Assessing effects of closed seasons in tropical and subtropical penaeid shrimp fisheries using a length-based yield-per-recruit model

ICES Journal of Marine Science, 55: 1112 1124. 1998 Article No. jm98415 Assessing effects of closed seasons in tropical and subtropical penaeid shrimp fisheries using a length-based yield-per-recruit model Y. Ye Ye Y. 1998. Assessing effects of closed seasons in tropical and subtropical penaeid shrimp fisheries using a length-based yeild-per-recruit model. ICES Journal of Marine Science, 55: 1112 1124. Seasonal closure of fishing is a widely adopted regulatory measure in tropical and subtropical shrimp fisheries. The methods used to analyse the consequences of closed seasons are mainly dependent on traditional age-structured yield-per-recruit models without considering the two most specific features of tropical and subtropical penaeids: short lifespan and seasonality of growth. This study presents a length-based yield-per-recruit model that takes into account growth and price differences of different size shrimp and provides improved estimates of yield per recruit (Y/R) and value per recruit (V/R). Its application to the Kuwait shrimp fishery shows that the new model produces an earlier opening date for a maximum Y/R or V/R, predicts a lower increase in Y/R and V/R when season closure is introduced, and estimates higher Y/R and V/R at a given effort. An opening date for a maximum Y/R is 1 September and for a maximum V/R, 1 October, given the current effort. With the opening date of 1 September, reducing effort from the current level by 3% would result in a loss of only 2.6% in V/R or 7.% in Y/R. Increasing the effort of the dhow fleet will have a negative effect on the total catch, but the degree is low, particularly when the opening date is late. 1998 International Council for the Exploration of the Sea Key words: shrimp, closed seasons, yield-per-recruit model. Received 8 October 1997; accepted 1 June 1998. Y. Ye: Kuwait Institute for Scientific Research, PO Box 1638, 2217 Salmiya, Kuwait. Tel: +965 5711 295; fax: +965 5711 293; e-mail: yye@safat.kisr.edu.kw Introduction Tropical and subtropical penaeid shrimp have quite different characteristics from temperate counterparts such as pandalids and crangonids. In general, penaeids exhibit a short life span and their presence in the fishery lasts only for about 1 year (Garcia and Reste, 1981). Shrimp of the genus Penaeus maintain the same sex throughout their life cycle. Shared ecological resources allow several species to occupy essentially the same habitat, and because penaeids grow to lengths of 2 cm or more, they often equal the ichthyofauna in importance in the benthic community (Boddeke, 1989). Fisheries in the tropics and subtropics often focus primarily on penaeids, and secondarily on finfishes. Recruitment is highly variable and rapid growth occurs in one season. Under these circumstances, tropical and subtropical penaeid shrimp fisheries are characterized by fishing one major cohort with strong seasonal patterns. In contrast, temperate pandalids and crangonids are comparatively small in size and represent a much smaller component of the benthic community. Their small adult size is credited with Crangon crangan and Pandalus borealis being protandrous (Boddeke, 1989; Parsons and Fréchette, 1989). Temperate fisheries target mainly finfish, with single shrimp species being of secondary importance (Boddeke, 1989). Stocks of Pandalus are comprised of several year classes and growth occurs over several seasons (Parsons and Fréchette, 1989). For population dynamic studies, the simplest yieldper-recruit (YPR) models from Thompson and Bell (Ricker, 1975) or Beverton and Holt (1957) are widely used (Garcia, 1985) as they are well justified when recruitment has not been shown to be dependent on stock size and when the fishery exploits one main generation. Tropical and subtropical shrimps are fast-growing and short-lived crustaceans with a high commercial 154 3139/98/61112+13 $3./ 1998 International Council for the Exploration of the Sea

