Estimating Biomass, Recruitment, and Harvest Rate ...

Estimating Biomass, Recruitment, and Harvest Rate for the Pacific Yellowleg Shrimp Farfantepenaeus californiensis from a Size-Based Model Author(s): Enrique Morales-Bojórquez , Juana López-Martínez and Luis Francisco Javier BeléndezMoreno Source: Journal of Shellfish Research, 32(3):815-823. 2013. Published By: National Shellfisheries Association DOI: http://dx.doi.org/10.2983/035.032.0325 URL: http://www.bioone.org/doi/full/10.2983/035.032.0325

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Journal of Shellfish Research, Vol. 32, No. 3, 815–823, 2013.

ESTIMATING BIOMASS, RECRUITMENT, AND HARVEST RATE FOR THE PACIFIC YELLOWLEG SHRIMP FARFANTEPENAEUS CALIFORNIENSIS FROM A SIZE-BASED MODEL

ENRIQUE MORALES-BOJO´RQUEZ,1 JUANA LO´PEZ-MARTIŃEZ2* AND LUIS FRANCISCO JAVIER BELEŃDEZ-MORENO3 1 Centro de Investigaciones Biolo´gicas del Noroeste SC, Instituto Politećnico Nacional 195, Col. Playa Palo de Santa Rita Sur, CP 23090, La Paz, Baja California Sur, Me´xico; 2Centro de Investigaciones Biolo´gicas del Noroeste, S.C. Carretera a las Tinajas s/n, CP 85454, Guaymas, Sonora, Me´xico; 3 Instituto Nacional de Pesca. Pita´goras 1320, Col. Santa Cruz Atoyac, CP 03310, Me´xico, D.F. ABSTRACT Catch-at-size data were analyzed for Farfantepenaeus californiensis from fishing seasons 1978/1979 to 1994/1995. The catch-at-size model could be fitted to the catch-at-size data for the different fishing seasons. It was observed that the recruitment to the fishery changed suddenly during the study period, and the recruitment to the fishery may occur over a range of length classes. The recruits were defined as size classes less than 93.5 mm in abdominal length. Recruitment varied from 200–3,800 million recruits. In contrast, the size classes were larger than 93.5 mm in terms of abdominal length, and the number of adults varied from 3,500,000–50,000,000. In the study zone, it was not common to find remnant biomass of adults. Consequently, the most abundant size intervals of abdominal length were 62.4 mm, 67 mm, and 72.2 mm. The results of the harvest rate-at-size showed that the size interval from 65–80 mm in abdominal length was less than 0.05. The highest levels of harvest rate-at-size were estimated to be 85–125 mm in abdominal length, with an estimated variation of 0.6–0.9. It was observed that individuals less than 93.5 mm in abdominal length are in the range of length classes in which recruitment to the fishery occurs. These recruits support the fishing pressure and the yield of the fishery; in contrast, the presence of adults is scarce. Therefore, this fishery in the region is strongly recruitment dependent. KEY WORDS: shrimp, Farfantepenaeus californiensis, growth, catch-at-size model, recruitment

INTRODUCTION

The offshore shrimp fishery in Mexico includes three important commercial species: the whiteleg shrimp (Litopenaeus vannamei Boone, 1931), the Pacific yellowleg shrimp (Farfantepenaeus californiensis Holmes, 1900), and the blue shrimp (Litopenaeus stylirostris Stimpson, 1874). The shrimp fishery evolved during the 1930s by modifying sardine boats. The fleet grew rapidly to 800 boats and remained stable until 1971. During the next decade, the fleet increased to 1,700 boats; however, landings have not increased and the catch level changed from only 25,000 t to 27,000 t. The total catch during the 1960s and 1970s has been almost identical, but the catch per unit effort decreased substantially from 40 t to 15 t. In the Gulf of California, the majority of the catch occurs near the states of Sonora and Sinaloa, although Oaxaca and Chiapas in the southern Mexican Pacific are areas that also contribute, but with smaller landings (Magalloń-Barajas 1987). Today, the landings in the Mexican Pacific are about 25,000 t. The Pacific yellowleg shrimp (Farfantepenaeus californiensis) is a well-developed fishery in the Gulf of California, Mexico. The fishery operates apparently on a single stock over its entire geographical range (Morales-Bojo´rquez & Lo´pez-Martı´ nez 1999). The life cycle of the shrimp is completed in the open marine environment, although the species can survive in shallow waters during its first postlarval stage (ValenzuelaQuinõnez et al. 2006). Since 1975, the fishing effort has varied between 300 vessels and 500 vessels per fishing season. The stock assessment of this fishery is based on commercial fishery data *Corresponding author E-mail: [email protected] DOI: 10.2983/035.032.0325

