Xu and Mohammed An alternative approach to estimating growth parameters 



147 



posed in this study to obtain length-at-age data in- 

 cludes the following steps: 1) arrange the monthly 

 length-frequency samples in sequential order (the 

 data series should begin with the month in which 

 the new recruitment is first detected); 2) identify the 

 mode representing the newly recruited cohort in the 

 length-frequency distribution of the first month (this 

 should be the smallest in size in the length distribu- 

 tion); 3) follow the movement of this mode from month 

 to month to find its location in the time series; 4) 

 define the width of the central location spreading 

 from the mode in each month; 5) use the length data 

 in the range of the central location to calculate the 

 mean length weighted by the frequencies (this mean 

 length is considered to be the mean length at month 

 i); and 6) according to the information on the spawn- 

 ing season, define the birth-month, a, for the cohort 

 (then the age for that cohort in month i can be esti- 

 mated by age= i-a ). A length-at-age data set is then 

 established. Like that in other length-frequency 

 analysis methods such as ELEFAN I (Pauly et al., 

 1984), age here should be considered relative age 

 instead of true age. One might be able to adjust it if 

 information on the observed spawning season for 

 each year was available. The change of relative age, 

 however, would only change the location but not the 

 shape of the growth curve. Note that step 3 might be 

 difficult for a long-lived species with highly overlap- 

 ping cohorts at old ages or for species with continu- 

 ous recruitment and thus result in multiple peaks 

 in the length-frequency distribution (Brothers, 1979). 

 For a species with distinct modes and discontinuous 

 recruitment in one year, like green tiger prawns in 

 Kuwait waters, the modal progression of a cohort can 

 be easily followed from month to month. This will be 

 shown below. Step 4 involves making subjective de- 

 cisions regarding the width of the central location. If 

 the length distribution is fairly symmetric around the 

 mode and the cohorts in the length distribution do not 

 highly overlap, the estimates of growth parameters 

 should not be sensitive to the subjective selection of 

 the width. The overlap index proposed by McNew and 

 Summerfelt ( 1978) can be applied as a guideline to de- 

 fine the degree of overlap among the adjacent age-class 

 distributions. The Cental Location Measure should 

 work like the trimmed mean for a single cohort case. 



Data collection 



In order to obtain a series of monthly length-fre- 

 quency samples that are representative of the popu- 

 lation, monthly research vessel surveys were carried 

 out from May 1986 to July 1990 in Kuwait waters 

 with RV Bahith, a stern trawler (679 tons in gross 

 tonnage) of the Kuwait Institute for Scientific Re- 



search. Surveys were interrupted in June 1986 and 

 December 1988 because of logistical problems. Each 

 monthly survey included 7 to 10 fixed stations in 

 Kuwait waters and each tow lasted from 30 to 50 

 min. All shrimp were sorted and weighed prior to 

 examination of the entire catch (or a 3- to 6-kg sub- 

 sample) to determine species composition and length 

 frequencies. Carapace length, rear margin of the or- 

 bit to the posterior edge of the carapace (Dall et al., 

 1990), was measured to the nearest 1 mm. 



Kuwait waters were partitioned into three areas 

 (Kuwait Bay, Middle Area, and Southern Area) on 

 the basis of species distribution and geographical con- 

 siderations (Xu et al., 1995). The relative size ratios 

 of the three areas of Kuwait Bay: Middle Area: South- 

 ern Area were 3: 4: 5, respectively. These ratios were 

 used as weighting factors in the compilation of 

 monthly length frequencies from the data of each 

 sampled station. 



Results 



Length at age 



The monthly carapace length (CD frequency showed 

 distinct modes and clear modal progression for the 

 1986, 1987, 1988, and 1989 spring cohorts of male 

 and female green tiger prawns. The central location 

 of the length distribution in each month was defined 

 by spreading the distribution from the mode up and 

 down for 2-3 mm. Tables 1 and 2 provide part of the 

 monthly length-frequency data for male and female 

 shrimp, respectively, to show the central locations 

 (bold numbers) used to calculate the mean length. 

 For a length distribution with a mode located in one 

 interval, three intervals from the mode to each side 

 were selected. Otherwise, for a mode located in more 

 than one interval, two intervals from the mode to 

 each side were selected. The number of sampled 

 shrimp was usually small for the new recruits owing 

 to gear selectivity, and for the oldest shrimp owing 

 to low abundance. The width of the central location 

 in these cases was defined by recognizing a breaking 

 point at which the smallest number was observed, 

 e.g. 20 mm in May 88 and 32 mm in August 89 for 

 males (Table 1). If two peaks are located closely (e.g. 

 June and July 1988 for females), a moving average 

 over three intervals was used to define the mode. 

 For example, the mean numbers of shrimp over 22- 

 24, 23-25, 24-26, and 25-27 mm were 59, 62, 62, 

 and 58, respectively, for July 1988 females; there- 

 fore the mode was defined from 23-26 mm. If two 

 peaks from the same cohort were located far from 

 each other (e.g. September 1988), they were consid- 