Assessing effects of closed seasons on penaeid shrimp fisheries 1113 value that increases with the weight of shrimp. In order to avoid growth overfishing and to prevent exploitation of undersized shrimp with little commercial value, the closure of fishing season was a management tool widely adopted in tropical and subtropical shrimp fisheries in Australia (Watson and Restrepo, 1995), the USA (Griffin et al., 1993), Kuwait (Gulland, 1989; Mohammed and Bishop, 1996), Oman (Al-Harrasy and Al-Abdisalaam, 1996), Saudi Arabia (Al-Yahia, 1996), and many other countries. The methods used for determining fishery closure are mainly dependent on traditional YPR models (Grant and Griffin, 1979; Garcia and van Zalinge, 1982; Gulland, 1989) that are age-structured and assume that recruitment takes place instantly and that fishing gear has a knife-edge selectivity. When the fishable lifespan of the stock is much longer than the duration of spawning season, such assumptions made in YPR models may be valid. However, for most tropical shrimp stocks, the fishable lifespan is only 1 year, but spawning seasons usually last for a few months (Robertson et al., 1985), and sometimes may be year-round (Garcia, 1985). The relatively long spawning season and consequently long recruitment period make the model assumption untenable, particularly in determining the production potential of a cohort by an average size or age. It is also difficult to relate the model-determined age-at-firstcapture for one generation to the real opening time because of the long duration of recruitment, even if a small age unit like a month is used. Watson and Restrepo (1995) recognized the disadvantages of traditional YPR models and used a simulation model to analyse the potential benefits of closed seasons for the tiger prawn (Penaeus esculentus) fishery in Torres Strait, northern Australia. They introduced monthly recruitment and described monthly fishing closure by changing the age at first capture of each cohort as traditional YPR models. This paper presents a YPR model that can take into account length distribution of a shrimp stock and growth differences of individuals of various sizes. It is designed to investigate closure regimes defined by the length and timing of closed seasons. It also incorporates the selectivity of different fishing fleets and can analyse the effects of increasing fishing effort in one fleet on the other. No effects of fishing on reproductive capacity have been considered in this paper as recruitment is not susceptible to fishing in penaeid fisheries (Garcia, 1983). The proposed approach is applied to the Kuwait Penaeus semisulcatus fishery. Materials and Methods Model development A yield-per-recruit analyis is commonly used to determine the best combination between the age at first capture and fishing mortality rate, or ascertain the age at first capture which maximizes yield-per-recruit for a given fishing mortality or vice versa (Ricker, 1975; Pikitch, 1987). The YPR models are basically developed from the catch equation and recursive exponential survival function. The most recent development tends to adopt discrete forms of the YPR models, analogous to the Thompson-Bell model (Ricker, 1975), which can readily accommodate age-specific gear selectivity and age- or size-related price data (Murawski, 1984; Pikitch, 1987; Gribble and Dredge, 1994). This kind of model can usually be written as follows: where Y is the yield, R is the recruitment, W t is the average weight of fish at age t, S t is the gear selectivity coefficient for shrimp of age t, F is fishing mortality for fully recruited shrimp. M t is the natural mortality of age t, t r is the age at recruitment and t λ is the maximum age of shrimp. In the above equation, the assumption of instant recruitment of a cohort remains, although a selectivity parameter was introduced to account for partial recruitment of various cohorts that have different mean sizes. The parameters in Equation (1) are all age-dependent, and stand for average values at a specific age t. As the fishable lifespan is 1 year, a common practice has been to use a month as the age unit. Tropical shrimp usually exhibit a spawning season of a few months, and if average length values are used, serious errors may be introduced because length distributions are usually not normal. Additionally, shrimp of different sizes differ greatly in growth rates. In order to overcome these shortcomings and to assess more reliably the effects of fishing season closure, a YPR model based on length distribution was developed. Assume that the length distribution of the stock at recruitment can be divided into n segments, i=1,2,...n, then L 1 and L n are defined as the lowest and highest boundary lengths, respectively. The width of each divided length class need not necessarily be the same. Let recruitment be R, and its distribution be described discretely by the proportion of length group i to the total number at recruitment, f(i). Then, the number of surviving shrimp at time t is: where Z k (L i ) is the total mortality of length class i at time k. The catch in weight at time t can then be calculated using the catch equation as:

1114 Y. Ye With the division of R from both sides of Equation (3), the summation of catch over time gives yield-per-recruit: where M is natural mortality that should be a function of length L i if relevant information is available. With a knowledge of the price for different sizes of shrimp, the monetary value per recruit can be easily calculated from Equation (4): where W t,i is the individual weight of length group i at time t and is defined as: W t,i =αl β t,i (5) where α and β are constants. If a fishing season closure is introduced at time period t, the corresponding fishing mortality, F t (L i ), should be zero. An essential point here is to calculate the length of each length class i at time t. As growth is temperature dependent, a seasonal growth equation (Pauly and Gaschutz, 1979) is used here: where L is the asymptotic length, K is the intrinsic growth rate, t is the age at which the length of the animal is, t s, and C are parameters defining the seasonal growth pattern. The length of class i is associated with its length at the previous time period, L t,i =g(l t 1,i ). Unfortunately, no analytical solutions could be found due to the complexity of the seasonal growth equation. Based on the initial length distribution data, the length of group i at time t can be numerically calculated from Equation (6). The relationship between length and its corresponding selectivity coefficient S is dependent on mesh size of the net and can be modelled by the following logistic selection curve (Watson and Restrepo, 1995; Al-Hossaini et al., 1984) where a and b are constants, and L stands for shrimp length. Given various fleets involved in the fishery with nets of different mesh sizes, the model calculates the instantaneous fishing mortality rates of each fleet for all length classes that are recruited where F is fishing mortality for length class L i, q is catchability coefficient, E is fishing effort, and fl refers to a fleet. The total mortality of length group i at time t is then: Z t (L i )=M+F(L i ) (9) where P(L i ) is market price for length class L i. Due to sexually dimorphic growth, both Y/R and V/R are first calculated for each sex separately and averaged for final estimates. Model application The Kuwait green tiger prawn fishery The Kuwait green tiger prawn (Penaeus semisulcatus) like other tropical shrimp species grows fast and exhibits a strong seasonal component. In addition to age, size differences are sex related with a maximum carapace length of 35.8 mm for males and 51.6 mm for females, respectively, in the 1988 1989 season (Xu and Mohammed, 1995). In Kuwait, this species spawning season occurs mainly from December to March (Al-Hossaini, 1981). The shrimp fishery consists of two components: industrial trawlers and artisanal dhow boats (Ye et al., 1996). The industrial sector uses trawl nets of a 5 mm stretched mesh size, and the artisanal fleet employs 38 mm stretched mesh size nets (Al-Hossaini et al., 1984). This mesh size regulation was introduced based on the fact that, historically, the artisanal fleet fished along the coastline with smaller mesh size nets and industrial trawlers operated further offshore with bigger meshes. With the introduction of fishing closure in Kuwait Bay and the 3-mile coastal zone, and of seasonal closure in succession, artisanal boats increased in size to fish in more offshore areas without a change in mesh size. Fishing grounds were similar in recent years, but dhow boats operated slightly more in northern waters because their nets of smaller mesh sizes allow them to catch, simultaneously, two smaller-size species, Metapenaeus affinis and Parapenaeopsis stylifera, and industral trawlers fished somewhat more in southern waters. Both components of the shrimp fishery have had the same opening and closing date since 1987 (Abdul- Ghaffar and Al-Ghunaim, 1994; Ye et al., 1996). The total fishing effort reached 29 boat-days per month in the 1993 1994 season and has been controlled at around 2 boat-days per month since then (Mohammed et al., 1998). This fishery has been managed with seasonal closures since 198, when, for the first time, trawling for shrimp was forbidden from 1 April through 3 June. Since then, season closures have lasted for 3 6 months, and the