(Morales-Bojo´rquez et al. 2001). The fishery begins its open fishing season during the summer; usually, September is the month when shrimp have grown to adequate size for optimal yield, and recruitment in the fishing ground has occurred. The fishing season for shrimp is closed from March to July every year. The fishing season can vary depending on the reproductive pattern (when maturity is observed in females), or decrease in abundance, yield, or catch per unit effort. The size composition of Farfantepenaeus californiensis was used because the age composition was not available for all fishing seasons. In addition, the determination of age in crustaceans may be hampered by inaccuracy, imprecision, or lack of valid aging methods. These difficulties are resolved in part by the use of an estimation procedure based on the length composition of the catch (Sullivan et al. 1990). Lo´pez-Martı´ nez (2000) used a deterministic approach of catch-at-size analysis (CASA) for Farfantepenaeus californiensis from 1978 to 1994. Zheng et al. (1995, 1998) used CASA in populations of the red king crab (Paralithodes camtschaticus Tilesius, 1815) and tanner crab (Chionoecetes bairdi Rathbun, 1924). In different taxa, the CASA model has been applied. During 2002, a modified CASA model made use of commercial catch-at-length data, effort data, and a recruitment index derived from survey data of the Scottish anglerfish (Lophius piscatorius Linnaeus, 1758). The method addressed known problems associated with age readings and the rapid expansion of the fishery, and provided a satisfactory fit to the data (Dobby et al. 2008). Sullivan et al. (1990) used a modified CASA that includes a stochastic model of growth. The CASA model has also been used for 3 populations of fish: the Pacific cod (Gadus macrocephalus Tilesius, 1810), the longneck croaker (Pseudotolithus typus Linnaeus, 1758), and the round scad (Decapterus russellii Ru¨ppell, 1830). Lai and

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TABLE 1.

Number of individuals sampled by fishing season in Guaymas, Sonora, Mexico. Fishing season

Individuals sampled (n)

1978/1979 1979/1980 1980/1981 1981/1982 1982/1983 1983/1984 1984/1985 1985/1986 1986/1987 1987/1988 1988/1989 1989/1990 1990/1991 1991/1992 1992/1993 1993/1994 1994/1995

3,725 8,550 9,790 10,340 6,200 7,650 5,550 6,690 8,960 4,160 5,480 5,820 5,660 7,520 8,960 12,460 6,670

Figure 1. Study area in the Gulf of California, Mexico.

Bradbury (1998) used CASA for the red sea urchin (Strongylocentrotus franciscanus Aggassiz, 1863) and identified that the parameters that should be estimated from the size–frequency data because a valid technique of age determination was not available. Here, the annual patterns of recruitment of Farfantepenaeus californiensis were estimated in the Guaymas basin, as was the impact of the harvest rate on size composition over time. Although the management of the Pacific yellowleg shrimp fishery has been successful, it is based only on controlling fishing efforts (Lo´pez-Martı´ nez et al. 2003). Crucial information is needed about the temporal variability in biomass, recruitment, and harvest rate during the fishing season. This information would provide additional valuable data to stakeholders, because they can improve the biological management through planning strategies associated with high abundance, as well as protect stock when biological variability, demographic instability, and environmental change have negative effects on the stock. In this study, the changes in biomass, recruitment, and harvest rate of Farfantepenaeus californiensis was analyzed from size composition data.

