Estimation of natural mortality of Kuwait's grooved tiger prawn Penaeus semisulcatus (de Haan) using tag-recapture and commercial fisheries data

Fisheries Research, 11 ( 1991 ) 109-125 Elsevier Science Publishers B.V., Amsterdam

109

Estimation of natural mortality of Kuwait's grooved tiger prawn Penaeus semisulcatus (de Haan) using tag-recapture and commercial fisheries data M.S.M. S i d d e e k 1 Mariculture and Fisheries Department, Kuwait Institute for Scientific Research, P.O. Box 1638 - Salmiya, Kuwait (Accepted for publication 26 November 1990)

ABSTRACT Siddeek,, M.S.M., 1991. Estimation of natural mortality of Kuwait's grooved tiger prawn Penaeus semisulcatus (de Haan) using tag-recapture and commercial fisheries data. Fish. Res., I l: 109125. A new simple optimization procedure was used to estimate the natural mortality (M) of the heavily exploited Kuwaiti Penaeus semisulcatus (de Haan) stock using tagging data. The new M estimator was based on two tagging experiments with similar (constant) SB values (i.e. the product of initial survival after tagging and the reporting rate ), but with different total mortality (Z) values. Two conventional methods were employed to evaluate M for direct estimation and comparison; one, modified GuUand's formulae, using 1982-1983 tagging-experiment data, and the other, catch per unit effort (CPUE) ratio, using 1986/87-1989/90 industrial fishery CPUE data. The Mestimate for males was 0.1314 per 20 days (2.4 per year) with a standard error of 0.0135. The female tagging experiments violated the critical assumption underlying the new M estimator; nevertheless, by comparing results from other methods, the male M value was accepted for females. The new M estimator and modified Gulland's formulae will likely produce reasonable estimates of M if compatible tagging experiments and fairly accurate Z values are used.

INTRODUCTION

The instantaneous natural mortality coefficient (M) is an important parameter in all analytical models of commercially exploitable marine fauna stock dynamics, but has not been reliably estimated for Kuwaiti Penaeus semisulcatus (de Haan). This paper describes an attempt to estimate M for P. semisulcatus using three simple methods, including a novel procedure. The most important factor affecting M in a shrimp (or fish) population is ~Present address: Sultan Qaboos University, Department of Fisheries Science and Technology, P.O. Box 32484, AI-Khod, Muscat, Oman.

0165-7836/91/$03.50

© 1991 - - Elsevier Science Publishers B.V.~

1 10

M.S.M. SIDDEEK

predation (Vetter, 1988). Predation mortality dominates in the pre-recruit stages of all stocks and probably in all stages of small shrimp. Euzen (1987 ) found that the mean size of shrimp eaten by finfish predators in Kuwaiti trawling grounds was 5.7 cm total length, or about 11 mm carapace length (CL). In Euzen's ( 1987 ) study, there was a likelihood ofundersampling large predatory finfish with prawn trawls, which may have underestimated the actual amount of large prawns eaten. However, his examination of a few large (potential) predators from market samples provided little evidence for largescale predation of large shrimp. Furthermore, the Kuwaiti P. semisulcatus stocks inhabit fairly shallow waters ( < 24 m). Thus, Euzen's findings are unlikely to be a gross underestimation of the true predation of large shrimps. P. semisulcatus does not recruit to the fishing ground until it reaches a size mode of 18-19 mm CL (Mohammed et al., 1981a), and its burying behaviour (Penn, 1984) provides further protection from predation. Thus, predation mortality on subadult and adult P. semisulcatus ( > 20 mm CL) must be low, and M is likely to be constant on the exploited stock. Catch curve analysis (Baranov, 1918 ) is the most reliable technique available to estimate M for an unexploited or lightly exploited populations, and involves fitting a straight line to the curve's right-hand limb (Ricker, 1975 ). M is, however, difficult to estimate in a heavily exploited population, such as the P. semisulcatus stock, because one has to estimate both total mortality and the fraction of that total mortality that is due to fishing. Methods that use commercial catch and effort data are mostly derived from Silliman's ( 1943 ) method, which requires varying effort levels or a series of steady states. Some direct methods use relationships between M and life history parameters, such as growth rate, age at sexual maturity, costs of reproduction and maximum age (Vetter, 1988). However, because of their empirical nature, they often produce imprecise and sometimes unrealistic estimates. Besides, such relationships have been established specifically for finfish (e.g. Pauly, 1980) and their applicability to shrimp stocks is, therefore, questionable. Traditional methods of analysing tagging data are restricted in their applicability because they require effort data or the assumption of constant fishing mortality (e.g. Gulland, 1955; Beverton and Holt, 1957; Chapman, 1961; Paulik, 1963; Lucas, 1975 ). Recently, estimates were made of the constant M (Hearn et al., 1987) and the variable M (Farebrother, 1988) that did not require either comprehensive effort data or the assumption of constant fishing mortality. Unfortunately, most of these techniques failed to produce a realistic M estimate because they did not take account of the important tagging-related errors: initial survival immediately after tagging and the reporting rate of recoveries. Siddeek (1989) developed a method based on Pope's (1972) cohort formulae for analysing tag-recapture data, obtained under either variable or constant intervening fishing mortality, without fishing effort. The analysis