Assessing effects of closed seasons on penaeid shrimp fisheries 1115 Percentage 5 45 4 35 3 25 2 15 1 5 5 1 15 2 25 3 35 4 45 Length (mm) Figure 1. Length distribution of Penaeus semisulcatus on 1 June 1996., male;, female. season opening date has been delayed from 1 July to 1 September (Abdul-Ghaffar and Al-Ghunaim, 1994). Seasonal closure is recommended when catches fall below 8 12 kg per boat-day in February or March (Mathews and Abdul-Ghaffar, 1986; Morgan, 1989; Ye et al., 1996). The purpose of shrimp seasonal closure is mainly to reduce fishing pressure, prevent growth overfishing and keep a certain escapement level of spawners. Gulland (1989) and Siddeek (1989) carried out studies on the best opening date of the shrimp fishery using Thompson and Bell model (Ricker, 1975). However, a single value of F derived from traditional YPR models is not operational for management. For a shrimp fishery that has two fleets and targets a stock with substantial size differences between sexes, it is not able to investigate the interactions between the two fleets without incorporating gear-related features and seasonal characteristics of the stock into the model. Incorporating the above considerations serves to produce more realistic results. Parameterization of the model Length-frequency distribution data at recruitment (1 June) for males and females (Fig. 1) were back calculated from the data of the preseason survey in July, 1997 (Bishop et al., 1997) using the exponential survival function [Equation (2)]. The July preseason survey in 1997 trawled 21 stations covering most of Kuwait s waters. From each trawl tow, either all or a 3 kg subsample of shrimp were saved for biological measurement. A total of 275 shrimp were measured for the length frequency distribution (Fig. 1) (Bishop et al., 1997). The growth parameters, the parameters defining the relationship between weight and carapace length, and natural mortality rates are all from published sources (Table 1). Net-related parameters of each of Kuwait s shrimping fleets are shown in Table 2. The selectivity curves of the two mesh sizes were interpolated from the selectivity experiments for a range of mesh sizes from 33. to Table 1. Model parameters of growth, natural mortality, and weight length conversion for male and female Penaeus semisulcatus. Males Females Growth parameters* L 35.8 mm 51.6 mm K 1.95 year 1 1.62 year 1 t.5 year.5 year C.75 year.54 year t s.42 year.32 year Natural mortality M.22 month 1.19 month 1 Weight length relationship α.14.146 β 2.92 2.799 *Xu and Mohammed (1995). Mohammed et al. (1998). Xu and Abdul-Ghaffar (1995). Table 2. Gear-related parameters. Dhow trawler Industrial trawler Selectivity (mm) a 6.16 7.22 b.386.344 Catchability q (boat-day 1 ) Male 2.76 1 4 2.83 1 4 Female 3.14 1 4 3.23 1 4

1116 Y. Ye Table 3. Wholesale shrimp prices in the 1996 1997 season. Size (g) <16.7 16.7 25. 25.1 33.3 33.4 5. >5. Price (KD* kg 1 ).75 2. 2.75 3.5 4.5 *KD=Kuwait dinar=1 fils US $3.3. Dec Nov 5 g/r Oct 1 g/r 11 g/r Opening date Sep Aug Jul Jun 1 2 3 Effort (boat-day per month) Figure 2. Yield-per-recruit contour of the Penaeus semisulcatus fishery. 4 56. mm carried out in 1983 (Al-Hossaini et al., 1984). Catchability coefficients were calculated from the effort and fishing mortality estimates of Mohammed et al. (1998), and the United Fisheries of Kuwait supplied the wholesale shrimp prices for the 1996 1997 season (Table 3). Results The best combination between fishing effort and opening date is revealed by Y/R and V/R estimates. As seen in Equations (4) and (1), Y/R and V/R are functions of fishing effort and season opening date. Here, a fishing year follows the main cohort from recruitment starting from 1 June to the end of May of the next year when fishing and natural mortalities have depleted the cohort (Xu and Mohammed, 1995). An