilidad entre lances de pesca observada en pesquerías de arrastre, se evaluó la forma apropiada de calcular estimadores no sesgados de la CPUE con el fin de disminuir la varianza en los estimadores de q. Cinco medidas de tendencia central fueron evaluadas: normal, lognormal, Delta, Finney-Sichel, y la media calculada a partir del Teorema del Límite Central. Para estandarizar el esfuerzo de pesca, se determinó la captura por km² de arrastre (captura por unidad de área, CPUA). Los resultados indicaron que las cinco estimaciones de q fueron confiables, con independencia del estimador de media usado. Sin embargo, los estimadores de q basados en la distribución lognormal fueron más precisos, por lo que se sugieren como insumos confiables en el modelaje de esta pesquería en el Norte de Chile.

Summary

Catchability coefficients (q) for two shrimp species (Heterocarpus reedi and Cervimunida johni) caught by trawl in Northern Chile fisheries were estimated. An inverse relationship between q and CPUE (catch per unit of effort) has been previously reported for H. reedi, but high values of variance associated to the mean estimates did not permit to assess the relative usefulness of both constant and variable q. No information is available for C. johni. Given the high between-haul variability observed in trawl fisheries, the appropriate way to calculate unbiased estimators for CPUE was evaluated, in order to diminish the variance in q estimators. Five central tendency measures were evaluated: normal, lognormal, Delta, Finney-Sichel, and that calculated from the Central Limit Theorem. To standardize fishing effort, catch was considered per  km² trawled and referred to as catch per unit of area (CPUA). The results indicated that q estimates were reliable, independently of the estimator of the mean employed. However, in terms of precision, estimators of q based on the lognormal distribution were better and are thus suggested as reliable inputs for modeling this trawl fishery in Chile.

Resumo

Estimaram-se os coeficientes de capturabilidade (q) para a pescaria de Heterocarpus reedi y Cervimunidia johni no Norte do Chile. Anteriormente, reportou-se uma relação inversa entre q e CPUE (captura por unidade de esforço) para H. reedi. No entanto, altas variâncias associadas a este tipo de estimações não permitem rejeitar a utilidade de estimações baseadas em um q estático. Não existem antecedentes para o caso de C. johni. Devido à alta variabilidade entre lances de pesca observada em pescarias tipo arrastão, avaliou-se a forma apropriada de calcular estimadores não viesados da CPUE com o fim de diminuir a variâncias nos estimadores de q. Cinco medidas de tendência central foram avaliadas: normal, lognormal, Delta, Finney-Sichel, e a media calculada a partir do Teorema do Limite Central. Para estandartizar o esforço de pesca, determinou-se a captura por  km² de arrastão (captura por unidade de área, CPUA). Os resultados indicaram que as cinco estimações de q foram confiáveis, com independência do estimador de média usado. No entanto, os estimadores de q baseados na distribuição lognormal foram mais precisos, pelo que se sugerem como insumos confiáveis na modelagem de esta pescaria no Norte do Chile.

Keywords / Catchability / Cervimunida johni / Chile / CPUA / Heterocarpus reedi /

Received: 09/21/2004. Modified: 01/10/2005. Accepted: 01/11/2005.

The catchability coefficient (q) is a technologically-related parameter, which represents the proportion of individuals of a stock caught per unit of effort exerted (Gulland, 1983). Ideally, estimates of q should be independent of standing biomass (Arreguín-Sánchez, 1996; Seijo et al., 1997, Pérez and Defeo, 2003; Pérez and Chávez, 2004). There are several methods that estimate q based on catch per unit of fishing effort (CPUE) and cumulative effort or catch during a certain time frame (Wolff, 1987; Hilborn and Walters, 1992; Arreguín-Sánchez, 1996). These methods are based on the assumption that the CPUE at any time is equivalent to

CPUE_t = qB_t                (1)

where B_t: stock biomass at time t.

After catching K tons in time t, decay of CPUE over time would be (Hilborn and Walters, 1992)

CPUE_t = qB₀-qK_t            (2)

where B₀: biomass at the beginning of the fishing period.