ESTIMATIONOF NATURALMORTALITYOF PENAEUS SEMISULCATUS

1 11

procedure, however, demands rigorous computations. This paper simplifies the procedure by providing easily identifiable criteria for selecting appropriate tagging experiments and by developing a simple M estimator based on two experiments. The new procedure and the modified Gulland's formulae (Chapman, 1961 ) were both applied to data from a series of tagging experiments conducted on the adult P. semisulcatus stocks in southern Kuwaiti waters from 1982 to 1983. The ratio of catch per unit effort (CPUE) method was applied to the 1986/ 87-1989/90 Shuaiba industrial (Kuwait's major industrial shrimp trawler fleet) fishery data. This paper presents and compares the results of these analyses. MATERIALS AND METHODS

Notations used in the text In the following, subscript i refers to a time interval and subscript j to a point in time; any notation without a subscript refers to a constant parameter. No ni Z~ Fi X M SB

= number of tagged animals released; = number of recaptures; = instantaneous total mortality coefficient; = instantaneous fishing mortality coefficient; = instantaneous natural mortality coefficient of tagged shrimp; = instantaneous natural mortality coefficient of untagged shrimp; = product of initial survival rate (due to initial tagging death, nonsystematic tag loss and emigration) and reporting rate of recoveries (i.e. Ricker's ( 1975 ) Type A error); t = last period for which tagging data were considered; CPUEj = catch per unit effort (numbers); qj = catchability coefficient; TW =tail weight (g); Wh.W =whole shrimp weight (g); tm = time at liberty of ruth recovery in an experiment; n = total number of recoveries in an experiment; ax = standard error (SE) of X; tc = age at first capture; t~ = maximum age; l =h-tc.

Development of M estimator Cohort formula The ideas behind the formulation and optimization of Siddeek's ( 1989 ) M estimator were that the SB value was constant among experiments, and two

1 12

M.S.M. SIDDEEK

groups of experiments considered for optimization suffered different magnitudes of Z. The same ideas were extended to the situation where several experiments were available, out of which only two could be selected to satisfy the above conditions. Accordingly, assumptions made in Siddeek ( 1989 ) were modified as follows: ( l ) M is constant. (2) SB is constant. (3) Numerous releases are made in each experiment to conform to deterministic mortality processes and to minimize dependence between successive recaptures. (4) At least two experiments suffering different magnitudes of Z are available. SB was estimated using Pope's ( 1972 ) formula ( 1.5 ) for initial population estimation from incomplete recoveries. Thus,

NoSB = n~ exp (X/2.1) + n2 exp ( X + X / 2.1 ) + ... + n~ exp[ ( i - 1 ) X + X / 2.1 ] +_.4

n,Z, exp[ ( t - 1 )X] Ft[ 1 - e x p ( - Z t ) ]

(1)

However,

Zt exp[ ( t - 1 )X] ~exp[ ( t - 1 )X] exp(X/2.1 ) Ft[1-exp(-Zt) ] ~ [1-exp(-Ft) ]