The monthly catch was obtained from the Subdelegacioń Federal de Pesca in Guaymas. This information involved records of shrimp trawlers fleet. We used the parameters for the von Bertalanffy growth parameters of Lo´pez-Martı´ nez et al. (2003) (Table 3). The abdominal length–abdominal weight relationship in conjunction with the total catch by fishing season was used to estimate the total number of Pacific yellowleg shrimp per abdominal length interval. The parameters of the abdominal length–abdominal weight relationship from 1978 to 1995 were a ¼ 2.0 3 10–5 and b ¼ 2.97, and natural mortality per fishing season is shown in Table 4 (Lo´pez-Martı´ nez 2000). The catch-at-length data were analyzed using CASA (Sullivan et al. 1990). The advantage of the CASA model is that it incorporates a stochastic model of growth that uses a lengthstructured mathematical model that considers exploitation and growth of individuals in the population in terms of length, and is formulated in terms of two relationships. The first relates catch-at-length to abundance; the second determines changes in numbers-at-length from one time interval to the next. The catch-at-length is expressed as Cl.t, where l represents the lengthclass and t is time. The number of individuals in the population is denoted Nl,t. The harvest rate (ml,t) is defined as the proportion

MATERIAL AND METHODS

Data were analyzed from the 1978/1979 to 1994/1995 fishing seasons. The biological data were collected on a monthly basis at the port of Guaymas, Sonora, during each fishing season (Fig. 1). The size composition was obtained from two sources. The first source was the daily packing-plant sampling of commercial captures at Guaymas, Sonora, with a total of 124,185 individuals sampled (Table 1). The biological samples were obtained during September through May of each fishing season, and data were grouped in monthly periods to obtain the length–frequency distributions. The second source was the commercial captures, which were sampled onboard trawlers of the commercial fleet that operated along the coast of Sonora from the 1989/1990 to 1994/995 fishing seasons (Table 2).

TABLE 2.

Number of individuals sampled onboard trawlers of the commercial fleet in Guaymas, Sonora, Mexico. Fishing season 1989/1990 1990/1991 1991/1992 1992/1993 1993/1994 1994/1995

Individuals sampled (n) 34,609 29,307 23,900 18,978 11,464 12,224

SIZE-BASED MODEL FOR PACIFIC YELLOWLEG SHRIMP TABLE 3.

Parameters for the von Bertalanffy growth model for Farfantepenaeus californiensis in Guaymas, Sonora, Mexico. Fishing season 1978/1979 1979/1980 1980/1981 1981/1982 1982/1983 1983/1984 1984/1985 1985/1986 1986/1987 1987/1988 1988/1989 1989/1990 1990/1991 1991/1992 1992/1993 1993/1994 1994/1995

k (annual)

La (cm, AL)

1.3 1.3 1.3 1.4 1.6 1.2 1.5 1.6 1.5 1.6 1.5 1.7 1.5 1.5 1.6 1.6 1.5

24.3 24.1 23.3 26.0 23.3 24.3 23.3 23.3 23.4 26.1 25.1 24.0 23.6 24.7 24.7 23.8 23.4

AL, abdominal length. Source: Lo´pez-Martı´ nez et al. (2003).

Fishing mortality (Fl,t) is a function of fishing effort and gear selectivity. Fishing mortality is modeled as the product of a length-specific selectivity coefficient sl and an annual full recruitment fishing mortality rate fl: Fl,t ¼ sl ft (Sullivan et al. 1990). The selectivity was assumed as a logistic function of size sl ¼

ml;t ¼

F l;t 1 eZ l;t ; Z l;t

where Zl,t represents the total mortality in length-class l at time t. The CASA model assumes that catch-at-length can be expressed using the Baranov catch equation, indexed in terms of length class: Cl;t ¼ ml;t N l;t (Sullivan et al. 1990, Quinn & Deriso 1999).

TABLE 4.

Natural mortality (M) estimated per fishing season for Farfantepenaeus californiensis in Guaymas, Sonora, Mexico. Fishing season 1978/1979 1979/1980 1980/1981 1981/1982 1982/1983 1983/1984 1984/1985 1985/1986 1986/1987 1987/1988 1988/1989 1989/1990 1990/1991 1991/1992 1992/1993 1993/1994 1994/1995 Source: Lo´pez-Martı´ nez et al. (2003).