inception of fishing on 1 June means an open fishery. Figures 2 and 3 show the contours of sex combined Y/R and V/R under various combinations of effort and opening date, assuming the ratio of fishing effort of dhow fleet to that of the industrial fleet remains the same as during the 1995 1996 season, 1:1.12 with a sex ratio 1:1 (Mohammed et al., 1998). In general, these contours are similar to those derived by traditional YPR models and no single maximum of either Y/R or V/R could be found. Both Y/R and V/R increase with increasing effort and delaying season opening within a certain time. In other words, a later season opening is required in order to have a higher Y/R or V/R when fishing effort increases. Like all other YPR models, the proposed method is ostensibly faced with a rather arbitrary decision as there is no clear choice of factors. This decision may be weighted between the fishing effort level and the season opening date taking into consideration the practical flexibility of regulatory measures in the fishery concerned. Effects on Y/R and V/R are major concerns when a season closure is adopted to protect juveniles in order to increase harvest sizes of shrimp, which fetch a higher market price. What is the best length of closure under different levels of fishing effort? Figure 4(a) shows the effects of season starting date on Y/R under various effort levels and differences between the new and traditional models. The estimation of the traditional model was carried out by deleting the component of length distribution, f(i) and replacing L i with a single average length of shrimp at recruitment in Equations (2 1). In

Assessing effects of closed seasons on penaeid shrimp fisheries 1117 Dec Nov 2 25 Oct 3 35 fils/r Opening date Sep Aug Jul Jun 1 2 3 Effort (boat-day per month) Figure 3. Value-per-recruit contour of the Penaeus semisulcatus fishery. 4 general, both models show that at low levels of effort, a closure of fishing season decreases Y/R; however, introducing a certain length of closed season at fairly high effort increases Y/R, which increases with effort. With a certain level of effort, there will be an opening date that produces a maximum Y/R, whereas a later opening will have a negative effect on Y/R (Fig. 4a). The values of Y/R from the new model (Fig. 4a) are slightly higher than those from the traditional one (Fig. 4b) when fishing effort is at the same level, however. This might be caused by the fact that the traditional model measures individual growth only by mean length and may underestimate the growth potential of shrimp individuals below the mean length. The new model also produced different best opening dates under various fishing effort levels, compared with the traditional one. The best opening date is 1 August for an effort of 1 boat-days per month, and 1 September when fishing effort is doubled (Fig. 4a). If the traditional model is used, the best opening date is 1 month later for both effort levels, 1 September and 1 October, respectively (Fig. 4b). With the effort of 2 boat-days per month in the 1995 1996 season (Mohammed et al., 1998), the opening date for a maximum Y/R was 1 September (Fig. 4a), rather than 1 October as indicated by the traditional model (Fig. 4b). Growth rate of individuals, and natural and fishing mortality rates of the stock determine the best opening date. Unlike Y/R, a certain length of season closure always increases V/R in the P. semisulcatus fishery (Fig. 5) although the extent of the increase at low effort levels is very small. A delay of fishing can leave more time for shrimp to grow bigger, and, consequently, result in a higher price. This increase shows that the gain in price surpasses the net loss of biomass due to natural mortality over growth even under low effort levels. The growth in V/R and the length of closure corresponding to a maximum V/R increases with fishing effort. When effort is equal to 1 boat-days per month, the opening date leading to a maximum V/R is 1 September (Fig. 5a). At the effort level of the 1995 1996 season, however, delaying the fishing-opening date by 1 month to 1 October would have a maximized V/R (Fig. 5a). The traditional model indicates that 1 October is the opening date to produce a maximum V/R for both effort levels (Fig. 5b). The estimated effects of seasonal closure on Y/R and