For trawl fisheries, marked between-haul variability in catches has been documented (Taylor, 1953). This could affect CPUE estimates derived from the use of the mean and normal variance, which might be skewed due to the mentioned variability (Smith, 1990). This has led to question which method is the most adequate one for representing the CPUE mean and variance (Pennington, 1983, 1986; Hilborn and Walters, 1992). This question is critical, as the mean is commonly used to estimate the abundance of the stock, and the variance is used to estimate the corresponding confidence intervals. Thus, bias in the mean and variance estimates could lead to over- or under-estimations of resource abundance. The question is also valid for the case in which the mean CPUE, used as an unbiased index of abundance, is used to estimate parameters q and B₀ in Eq. 2. Bias in mean estimates would directly affect q estimates and, indirectly, the estimated CPUE used to validate observed trends in CPUE through time; furthermore, it would lead to incorrect estimates of B using Eq. 1.

The crustacean trawl fishery in Chile operates between the III and VIII Regions (Figure 1). The main species are the "nylon shrimp" Heterocarpus reedi, the "Chilean squat lobster" Cervimunida johni, and the "red squat lobster" Pleuroncodes monodon. Each species is subject to different management strategies: the H. reedi fishery has been declared fully exploited between the II and VIII Regions (Figure 1); C. johni is considered fully exploited only from the III to the IV Region, while towards the south, access to this resource is granted by means of a license fee system of catch quotas. The fleet that uses the port of Coquimbo, IV Region, as its base (Figure 1), accounts for an important amount of the H. reedi catch, while large portions of the catch of C. johni have been reported in the III Region (Acuña et al., 1998, 1999). In the process of formulating a model for this fishery, a reliable estimation of q is needed. Recently, Pérez and Defeo (2003), reported an inverse relationship between CPUE and q for the nylon shrimp H. reedi fishery, and suggested that CPUE was not a reliable index of abundance and, thus, estimates provided by Eq. 2 could be biased. However, Pérez and Chávez (2004) have shown that, for simulation purposes, static estimations (assuming constant q as in Eq. 2) can be useful when high variances were associated to dynamic estimations for catchability. Given reasonable doubts about the possible estimate of this parameter for H. reedi and C. johni fisheries, the main objective of this study was to compare static estimates of q provided by the use of different estimators of central tendency. The study was carried out on the H. reedi and C. johni fisheries of Northern Chile, because of the reliable database generated in close collaboration with the fishing industry.

 

Materials and Methods

Data were obtained from the trawl fishery based in Coquimbo, in the IV Region (Figure 1). The fleet mainly operates in the III and IV Regions, and catch is landed at four ports, two of which are located in the III Region (Caldera and Huasco) and two in the IV Region (Coquimbo and Los Vilos). Acuña et al. (1998, 1999) recognized four main fishing areas according to the analysis of historical data series (Figure 1): North Caldera (Ca-N), South Caldera (Ca-S), North Coquimbo (Co-N) and South Coquimbo Co-S).

The information gathered consisted of individual hauls registered in the logbooks of each vessel between September 1, 1997 and June 30, 1998. Two management strategies, which were important for the crustacean fishery, were implemented during this period: between July 1 and August 31, the season remains closed for nylon shrimp, while the Chilean squat lobster season is closed between January 1 and March 31 (Subpesca, 1999a, b). Thus, the data gathered covered the whole fishing season for the nylon shrimp and an important part of that of the Chilean squat lobster, which constitutes the primary target when the shrimp fishery season is closed. Due to their importance and representativeness in terms of catch volume, the III and IV Regions (Figure 1) were selected as fishing areas for later calculations.