M 2.59 2.59 2.62 2.68 2.98 2.73 2.82 2.96 2.33 3.05 2.75 2.41 2.72 2.70 2.83 2.83 2.72

1 ; 1 þ as ebs l

where as and bs are constants in the logistic model. The total mortality of individuals in length class l at time t is the sum of natural mortality (Ml,t), assumed to be constant, and fishing mortality—in other words, Zl,t ¼ sl ft + Ml,t. Seasonspecific estimates were used for natural mortality (Table 4). The relationship between Nl,t and Nl,t + 1 relates to the number of shrimp at length surviving into the next period: Nl,t + 1 ¼ Nl,t exp – Zl,t. This expression assumes that the growth and recruitment are negligible for shrimp initially in length class l at time t. The total number of shrimp in length class l surviving to time t + 1 is then reduced only by mortality. Individual growth was modeled by using a transition matrix. Gamma distribution was used with parameters al and bg to describe the variation about the mean growth increment, which was modeled using a von Bertalanffy growth equation: g xjal ; bg ¼

of individuals that die because of fishing mortality (Fl,t) in the length-class l at time t:

817

1 xal1 3 ex=bg ; bgal Gðal Þ

where x represents Dl, the growth increment given that a shrimp was originally in length class l. The mean change in length is The expected Dl ¼ al 3 bl, and the variance is s2l ¼ bg 3 D: proportion of individuals growing from length-class l to length-class l + 1 can be found by integrating over the length range l + 11, l + 12 as ð lþ12 g xjal ; bg dx: Pl;lþ1 ¼ lþ11

The population dynamics of shrimp, accounting for growth, recruitment, and total mortality, is X N lþ1;tþ1 ¼ Pl;lþ1 N l;t eZ l;t þ Rlþt;tþ1 : l

Recruitment was estimated assuming that a proportion of recruits goes into each length-class {l: l ¼ 1, . n}. Lengthspecific selectivity is then combined with recruitment to the population to reflect the effective entry of individuals to the catch. In this way, the recruitment is separated into a time-dependent variable Rt and a length-dependent variable pl, representing the proportion of recruits going into the length-class l: Rl;t ¼ Rt 3 pl : The proportion (p) was estimated using a gamma distribution with parameters ar and br. Recruitment was defined as the number of individuals at some age or stage added to the exploitable stock each year because of growth or migration into the fishing area. The choice of the age and stage varies (Myers 2002). In marine fisheries, recruitment usually refers to the first age when fishing occurs (Hilborn & Walters 1992, Quinn & Deriso 1999, Haddon 2001). Boyle and Rodhouse (2005) defined recruitment as the number of individuals that reach a specified stage of the life cycle— for example, metamorphosis, settlement, or joining the fishery.


818

Different measures of recruitment are valid, and the choice often depends on the ease of measurement. The accepted concept of recruitment given by Myers (2002), Hilborn and Walters (1992), Quinn and Deriso (1999), and Haddon (2001) was used in this study. According to Sullivan et al. (1990), the determination of age in crustaceans may be hampered by inaccuracy, imprecision, or lack of valid aging methods. Consequently, the age of recruitment in Farfantepenaeus californiensis is unknown. An alternative is to estimate it from catch-at-size data. Sullivan et al. (1990) suggested that the recruitment to the fishery may occur over a range of length classes. Recruitment specified in this way represents more generally the type of recruitment observed in nature in which variation in growth, behavior, or food supply can result in individuals entering the main body of the population at various sizes (Sullivan et al. 1990). The CASA model describes a linear transition of the number of individuals in length class l at time t to the numbers in length class l + 1 at time t + 1. The model in matrix notation is 3 N 1;t 2 3 2 0 S1;l 0 P1;2 0 6 N 2;t 7 6 7 6P P 6 0 7 7 6 0S2;l 6 7 6 1;2 2;2 6: 7 6 7 6 736 6 7 6 Pl;t S3;l 7 6 6 : 7 ¼6 6 7 6 7 6 Pl;t 0 5 4 6 7 4 4: 5 Pn;m P1;n P1;n N n;t 2 3 2 3 R1;l N 1;l 6 N 2;l 7 6 R2;l 7 6 7 6 7 6 7 6 7 6: 7 6: 7 6 6 7 7, 36 7þ6 7 6: 7 6: 7 6 7 6 7 4: 5 4: 5 2