V/R from the tradition model are much greater than those predicted by the proposed model (Fig. 6). The traditional model estimates an increase of about 39% in Y/R if fishing starts on 1 October with an effort of 2 boat-days per month (Fig. 6a), compared with an open fishery. The new model, which takes into account the length distribution, suggests an increase of about 15% in Y/R with an opening date of 1 September (Fig. 6a). The maximum increase in Y/R estimated by the new model is much lower than that of the traditional model. There is also a difference of 1 month in opening date for a maximum Y/R, 1 September vs. 1 October (Fig. 6a). The degree of difference in Y/R and the difference in opening date vary with fishing effort. Given an effort of 1 boat-days per month, the increase in Y/R is much lower, but the difference of 1 month in opening date remains if a maximum Y/R is targeted (Fig. 6b). Traditional models exaggerate economic results much more than the new model (Fig. 7). Opening fishing on

1118 Y. Ye 12 (a) 1 2 boat-days per month 8 Y/R (g) 6 4 1 boat-days per month 2 12 2 boat-days per month Jun Jul Aug Sep Oct Nov Dec Jan (b) Feb 1 2 boat-days per month 8 Y/R (g) 6 4 1 boat-days per month 2 2 boat-days per month Jun Jul Aug Sep Oct Nov Dec Jan Feb Opening date Figure 4. Effects of opening date on Y/R under different levels of fishing effort. (a) new model; (b) traditional model. 1 October increases V/R by 168% according to the estimation of traditional model, but this increase is only 89% in the estimation of the new model (Fig. 7a). The greater difference in the estimation of V/R between the two models is caused by the biased value in using the price of average-sized shrimp overall in the traditional model. Both models give the same opening date, 1 October, which maximizes V/R under the current fishing effort. This is not surprising if both the high effort level and the stability of the shrimp price beyond a certain size (Table 3) are taken into account. A decrease of fishing effort reduces the rate of increase of V/R, and the difference in opening date for a maximum V/R becomes clearer between the traditional and proposed models (Fig. 7b). The consequences of increasing effort taking into consideration different season opening dates can be analysed with both the new and traditional models. The Kuwait shrimp fishery has fixed its opening date on 1 September since 1987 (Abdul-Ghaffar and Al-Ghunaim, 1994). Under this regulation, Y/R increases to a plateau with expansion of fishing effort although the increasing rate slows down gradually (Fig. 8). In this situation, beyond the first part of the curve, a large increase in fishing effort produces only a very small increase in Y/R. In contrast, V/R increases rapidly initially, but decreases slightly after fishing effort exceeds a certain level (Fig. 9). A maximum V/R was observed at an effort of around 22 boat-days per month for the new model and 17 boat-days per month

Assessing effects of closed seasons on penaeid shrimp fisheries 1119 35 3 (a) 2 boat-days per month 25 V/R (g) 2 15 1 boat-days per month 1 5 2 boat-days per month Jun Jul Aug Sep Oct Nov Dec Jan Feb 35 3 (b) 2 boat-days per month 25 V/R (g) 2 15 1 boat-days per month 1 5 2 boat-days per month Jun Jul Aug Sep Oct Nov Dec Jan Feb Opening date Figure 5. Effects of opening date on V/R under various levels of fishing effort. (a) new model; (b) traditional model. for the traditional model (Fig. 9). An effort exceeding 14 boat-days per month cannot have significant effects on Y/R and V/R for both models, however. This result supports rigid control of the fishing effort. In fisheries where an artisanal fleet coexists with an industrial fleet, there is a concern about the effects of increasing the effort of one fleet on the total catch. In the Kuwait shrimp fishery, the dhow fishery uses nets of a smaller mesh size than that of the industrial fleet. Does increasing the dhow effort decrease Y/R or V/R? If the total effort stays unchanged, then increasing the dhow effort by 5% will result in a reduction in V/R by a maximum of 4%, depending on the level of fishing effort. The traditional model estimated a slightly larger reduction in V/R with a maximum of 6%. This result is similar to the conclusion of Garcia (1977). Such influence decreases rapidly with the delay of season opening. The effect on Y/R is less than that on V/R. Discussion The application of the proposed YPR model to the Kuwait green tiger prawn fishery shows that at the current effort level, the opening date is 1 September for a maximum Y/R and 1 October for a maximum V/R. In comparison with the results of the traditional YPR model, the new model produces an earlier opening date for a maximum Y/R (Fig. 4) or V/R (Fig. 5), predicts a lower increase in Y/R and V/R when season closure is