(2)

Thus,

SB=-~o (nl exp(X/2.1 ) + n2 exp(X+ )(/2.1 ) +... + ni exp[ ( i - 1 )X+)(/2.1 ] - • °o° - -~ n, exp[ ( t - 1 )X+X/2.1 ]'~ [1-exp(-Ft) ] J

(3)

where

(f)

ni= (Fi/Zi) (NoSB) exp -

Zp [ 1 - e x p ( - Z , ) ]

(4)

Different authors have proposed different approximation functions (or factors) for the usual Gulland's (1965) virtual population analysis (VPA) formula that are more accurate than Pope's (1972) equation (1.2) under different ranges of Z (e.g. Gray, 1979; MacCall, 1986; Allen and Hearn, 1989 ). The approximation factor 2.1 used in eqns. ( 1 )- (3) fitted the actual range of Zi on the two selected tagging experiments well, with < 0.25% error from GuUand's VPA formula. When two tagging experiments with similar SB values but differing Z val-

ESTIMATION OF NATURAL MORTALITY OF PENAEUSSEMISULCATUS

1 13

ues (rendering differing Ft values) are available, a unique X value based on Silliman's ( 1943 ) method can be determined using eqn. (3). Ft values can be selected by trial and error to satisfy Z=Ft+X, where Z values are the slopes of the simple regressions (eqn. (5), below) of the two selected experiments and X is the result for a particular pair of F, values that produced the minimum difference (i.e. the optimum condition) between the two SB estimates. A FORTRAN program was written for this purpose, incorporating a simple grid-search method. In this program, F,, (Ft in the experiment having the lower Z value, say Z~ ) was varied from 0 to Z~ by an arbitrary small step. At each step, an X value was determined to satisfy Z~ = F n +X. This X value was then used to evaluate F,2 from Zz = F,2 q-X, where Z 2 and F,2 were the corresponding mortality parameters of the second experiment. It was assumed that X < Z1, which was reasonable. Using the above Fn, F,2 and the X values in eqn. ( 3 ), SB values for the two experiments were determined. The square of the difference between these two SB values was then evaluated for minimization.

Tagging experiments A long series of tagging experiments was conducted between 1974 and 1983 on Kuwaiti P. semisulcatus stock (Farmer and A1-Attar, 1981; Mohammed et al., 1981 b; A1-Shoushani et al., 1983 ). The 1982-1983 experiments considered in this analysis were of subadult and adult shrimp (20.5-49.7 mm CL) tagged with vinyl streamer tags and released in the southern fishing grounds dominated by P. semisulcatus (Farmer and Ukawa, 1986 ). Most recaptures were reported from the southern fishing grounds by Kuwaiti trawlers. The releases were grouped into major experiments separately for each sex with respect to area and time of release. Only experiments with > 900 releases and > 5% recoveries were considered for the screening process. These arbitrary limits were set to ensure deterministic mortality processes (Chapman, 1961 ) among the selected experiments, as well as to exclude abnormal experiments. Recapture rates of these experiments varied between 8.5 and 17.3% for males, and between 5.4 and 15.6% for females. They were grouped into 20-day periods (Table 1 ). Because most recoveries were reported within 4-5 months of release and dependence between successive recaptures becomes significant when the tagged shrimp population is low (Chapman, 1961 ), only recoveries up to 140 days were considered. The Z value for each experiment was determined using the following equation In ( ni+ ~) = In{ (FNoSB/Z) [ 1 - exp ( - Z) ] } - iZ

(5)

This Z value was used to select a pair of X and F, values to estimate SB for each experiment. Only Experiments 2 and 3 produced closer SB values (for

5.4 11.7 15.6

8.5 14.3 17.3

Recapture percentage

18 4 12

19 2 9

1-20

16 40 30

37 53 36

21-40

Time period

mAllrecoveries whose recapture time periods exceeded 140 days were pooled.