N n;l

0 0

3

7 7 7 7 7 7 Sl;l 0 5 Sn;l

Rn;l

where Sl,t represents the exponential survivorship exp–Zt,l. The Baranov catch equation can be expressed in matrix form as 3 3 2 2 3 2 N 1;l C1;l m 0 0 1;l 6 C2;l 7 6 N 2;l 7 7 6 7 6 6 0 7 7 6: 7 6 : 7 6 0m2;l 76 7¼ 6 7 6 m 3;l 7 6 : 7: 6: 7 6 5 7 40 7 6 6 m 0 l;l 4: 5 4: 5 0 mn;l Cn;l N n;l The parameters in the CASA model were estimated using the sum of squares (SSQ) algorithm X 2 SSQ ¼ Cl;t Cl;t ; l;t

where Cl;t is the predicted catch-at length at time t and C l;t is the observed catch-at-length at time t. The parameters to be estimated were the full-recruitment fishing mortality ðf l Þ, the initial population number at length N l;0 , the recruitment to the fishery ðRt Þ, the recruitment distribution parameters ðar ; br Þ, and the growth bg parameter. Known growth parameters of La and k were used, and were estimated during each fishing season (Lo´pez-Martı´ nez 2000) (Table 3). The as and bs parameters for the selectivity function were estimated independently (Sullivan et al. 1990, Lai & Bradbury 1998). The parameters in the objective function SSQ were estimated by

minimizing the objective function with a nonlinear fit using the Newton algorithm (Hilborn & Walters 1992, Neter et al. 1996, Hilborn & Mangel 1997). RESULTS

The time series fitted for the CASA model from the fishing seasons of 1978/1979 to 1994/1995 are shown in Figure 2. Six fishing seasons were observed (1978/1979, 1979/1980, 1980/ 1981, 1985/1986, 1986/1987, and 1987/1988) to have a narrow size interval, varying between 80 mm and 90 mm in abdominal length. For the next fishing seasons, the abundance-at-size was broader; the greater abundance was observed from abdominal lengths of 85–100 mm. For all fishing seasons, the CASA demonstrated the applicability of this approach when using actual shrimp data. The variation in peaks clearly identified for some fishing seasons may be associated with changes in recruitment pattern as a factor of time. This means that during 1978/1979, 1979/1980, 1980/1981, 1985/1986, 1986/1987, and 1987/1988, the recruitment showed greater abundance but with a narrow knife-edge size interval, in comparison with the rest of the time series in which the recruitment showed a broader range of a different size interval. The results of the harvest rate-at-size showed that the size interval from 65–80 mm in abdominal length was less than 0.05. The highest levels of harvest rate-at-size were estimated from abdominal lengths ranging from 85–125 mm, and the values estimated varied from 0.6–0.9 (Fig. 3). The fishing seasons with high levels of harvest rate-at-size were 1978/1979, 1979/1980, 1980/1981, 1981/1982, and 1986/1987. The last 4 fishing seasons of the time series showed that harvest rate-at-size was less than 0.5. This pattern was also estimated to have occurred during 1983/1984, 1984/1985, and 1985/1986 (Fig. 3). The analysis showed a change in harvest rate-at-size and the availability of Pacific yellowleg shrimp. The pattern estimated showed that the harvest rate-at-size from 1978 to 1990 was greater than that estimated from 1991 to 1994. However, during from 1980 to 1990, the harvest rate-at-size was found to decrease, and although some recoveries in harvest rate-at-size were estimated (1986/1987 and 1987/1988), a negative trend in harvest rate was found, indicating a potential decrease in the yield of this fishery off Guaymas. From 1978 to 1990, it was estimated that there was a high harvest rate-at-size of individuals between 80 mm and 100 mm in abdominal length (0.1–0.9), and a high harvest rate-at-size of individuals larger than 100 mm in abdominal length (0.4–0.8). However, from 1991 to 1994, the harvest rate-at-size for individuals less than 100 mm in abdominal length diminished to values between 0.2 and 0.5 (Fig. 3). In Figure 4, the abundance-at-size for fishing seasons from 1978/1979 to 1994/1995 are estimated. The most abundant size intervals in abdominal length were 62.4 mm, 67 mm, and 72.2 mm. During these fishing seasons, the peaks of abundance were observed during 1980/1981, 1990/1991, 1991/1992, and 1994/1995. From the 1981/1982 to 1988/1989 fishing seasons, the abundance of these size intervals showed low values. A different pattern of abundance was observed for values of abdominal length 78.6 mm, 84.6 mm, 88.7 mm, and 95.3 mm. During 1980/1981, 1990/1991, 1991/1992, and 1994/1995, the abundance in these size intervals of abdominal length decreased. For these size intervals, new peaks were observed during 1979/1980, 1982/1983, 1986/1987, and 1993/1994. For individuals