The model proposed by Wolff (1987) was used to estimate q. This model includes a modification of the depletion method of Leslie and Davis (Hilborn and Walters, 1992), by incorporating losses due to natural mortality (M) in addition to catch (fishing mortality) in cases when, as here, the analysis is carried out over a prolonged period of time (Wolff, 1987). The model is expressed as

where CPUA: capture per unit area (ton·km^-2) over time t; K_t: accumulated catch, calculated by summing half of the catch in time t with the total catch in prior t intervals; and Mt: the natural mortality during time t. For the Chilean squat lobster, M= 0.8·year^-1 (0.015·week^-1) was used (Wolff and Aroca, 1995), whereas M= 0.35·year^-1 ( (0.007·week^-1) was used for the nylon shrimp (Sernapesca, 1997; Pérez, 2003). It was decided to use CPUA instead of CPUE (capture per haul) in order to avoid the inherent variability generated by the largely dissimilar duration of individual hauls.

Two sources of information were used for calculating the total weekly catches: i) daily information from the Trawl Fleet Activity Monitoring Program (Acuña et al., 1998, 1999, 2000) for the fleet using Coquimbo as port of origin. Information was expressed as CPUA (tons·km^-2) per haul per day; however, this database did not contain information about other vessels operating far away from Coquimbo. Thus, ii) ancillary information on monthly catches contained in the Annual Fisheries Statistics (Sernapesca, 1998, 1999, 2000) was employed. To estimate the total catch of all vessels operating in the III and IV Chilean Regions, it was assumed that the catch obtained by the Coquimbo fleet was representative of the fleet operating in both Regions. The fraction caught per day was determined from the above figures, and this value was multiplied by the total monthly catch of the entire fleet (contained in the Annual Fisheries Reports, Sernapesca 1998, 1999, 2000) to obtain an estimate of the total daily catch. This was later grouped on a weekly basis.

Since the primary objective of this study was to estimate q according to different estimators of central tendency, trajectories of CPUA over time were considered as a function of five estimators of the mean: normal, lognormal, Delta (D), Finney-Sichel, and that calculated from the Central Limit Theorem (TLC). The variance associated with each of these was also determined.

The normal mean was determined using

where n: total number of hauls, including hauls with no catch. The variance is calculated as

An estimator of the mean calculated using the TLC is based on the assumption that the distribution of means obtained from a non-normal population tends to normality as the number of samples increases (Zar, 1995). For this purpose, the distribution of means for each sample of N values for weekly CPUA (including zero values) was calculated using the "bootstrap" technique (Efron, 1981), which consists in a random sampling with replacement. Thus, a subsample with an n size equal to 25% of the hauls observed was randomly selected, including those with no catch, for each week. The mean was estimated from 3000 random subsamples (Eq. 4), and the variance of the population of all possible means using samples of size n from a population with a variance of s² was given by (Zar, 1995) as

A third estimator was based on the lognormal distribution, which does not allow for zero observations and is defined as the random variable X’ whose natural logarithm has a normal distribution with mean µ and variance s².

The unbiased estimator of the mean is given by Conquest et al. (1996) as

 

and the variance is

The fourth estimator was based on the Delta (D) method, a modified lognormal distribution that takes into account zero-value observations. Thus, there is a sample size N with a finite probability D for a CPUA of zero, and a lognormal distribution for CPUA values greater than zero (p=1-D). According to Pennington (1983, 1986) and Smith (1988, 1990) the model-based, unbiased estimator of the mean with a sample size N, and with m values greater than zero, mean of µ and variance s² is given by

and its variance is

Finally, the Finney-Sichel (FS) estimator was used, by which the mean CPUA was calculated using the equation of Roa et al. (1995)

where mean CPUA obtained from non-zero data, and

where t: s²/2, m: number of data greater than zero. The variance is determined by

The estimators of the lognormal, D, and FS distributions require that the natural log of the non-zero observations have a normal distribution. This prior condition was evaluated using X² (Zar, 1995). Once this condition was met, the mentioned estimators were calculated.

Mean weekly estimates of q were compared using the non-parametric X²  test (Zar, 1995). Then, once Eq. 3 was fitted to each group of means, slopes (representing q) and intercepts (initial biomass in the fisheries zone, B₀) were compared using an ANCOVA (Zar, 1995), with the different estimators as treatments, and the CPUA as covariable. B₀ was determined following Eq. 3, dividing the corresponding intercept by the slope.