1189 1026 907

Femalerecaptu~s 1 12-14 September1982 2 13-16 June 1982 3 20-22 June 1983

Number released

1298 932 1089

Release date

Male recaptures 1 12-14 September1982 2 1 3 - 1 6 J u n e 1982 3 2 0 - 2 2 J u n e 1983

Experiment No.

Grouping of tagged P. semisulcatus recaptures by 20-day time period

TABLE 1

8 34 45

27 24 57

41-60

6 18 16

14 21 14

61-80

11 3 14

5 5 24

81-100

2 9 6

4 10 17

101-120

0 5 7

1 10 7

121-140

3 7 11

3 8 24

141+ I

4~

ESTIMATION OF NATURAL MORTALITY OF PENAEUS SEMISULCATUS

1 15

males) at a range of X and Ft values. Thus, these two experiments were considered for optimization.

CPUE ratio method CPUE ratio The CPUE ratio of a cohort at two points in time can be related to Zp, the total mortality within that time period, p, by the equation In (CPUE~/CPUE2 ) = In (ql/q2 ) + Zp

(6 )

When q~= q2, these CPUE values can be used to estimate Zp (Gulland, 1983 ). This procedure was, however, applicable when either there was no migration or emigration was roughly balanced by immigration (i.e. the equilibrium condition). Strict enforcement of an annual closed season in the Kuwait shrimp fishery since the 1987/88 season (i.e. the biological year from 1 July to the following 30 June; Siddeek et al., 1989) provided an opportunity to estimate M using eqn. (6), since Zp corresponded to Mp when there was no fishing.

Commercial CPUE data The Shuaiba industrial fishery weight-frequency data in the closing and following opening months of the 1986/87-1989/90 seasons were considered. The CPUE of this fleet was more representative of P. semisulcatus stock abundance than those of the other two Kuwaiti fleets (i.e. traditional dhow boats and private steel vessels) because the fishery targeted this species for the export market. Furthermore, it provided complete catch, effort and weekly shrimp (tail) samples at each size category (i.e. under 15 to 91-1 l0 pieces per pound) for estimating various statistics, including monthly CPUE and weight frequencies by species and sex (Bedford, 1982 ). The bulk of Shuaiba industrial catches, destined for export, is reported as tail weight; the small balance, intended for the local market, is reported as whole-shrimp weight. Thus, a raising factor [ = (total tail weight converted into whole-shrimp weight+ whole-shrimp weight)/total tail weight converted into whole-shrimp weight] was used to raise the weight frequencies of the total tail catch to gross whole-shrimp catch. To convert the tail weight of each shrimp into wholeshrimp weight, the following formulae (A.R.A. Ghaffar, Kuwait Institute for Scientific Research (KISR), unpublished data, 1988 ) were used (male) TW=0.10290+0.62137 Wh.W

(7)

(female) TW = 0.33032 + 0.59266 Wh.W

(8)

Because shrimp cannot be aged, the change in abundance of a group of length classes through the closed season was considered for M estimation. Two tailweight intervals, one for each sex, were arbitrarily chosen from the season's

116

M.S.M. SIDDEEK

final-month weight-frequency distribution. The weight limits of these intervals were then converted into CL limits using the following formulae (A.R.A. Ghaffar, KISR, unpublished, 1988 ) in conjunction with eqns. (7) and (8) (male) TW = 0.00091696 CL2"958 (female) TW=0.00117131 EL 2"867

(9) (10)

These two length limits were projected through the closed-season time period onto the following opening month fishery length-frequency distribution using the seasonal growth equation of Pauly et al. (1984) with known parametric values (male: L~o (CL)= 39.5, K (year -1 ) = 1.33, to (year)=-0.208, ts ( y e a r ) = - 0 . 4 9 5 , C = I ; female: L~=48.0, K ( y e a r - l ) = l . 6 9 , to ( y e a r ) = - 0 . 0 2 7 , ts ( y e a r ) = - 0 . 4 5 5 , C = l (Siddeek and Abdul-Ghaffar, 1991 ). This carved out a portion of the length-frequency distribution within the original and projected limits, to follow through the decay of a cohort. The CPUE values were evaluated within the original and the projected limits. The natural log of the ratio of the two CPUE values was calculated as the amount of natural mortality suffered between the mid-dates of the closing and reopening months; M was estimated from this.