SIZE-BASED MODEL FOR PACIFIC YELLOWLEG SHRIMP

819

Figure 2. Catch-at-size analysis for Farfantepenaeus californiensis. The line is the CASA model and the points are the observed catch-at-size.

larger than 100 mm in abdominal length, only 1 peak was estimated—during 1982/1983 fishing season (Fig. 4). The change in size structure during the study period showed that small individuals (100 mm in abdominal length), which were available only during the 1982/ 1983 fishing season. The estimates of recruitment of Farfantepenaeus californiensis showed 4 peaks of abundance during the 1980/1981, 1986/1987, 1991/1992, and 1994/1995 fishing seasons (Fig. 5). The most abundant peak occurred during 1980/1981 fishing season, and the recruitment was also 10,000 3 106 individuals. During the next 7 fishing seasons, recruitment decreased to values less than 3,000 3 106 individuals. A recovery in recruitment was estimated during the 1990/1991 fishing season, and 2 peaks were estimated during the 1991/1992 and 1994/ 1995 fishing seasons. Throughout the time series, it was evident that a failure in recruitment occurred after the 1980/

1981 fishing season, and recovery was slow after the 1988/1989 fishing season. DISCUSSION

A variation was observed in abundance of size classes, changing between fishing seasons. The peaks of abundance varied between 70 mm and 90 mm in abdominal length; and another occurred between 80 mm and 110 mm in abdominal length. This variation may be explained by variability in recruitment. Sullivan et al. (1990) explained that the recruitment to the fishery may occur over a range of length classes. Recruitment specified in this way represents more generally the type of recruitment observed in nature, where variation in growth, behavior, or food supply can result in individuals entering the main body of the population at various sizes. In this study, recruitment was defined as the number of individuals at a certain age, size, or stage added to the exploitable stock each year as a result of growth and/or migration into the

820


Figure 3. Estimates of harvest rate-at-size for Farfantepenaeus californiensis.

fishing area. The choice of the age and stage varies (Myers 2002). In marine fisheries, recruitment usually refers to the first age at which individuals are targeted for harvest (Hilborn & Walters 1992, Quinn & Deriso 1999, Haddon 2001). The recruitment to the fishery changed during study period. The fishing season of 1978/1979 showed abundance of size classes between 70 mm and 100 mm in abdominal length, but during 1979/1980, only size classes between 80 mm and 90 mm in abdominal length were fished. A recovery of length classes of 90–100 mm in abdominal length occurred during the 1980/1981 fishing season. These changes in abundance-at-size could be attributable to recruitment; however, interannual variations in the growth of shrimp can have effect changes in size of the individuals over time. Russo et al. (2009) explained that the intraspecific variability in growth is a complex interaction of genetic and environmental factors, and they affect growth rates. In the CASA model, recruitment and growth are assumed to have a gamma distribution; consequently, the variability in recruitment can be estimated if the abundance of recruits is distributed in a narrow or a broad range of size classes. The

same effect is observed for growth; often, the von Bertalanffy growth function is used frequently to describe average growth, but it does not account for the variability among individuals within an age group or size class. The CASA model used for Farfantepenaeus californiensis was based on the premise that a biomass-based analysis that incorporates stochastic growth can account for changes in population biomass resulting from changes in individual growth length, and thereby gives more accurate estimates of population biomass, in comparison with the typical Jones length cohort analysis (Sullivan et al. 1990). According to Zhang and Megrey (2010), using catch-at-size would be a reasonable tool to estimate biomass and fishing intensity based on length data because length data are easily obtainable in most circumstances. If the variability in both recruitment and individual growth influence biomass, the harvest rate is another controlling force that influences the population dynamics of Pacific yellowleg shrimp. The results show that estimates of harvest rate-at-size have been decreasing since 1978. The fishing pressure on sizes classes less than 70 mm in abdominal length is scarce; however,