112 Y. Ye 5 (a) 4 Increase (%) in Y/R 3 2 1 Jun Jul Aug Sep Oct Nov Dec 18 16 (b) 14 Increase (%) in Y/R 12 1 8 6 4 2 Jun Jul Aug Sep Oct Opening date Figure 6. Comparison of estimates of increases in Y/R between the proposed ( ) and traditional ( ) models when effort is fixed at 2 boat-days per month (a) and 1 boat-days per month (b). Nov Dec introduced (Figs 6 7), and estimates higher Y/R and V/R using the same levels of effort and fixed season opening date (Figs 8 9). The main reason for the differences is that the traditional model assumes instant recruitment and knife-edge gear selection. Information on fishing season opening is reflected in traditional YPR models by using an average age-at-first-capture. For long-lifespan species, recruitment can be regarded as instantaneous relative to total lifespan, and an average age may describe the production potential of a cohort fairly well. Tropical/ subtropical penaeids, however, exhibit a 1-year fishable lifespan and a spawning season lasting a few months. Consequently, the size distribution at recruitment is relatively wide (Fig. 1), and the growth potential of individuals cannot be expressed simply by an average size or age, particularly when the length is not normally distributed as usually assumed. If all of the shrimp had the same growth and mortality rates after hatching, then length distribution could be interpreted to represent percentages of shrimp hatched at a previous period (Sparre and Venema, 1992). Spawning peak and its duration are affected greatly by environmental conditions that are highly variable (Buckworth, 1985; Preston, 1985; Siddeek et al., 1989). When the spawning season lasts longer due to particular environmental conditions, length distribution will then become kurtoic or skewed. This may explain why length distribution is often seen not exactly normal (McNew and Summerfelt, 1978; Siddeek et al., 1989; Xu and Mohammed, 1995). The impact of non-normal distributions on Y/R can be reduced in the length-based YPR model. The consequence of delaying season opening depends on the gain from growth and loss due to natural mortality. Traditional models calculate growth according to average size, and do not consider the difference between juvenile and adult shrimp. As the growth equation [Equation (6)] shows, shrimp exhibit a seasonal

Assessing effects of closed seasons on penaeid shrimp fisheries 1121 2 (a) 15 Increase (%) in V/R 1 5 Jun Jul Aug Sep Oct Nov Dec 7 (b) 6 Increase (%) in V/R 5 4 3 2 1 Jun Jul Aug Sep Oct Opening date Figure 7. Comparison of estimates of increases in V/R between the proposed ( ) and traditional ( ) models when effort is fixed at 2 boat-days per month (a) and 1 boat-days per month (b). Nov Dec growth pattern, and different size shrimp have very different growth rates. The newly developed model presented here considers the differences in growth of various size shrimp and produces a more precise estimation. The Kuwait shrimp fishery shows no single maximum in Y/R or V/R. With increasing fishing effort, a later season opening is required to obtain a higher Y/R or V/R. In addition to providing recruitment reference points to reduce risk of recruitment failure (Garcia, 1996), fishery management can also attempt to maximize catch, profit, or employment. A suitable combination between fishing effort and opening date should be decided on the basis of practical flexibility of fishery regulatory measures. In general, the positive effects of delaying season opening on Y/R or V/R are larger at high levels of effort than those at lower levels. Biomass of a cohort may increase or decrease depending on the gain from individual growth and loss due to natural death. Normally, there is a peak in biomass at some life stage of a cohort. High effort can fish out shrimp very quickly and reduce any loss after the