Modified Gulland's formulae method Modified Gulland's formulae Gulland (1955) derived a set of formulae to estimate X, F and Z from tagging data, assuming constant mortalities and binomial sampling. Chapman (1961 ) recognized the inherent biases in the estimates and provided almost unbiased formulae to estimate the mortalities with their standard errors. The following formulae were essential for this study Z=(n-1)/

~ tm

(11)

m=l

X=(No-n)(n-1)/

No

Ft=Z-X a 2 =X(F 2+XF+X 2)/NoF

it,,

(12) (13)

(14)

Equation (12) generally overestimates X (Siddeek, 1989), whereas eqn. ( 14 ) underestimates tr2. To overcome these defects, the parameter No in these formulae was modified to NoSB.

ESTIMATION OF NATURAL MORTALITY OF PENAEUS SEMISULCATUS

1 17

Tag-recapture data Experiments 1, 2 and 3 (Table 1 ) were used in this analysis. The best SB values (and hence NoSB) were calculated using eqn. (3) with optimum X and Ft values obtained in the previous sections, and using eqns. ( 11 ) and ( 13 ) with previously obtained best X values. RESULTS

Estimates of X from M estimator The new M estimator was not applied to the female experiments because they did not satisfy the critical assumption - the SB values are the same - for successful optimization. On the other hand, the male experiments Nos. 2 and 3 satisfied this condition and were, therefore, used in the M estimator. The grid search was initiated with Z values obtained from the simple linear regression slopes (Fig. 1 ). Estimates of X and SB at the best choices of Ft for the selected male experiments are presented in Table 2. Optimization was repeated at Z values varied by 5%, which produced results differing by 1112% from the optimum (Table 2). Thus, the result was fairly sensitive to variation in the Z estimate, highlighting the need to obtain a fairly accurate Z value to select the best Ft for each experiment. The following results were selected from the optimization: Experiment 2 Experiment 3

Xper20days 0.1314 0.1314

SB 0.3000 0.3001

Estimates of M from CPUE ratio method The closing-month weight intervals (i.e. the initial size limits) were selected to accommodate only early adults, and to minimize the inclusion of very young recruits and old shrimp which would otherwise bias the results. The bulk of tagged shrimp releases were also in this size group. The 1987 sampling appears to have satisfied the assumption behind the CPUE ratio method. Because past tagging experiments showed restricted movement of P. semisulcatus (Mohammed et al., 198 lb; A1-Shoushani et al., 1983 ) and the Shuaiba industrial fleet operated in all Kuwaiti P. semisulcatus grounds, it was reasonable to assume that emigration was low. However, the possibility of immigration could not be ruled out for the 1988 and 1989 high recruitment years (unpublished catch data ) because of the existence of similar production trends in Kuwaiti and neighbouring Saudi Arabian grounds (Morgan and Garcia, 1982 ). Furthermore, the 1987 biological sampling was the most comprehensive of the three; therefore, the 1987 estimates of 0.1434 and 0.0885

1 18

M.S.M. SIDDEEK MALE

5,

FEMALE

(1)

(I)

b = - 0.7089

4, ®

b=-O.~

a = 4.5715

a =

r

r

=-0.9797

n = 6

O

•

7

1

2

3.0991

= -0,7~3

n =

5

=,2

1

5

2

3

4

5

6

MALE

b = -0.3543 5

(2)

A4

a = r

3.9746

4

5

6

FEMALE

6

.~2

7

b = -0.4662 a =

(2)

= - 0.7969 4

n =

I

3

r

=

n =

3

4.1195 -0.8268 6

2 O

o I

2

3

4

5

6

MALE

7 b = -0.3222

(3)

a = •

4'

n = -0.8172

•

n

+.3.

=

•

FEMALE

5'

b = -0.3844

(3)

4.1650

a : •

4

r

•

6

4.0717

= -0.9112

n =

8

3

® ®

•

o

2

o 1

2

3 Time

4 Period

5

6 (r)

7

,

1

,

2

,

3 Time

.

,

.

.