SIZE-BASED MODEL FOR PACIFIC YELLOWLEG SHRIMP

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Figure 4. Estimates of number of individuals-at-size for different size classes.

the inverse pattern was observed for sizes classes greater than 80 mm in abdominal length, although from 1990 onward, the harvest rate-at-size has decreased. This size interval is relevant in the Pacific yellowleg shrimp because the recruits observed in these size classes, and the variability in harvest rate associated with the recruits, was estimated. The biomass availability and spatial distribution of Farfantepenaeus californiensis affects the yield in the fishery. The interannual variability in captures is assumed to be a consequence of both environmental variability and fishing effort (Gracia 1991, Criales & Lee 1995, Sheridan 1996). In this study, potential effects of the environment were not analyzed; however, the time series of the fishing seasons of 1982/1983, 1983/1984, and 1992/1993, 1993/1994 were influenced by the impact of the El Ninõ event (Fiedler 1984a, Fiedler 1984b, Hamman et al. 1995, Murphree & Reynolds 1995). Although the El Ninõ event was observed during these fishing seasons, the decrease in harvest rate-at-size was estimated to

have occurred between 1978 and 1979. Consequently, harvest rate-at-size was assumed to be an indicator of the effects of fishing. Because fishing is a size-selective process, the potential response to variability in recruits and biomass may be explored from changes in harvest rate-at-size along a timescale (Pope et al. 2006). The analysis of abundance-at-size showed that individuals larger than 93.5 mm in abdominal length were scarce, and there was a difference between abundance of recruits and adults. The fishery begins its open fishing season during the summer, usually September, when the growth of the shrimp yields an adequate size for optimizing yield, and recruitment in the fishing ground has been completed (Morales-Bojo´rquez et al. 2001). Consequently, the low abundance of adults can be explained by the remnant biomass of old individuals; the cycle life of Farfantepenaeus californiensis is oceanic, although its incursion into estuaries or coastal lagoons in early stages has been

822


Figure 5. Estimates of recruitment of Farfantepenaeus californiensis from 1978 through 1994.

reported (Romero-Sedano et al. 2004). In this manner, the expected abundance of large sizes must be scarce, in contrast with small sizes, because these represent the recruits and the success of recruitment to the fishery. Size classes less than 78.6 mm in abdominal length varied between 200,000,000 and 3,800,000,000 recruits; in contrast, size classes larger than 93.5 mm in abdominal length varied between 3,500,000 and 50,000,000 adults. In the study zone, it is uncommon to observe the presence of remnant adult biomass, although there have been exceptions, such those reported during 1978, 1982, and 1986 (size classes of 100.4 mm and 108.2 mm in abdominal length), and only in 1982 were sizes classes observed larger than 115.6 mm in abdominal length. Consequently, the recruitment is influenced by individuals less

than 100.4 mm in abdominal length and is where the fishing pressure, estimated by harvest rate-at-length, is mainly affected. The abundance of recruits and the changes of harvest rateat-length could be an explanation for understanding more completely of the variability in total recruitment of Farfantepenaeus californiensis. In conclusion, because fishing is a size-selective process, the potential responses to changes in biomass-at-size, harvest rateat-size, and recruitment of Farfantepenaeus californiensis can be analyzed with a size-based model. The catch-at-size model can be fitted to the catch-at-size data for the different fishing seasons. The CASA model was able to estimate the different size–frequency distributions for F. californiensis. Consequently, it was observed that individuals smaller than 93.5 mm in abdominal length are in the range of length classes in which recruitment to the fishery occurs. These recruits support the fishing pressure and the yield in the fishery. In contrast, the presence of adults is scarce. Therefore, this fishery in the region depends strongly on recruitment.

ACKNOWLEDGMENTS

We are indebted to Alma Rosa Garcı´ a-Jua´rez and technical personnel of the Centro Regional de Investigaciones Pesqueras Guaymas who took part in the data collection, fieldwork, and statistical data of the Pacific yellowleg shrimp. This research was supported by grants from the Instituto Nacional de Pesca (INAPESCA) and the Consejo Nacional de Ciencia y Tecnologı´ a of Me´xico (CONACYT CB-2012-01 179322).

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