peak. Therefore, delaying season opening is a regulation more efficient at high effort than with low fishing pressure. Postponing season opening shows a larger positive effect on V/R than that on Y/R. This is caused by a sharp increase in value with the size of shrimp (Table 3). The effort expended in the 1995 1996 season was about 2 boat-days per month on average (Mohammed et al., 1998). If fishing effort remains at the current level, the Y/R analysis suggests an opening date of 1 September (Fig. 4a), however, the V/R examination indicates a maximum occurs when fishing postponed until 1 October (Fig. 5a). The current commencement of fishing on 1 September is a good choice in terms of Y/R. The results concerning the Kuwait shrimp fishery are based on the length distribution of the 1997 preseason

1122 Y. Ye 14 12 1 Y/R (g) 8 6 4 2 1995 1996 effort level 2 8 14 2 26 32 38 Effort (boat-days per month) Figure 8. Effects of fishing effort on Y/R given a fixed opening date of 1 September. 35 3 25 V/R (fils) 2 15 1 5 1995 1996 effort level 2 8 14 2 26 Effort (boat-days per month) Figure 9. Effects of fishing effort on V/R given a fixed opening date of 1 September., new model;, traditional model. 32 38 survey. Different length distribution may lead to different conclusions. A well-designed survey and an adequate number of sampling stations are required to obtain an unbiased length distribution. Environmental conditions also have a great impact on the level and timing of recruitment in shrimp fisheries (Garcia, 1983; Dall et al., 199; Caputi, 1993). The best combination between opening date and effort level should be reviewed every year to take into account the yearly variation in recruitment. Although the current effort level is close to the effort for a maximum V/R, reducing this effort level to 14 boat-days per month, a decrease of 3%, with a same season opening date of 1 September would result in a loss of only 2.6% in V/R (Fig. 9) or 7.% in Y/R (Fig. 8) as estimated by the new model. This result indicates that there is a great waste of effort in the current shrimp fishery. If cost data of fishing effort were available, an economic analysis could reveal the loss in net profit to the fishery. In common with many shrimp fisheries, an artisanal fleet coexists with an industrial fleet in the Kuwait shrimp fishery. The interaction between these two sectors is a fundamental issue to manage the fishery

Assessing effects of closed seasons on penaeid shrimp fisheries 1123 effectively and efficiently (Willmann and Garcia, 1985; Sparre and Willmann, 1993). Assuming no change in total fishing effort, increasing the effort of the dhow fleet by 5% will cause a reduction in V/R by a maximum of 4% depending on the level of fishing effort. The effect of Y/R is less than that on V/R. If the mesh size is small enough, any redistribution of effort between these two fleets will not lead to any difference in total catch. For the Kuwait shrimp fishery, the two fleets operate in similar locations. The two mesh sizes, 38 mm in artisanal sector and 5 mm in industrial sector, do not make a great difference as it was assumed that recruitment occurs on 1 June when shrimp are quite big (Fig. 1). The effect of increasing dhow effort on the total catch would be more significant if an earlier fishing season were assumed. The proposed model offers potential application to studies on the interactions between the artisanal and industrial fleets in tropical fisheries as fleet related characteristics are well presented. The model can also be used to investigate the effects on the fishery of changing mesh size by simply replacing the parameters of the selectivity equation [Equation (7)]. Acknowledgements The author thanks Dr James M. Bishop and Mr Hussain Mohammed for their contributions of ideas and information. Two anonymous reviewers provided many valuable comments and suggestions that greatly improved the paper. References Abdul-Ghaffar, A. R., and Al-Ghunaim, A. Y. Y. 1994. Review of Kuwait s shrimp fisheries, their development and present status. Proceedings of the Technical Consultation on Shrimp Management in the Arabian Gulf. Al Khobar, 6 8 November 1994, Saudi Arabia, pp. 1 26. Al-Harrasy, A. S. A., and Al-Abdisalaam, T. Z. 1996. Present status of shrimp fishery in Oman. 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