4

5

6

7

Period

(r)

Fig. 1. Natural log ofP. semisulcatus recaptures against the period of recoveries for releases on: ( 1 ) 12-14 September 1982; (2) 13, 15 and 16 June 1982; (3) 20-22 June 1983 (a=intercept, b = gradient, r = correlation coefficient and n = number of points (closed circles ) considered in

the regression).

for males and females, respectively (Table 3), were considered for further examination. The female result could not be confirmed as the best because no comparable results were obtained by the other methods (see the next section ); moreover, the estimates were sensitive to changes in the size limits (see male results for 15.3.89 samplings, Table 3). The lowest estimate of 0.0173 for males in 1988 was also rejected on the grounds that tropical penaeids are short lived with a life span of nearly 2 years (Garcia and Le Reste, 1981 ). The mean life expectancy based on this M value was 3.17 years ( = 20/0.0173 × 365; Seber, 1982, p. 4), which was not feasible on biological grounds. The highest estimate of 0.2463 in 1989 was also rejected using Beverton and Holt's ( 1957 ) formula (5.14) for catch mean age (/~) determination

119

ESTIMATION OF NATURAL MORTALITY OF PENAEUS SEMISULCATUS

TABLE 2 Optimized results from cohort formula with male P. semisulcatus tagging Experiments 2 and 3 Time span Regression of recoveries method (days) f t2

Square of SB difference

Optimized results

Ft3

X

SB 2

Remarks

SB 3

140

0.2229 0.1908 0.1314 0.3000 0.3001 0.1584×10 -7

140

0.2195 0.1890 0.1171 0.2838 0.2839 0.5500X10 -8

140

0.2245 0.1908 0.1475 0.3209 0.3207 0.1638X10 -7

Inputs from regression Z estimate Inputs from 5% less than the regression Z value Inputs from 5% more than the regression Z value

/7, and X values are given for a 20-day period; S B 2 and SB3 refer to SB values of Experiments 2 and 3, respectively.

T= 1/Z-~ tc - tt exp ( - Zl) 1 -exp(

-

Zl)

( 15 )

For the 1989/90 season (tc,~0.50, h~2.0, 1=1.5, and Z = q × e f f o r t + M,~ 0.00039 X 4124 + 4.49 ~ 6.10, where all figures were given on an annual basis and the q value was obtained from Morgan and Garcia ( 1982 ) ), 7 ~ 0.66 years. Thus, the average age of male catches was < 2 months above the 1989/ 90 recruitment age; such a catch would be composed of early adults. This was contrary to unpublished commercial catch and KISR research vessel survey length-frequency data for 1989/90, when good P. semisulcatus catches were observed for nearly 6 months after recruitment with no apparent major autumn recruitment peaks. Estimates of X from modified Gulland's formulae method Experiment 3 for males produced the X value (0.1334) closest to that of the input X value (0.1314 ) using the modified GuUand's formula Z estimate. The SB value (0.3231 ) was also comparable with that obtained by the cohort formula method (Table 4). The female X estimate was, however, inconclusive. Experiment 1 provided the Xvalue (0.0933) closest to that of the input Xvalue (0.0885) derived by the CPUE ratio method using the modified Gulland's formula Z estimate. On the other hand, this experiment and Experiment 3 both produced X values (0.1358 and 0.1353, respectively) closer to that of the input male X value (0.1314) derived by the cohort formula method using the regression Z estimate. The SB values of Experiment 1 were, however, extremely low and the standard errors of X were higher than the rest (Table 4). Moreover, unlike the other experiments, the releases were made in September during peak fish-

7.5/3/87

7.5/4/88

15/3/89

15/3/89

7.5/3/87

7.5/4/88

15/3/89

Male

Male

Male

Female

Female

Female

Closing month

15/9/89

15/9/88

15/9/87

15/9/89

15/9/89

15/9/88

15/9/87

Opening month

Mid-date of fishing

Male

Sex

184

160.5

191.5

184

184

160.5

191.5

Duration (days)

21.50-33.49

21.50-33.49

21.50-33.49

15.50-20.49

14.50-20.49

15.50-20.49

15.50-20.49

Tail weight range (g)