Results

With the exception of weeks 2, 5, and 38, the hauls with a catch greater than zero were normally distributed (X² , p>0.05). As it is impossible to plot each one of the weekly results, Figure 2 shows, as an example, the behavior of the data with and without catch (zero hauls) for week 31; 12 hauls occurred without catches, and the data were not normally distributed (X² , p=0.002). The natural log of the data greater than zero behaved normally (p=0.15), thus giving support to the mean estimators based on the lognormal distribution.

  

Different estimates of mean CPUA discriminated by species and zones did not differ between each other (X² , p>0.05; Figures 3 and 4). Between-estimator differences were found in their standard deviations only in the case of the nylon shrimp (Figure 5). The standard deviation calculated using the normal distribution was larger than those provided by the other estimators based on the lognormal distribution. For the Chilean squat lobster, the standard deviation provided by the different estimators did not differ between them, but the mean obtained by TCL showed a lower standard deviation (Figure 6) compared with the other ones, suggesting a higher degree of precision.

 

 

 

Once the weekly trends of CPUA were calculated, q was estimated for the time period when the inverse relation expected between the accumulated catch K_t and CPUA was evident. In the case of the nylon shrimp, the period comprised between weeks 19 and 33 (Figure 3) was chosen, while weeks 31 to 40 were selected for the Chilean squat lobster (Figure 4).

Values of the intercept and the slope of Eq. 3 (Table I) did not show significant differences between different estimators of the mean (ANCOVA, p>0.05). However, the percentage of variance explained by the linear model was larger when the TCL estimators were used in the case of the nylon shrimp, and with the FS estimator in the case of the Chilean squat lobster (Table I).

B₀ varied between 912 and 2103 tons in the case of the Chilean squat lobster (Table I). Results obtained using the normal estimator of the mean and the TCL estimation showed a level of 1400 tons. In the case of the nylon shrimp, B₀ fluctuated between 3031 and 3405 tons (Table I).

Discussion

The analysis of information arising from the crustacean trawl fishery in Northern Chile did not show statistically significant differences between q estimators. Conquest et al. (1996) compared differences between model-based and design-based estimators based on the Delta and normal distributions for the artisanal croaker fishery in the Gulf of Nicoya, on the Pacific coast of Costa Rica. The most important difference found was based on the degree of precision of the estimator, with the Delta distribution showing a more robust behavior. Pennington (1983, 1986) suggested that the normal mean was not robust in the case of small sample numbers. In the present study, the similarity found among estimators might be due to the large number of samples obtained. If, as demonstrated, there are no differences among estimations of q and B₀, each one of the cited estimators of central trend may be used for the estimation of q using Eq. 3. A different scenario arises when the variance of the observations is used to assess the confidence of the estimates. In this case, estimators based on the lognormal distribution had greater precision than those based on the normal distribution. Although there is a marked mistrust to use estimators coming from non-dynamic models (i.e., constant estimators when they are objectively variable over time), Pérez and Chávez (2004) showed the usefulness of this kind of calculations, because of the high variance in CPUE data that commonly occur in trawl fisheries (Taylor, 1953). For Mesodesma donacium fishery, static estimation of q allowed more precise simulation for critical performance variables (e.g. catch, CPUE) in this fishery, as compared with dynamic estimation. In this way, static estimation for key parameters might not be completely discarded (Pérez and Chávez, 2004), even though this could be a wrong initial assumption in a modeling process.

The results suggest that, for the crustacean fisheries of the Northern Chile, estimates of q are reliable, independently of the estimator employed. However, in terms of precision, those based on the lognormal distribution (lognormal, FS, Delta) produced better results under all circumstances, confirming conclusions by Conquest et al. (1996) in the sense that the normal mean is not a reliable central tendency measure for fishery data. Estimators based on TCL constituted a powerful tool for calculating fisheries parameters based on CPUA, given its precision around mean estimates. Therefore, the present results could be used with confidence in order to develop simulation models for these fishery resources directed to evaluate the biological and economic impacts of alternative exploitation strategies.

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