36.65-42.87 40.47-46.52

36.65-42.87 40.22-46.44

36.65-42.87 40.60-46.53

31.49-34.63 33.96-37.41

30.79-34.63 32.71-37.41

31.49-34.63 33.17-37.38

31.49-34.63 34.22-37.42

Length range (CL, mm)

0.1434

0.0173

0.1384

0.2463

0.0885

0.0697

0.0925

1605 1397 6450 1806 6295 653 574 246 1120 640 2003 855

137 303 218 244 218 244 223 672 137 303 218 244

219879 423230 1,406096 440561 1,372333 159223 128098 165599 153483 193934 436642 208651

M (per20 days)

1631 413

boatdays )

(no./

CPUE

223 672

Effort (boatdays)

363692 277758

(no.)

Catch

Estimates of M from Shuaiba industrial fishery CPUE data for P. semisulcatus

TABLE 3

Some size grades were not available for measurement

Some size grades were not available for measurement

Comprehensive measurement of size grades

Some size grades were not available for measurement

Some size grades were not available for measurement

Some size grades were not available for measurement

Comprehensive measurement of size grades

Remarks

7~

1298

932

1085

1189

1026

907

Male 1

2

3

Female 1

2

3

141

120

64

1842

133

110

Number recaptured

8911

7384

3178

13032

8661

5367

tm (days)

0.3142 0.3844

0.3223 0.4622

0.39651 0.3840

0.2808 0.3222

0.3048 0.3543

0.40621 0.7089

Z (per 20 days)

0.2387 0.2730

0.1737 0.1889

0.0704 0.0819

0.3231 0.3012

0.3321 0.3000

0.1168 0.1134

SB

0.2046 0.2491

0.2170 0.3395

0.3032 0.2482

0.1474 0.1995

0.1310 0.1945

0.2947 0.6063

F (per 20 days)

0.1096 0.1353

0.1053 0.1227

0.0933 0.1358

0.1334 0.1227

0.1738 0.1598

0.1115 0.1026

X (per 20 days)

0.0137 0.0158

0.0149 0.0179

0.0218 0.0253

0.0124 0.0122

0.0173 0.0167

0.0182 0.0225

SE of X

First-row SB value was estimated at X = 0.0885 with Ft= Z - 0.0885, whereas the second-row SB value was estimated at X = 0.1314 with Ft=Z-O.1314 First-row SB value was estimated at X=0.0885 with Ft = Z - 0 . 0 8 8 5 , whereas the second-row SB value was estimated at X = 0.1314 with Ft=Z-O.1314 First-row SB value was estimated at X = 0.0885 with F t = Z - O . 0 8 8 5 , whereas the second-row SB value was estimated at X = 0.1314 with Ft=Z-0.1314

SB values were estimated at X=0.1314 with FI=Z--0.1314 SB values were estimated at X=0.1314 with Ft=Z-0.1314 S B values were estimated at X=0.1314 with Ft=Z-0.1314

Remarks

~First-row Z values were estimated from modified Gulland's formula, and second-row Z values from linear regression. -'Four recaptures were not considered because the reported times o f recapture were suspicious. Accordingly, four releases were deducted from the total number of releases ( 1089 ) to estimate SB.

Number released

Experiment No.

Estimates of Z, X, F and the SE of X using modified Gulland's formula on data from P. semisulcatus tagging experiments

TABLE 4

r~

©

r-

©

r-

Z

z ©

m

122

M.S.M. SIDDEEK

ing activity, which may have prevented proper mixing of tagged shrimp with the non-tagged population. Thus, the results of this experiment appear to be questionable. On the other hand, the Xvalue (0.1353) for Experiment 3 seems to be acceptable for females because the high SB value (0.2730) of this experiment was comparable with that obtained for the corresponding male releases, and the standard error (SE) was also low. It should be noted that even Experiment 1, with a very low SB value, produced a realistic X estimate after that particular SB value had been substituted in eqn. (12). Furthermore, the modified Gulland's formula was robust enough to provide biologically meaningful results under high intervening fishing mortality, even if it was not constant, as demonstrated by Leigh ( 1988 ). Using eqn. (14) with mean No (1008), optimum X (0.1314), mean Ft (0.2068) and mean SB (0.30) values from Experiments 2 and 3 (Table 2), an approximate SE for male Xwas determined to be 0.0135. DISCUSSION

The new X estimator was ideal in a situation where a few tagging experiments were available, effective fishing intensity was difficult to determine or unavailable, the tagged population suffered different magnitudes of intervening fishing mortality, and initial tagging mortality and non-reporting of tagged recoveries pertained. CPUE ratio and modified GuUand's formula methods were used to obtain estimates to validate results derived from the new method, as well as to obtain an estimate for females, which could not be determined using the new method. However, both of these methods had drawbacks: results from the former were sensitive to variation in the size intervals considered, whereas estimates from the latter were sensitive to input X and Ft values, which were needed to estimate the effective initial tagged shrimp population (i.e. NoSB). Because the new method also demanded fairly accurate Z values for successful optimization owing to the fewer experiments involved (Siddeek, 1989), the best X values were chosen by comparing the estimates from all three methods. The best X estimate for males was 0.1314 per 20 days (2.4 per year) with an SE of 0.0135. The CPUE ratio method provided a low M value of 0.0885 per 20 days for females, whereas the modified Gulland's formula provided results (0.1227-0.1358 per 20 days ) closer to that of males with regression Z values. In the absence of any conclusive evidence for low M for females, the male value was provisionally accepted for females. Earlier workers used M = 3 for both sexes (e.g. Garcia and van Zalinge, 1982; Morgan and Garcia, 1982), obtained by regressing Z on effort (van Zalinge et al., 1981 ). This value appears somewhat high (see the argument put forward in the CPUE ratio method section). Mathews et al. (1987) obtained an estimate of 1.8 (per year ) for both sexes using Pauly's ( 1980 ) equa-

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tion. This estimate was questionable because of the invalidity of Pauly's equation for shrimp stocks, as well as the fact that historical K and Lo~ values used by Pauly to develop this equation were largely derived from the non-seasonal von Bertalanffy growth equation. The current estimate fell between 1.8 and 3.0, and was also biologically meaningful. The optimum X value would be an overestimate if Ricker's ( 1975 ) Type B errors - systematic tagging mortality, tag losses and emigration - existed. Previous tagging experiments in Kuwaiti water have shown restricted taggedshrimp movement (Mohammed et al., 1981b; A1-Shoushani et al., 1983). Thus, systematic migration was assumed to be low. Because of the short time span of tag recoveries ( 140 days), systematic tagging mortality and tag losses were also assumed to be low. Indeed, the optimum male X value (0.1314 ) from the cohort formula method and the best M value (0.1434) from the CPUE ratio method were closer, providing evidence for the non-existence of (or negligible) Type B errors. It was also assumed that the catchability of tagged shrimp was similar to that of those untagged, i.e. that Ricker's ( 1975 ) Type C errors were absent. Subject to the validity of this assumption, the estimate of X using the new method could be taken as being close to the true M. Because young and old shrimp were not included in the experiments, Assumption 1 (constant M) was largely satisfied by the tagged shrimp population. Assumption 2 (constant SB), which is critical for successful optimization, was satisfied only by the two male experiments, thus enabling estimation of X. Assumption 3 (numerous releases) was satisfied by both male and female experiments, where releases exceeded 900. Assumption 4 (two experiments with different Z values) was also satisfied by both the male and female experiments. The major drawback of the new method is the necessity for at least a pair of experiments having similar SB and different Z values for optimization. If a number of tagging experiments (more than three) were conducted under similar conditions (i.e. the same season and tagging methods), the probability of finding two such experiments would be much greater, leading to a great possibility of estimating M. ACKNOWLEDGEMENT The author is very grateful to KISR for providing facilities to carry out this study and wishes to thank J.U. Lee of KISR for his suggestions. REFERENCES Allen, K.R. and Hearn, W.S., 1989. Someproceduresfor use in cohort analysis and other population simulations. Can. Fish. Aquat. Sci., 46: 483-488.

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