by
B. Bautil
FAO Fisheries Project (RAF/79/065),
P.O. Box 487, Victoria, Mahe, Seychelles.
And
C.R. Samboo
Albion Fisheries Research Centre,
Albion, Petite Riviere, Mauritius.
INTRODUCTION
BASIC DATA
ESTIMATION OF GROWTH PARAMETERS
TOTAL MORTALITY COEFFICIENT
LENGTH AT FIRST CAPTURE
FISHING AND NATURAL MORTALITY COEFFICIENTS
YIELD PER RECRUIT
CONCLUDING COMMENTS
BIBLIOGRAPHY
Lethrinus mahsena is the most important species taken from the waters of the Nazareth Bank. It contributes some 80 to 90 percent to the total catch, or some 1,000 tonnes annually in recent years. The fishing period extends from September to July. The gear used are handlines operated from dories worked in conjunction with motherships. The fishing depths are from 15 to 50 m. The fish are gutted shortly after capture and landed in Mauritius as frozen product.
According to research on the stocks inhabiting the Saya de Malha Bank, the fish is a protogynic hermaphrodite. As a consequence there are few females longer than 35 cm. (fork lengths are used in this paper), and few males with lengths less than 20 cm; see Bertrand et al (1986). The mean age at which the sex reversal takes place has been given as 5 to 6 years; some 2 to 3 years after the earliest onset of sexual maturity. In respect to spawning seasons, the latest work of Bertrand (1986) suggests a single spawning season each year, in the period between October and February. Some earlier work had led to the opinion that there were two spawnings each year; see Wheeler and Omanney (1953).
The lengths of the fish were measured at the landing site during the period October 1977 to August 1987. Those for the months before July 1985 were taken as total lengths, but were subsequently converted to fork lengths using the relationship given in Lebeau and Cueff (1976). The analyses described here utilised the lengths grouped by quarter as shown in Table 1.
Table 1: Fork length frequencies for Lethrinus mahsena caught by Mauritian boats on Nazareth Bank.
The method of Bhattacharya (1967) was used in order to determine the mean lengths for each of the normally distributed components in the quarterly length frequencies. An example resolution is shown in Figure 1. As an aid to interpretation the mean lengths were then arranged into groups by quarter. The groups were then moved laterally relative to each other, to achieve an arrangement consistent with positive growth between months. Amongst a number of possible arrangement, that shown in Table 2 seemed the most reasonable. (Within the table the question marks indicate the presence of components believed to exist, but which could not be found from the application of the Bhattacharya method.)
Figure 1. Plot of an example length frequency showing normally distributed components determined by Bhattacharya Method.
Table 2: Lateral arrangement for the component identified with the Battacharya method (Birthday 1st January)
1ST QUARTER (midFebruary)  
1978 
23.75 
27.33 
29.70 
32.98 
35.59 
37.32 
39.90 
41.94 


1980 
23.77 
28.12 
? 
33.31 
36.03 
38.90 
? 
43.49 


1982 
24.41 
? 
30.41 
34.59 
? 
38.72 
41.75 
? 
? 
46.24 
1983 
23.59 
? 
30.19 
? 
35.95 
? 
? 
42.24 
? 
47.02 
1986 
24.52 
28.87 
? 
32.64 
? 
37.46 




2ND QUARTER (midMay)  
1978 


29.40 
32.58 
? 
37.37 
40.54 



1980 
23.19 
28.67 
31.44 
? 
37.38 
37.38 
? 
42.42 
? 
46.14 
1981 
24.24 
? 
29.07 
? 
34.37 
38.63 
? 
42.01 
44.64 
47.60 
1982 
23.63 
? 
31.76 
? 
? 
39.39 




1983 


29.07 
33.93 
? 
38.53 
? 
? 
44.69 

1987 
24.23 
28.72 
31.95 
? 
36.62 
? 
41.50 
? 
? 
47.19 
3RD QUARTER (midAugust)  
1981 
26.08 
29.68 
32.61 
36.06 






1982 

29.63 
? 
36.22 






1987 
26.98 
? 
33.55 
? 
38.76 
41.55 
? 
? 
47.42 

4TH QUARTER (midnov)  
1977 
27.00 
30.44 
32.94 
36.31 
38.06 
41.66 
? 
44.97 


1981 
28.03 
31.88 
? 
35.24 
37.54 





1982 
28.71 
31.64 
? 
35.57 
39.81 
42.23 




1983 
? 
29.08 
32.14 
? 
39.14 





1986 
? 
? 
32.19 
? 
37.88 
? 
? 
45.40 


The next procedure involved the assignment of ages in respect to each of the mean lengths. The latter were presumed to reflect the lengths of individual cohorts or year classes. This was done relative to an arbitrarily chosen birthday date of January 1, and assuming that the fish having lengths of 23 to 25 cm. were between 4 and 5 years old (as indicated in Bertrand et al, 1986). The mean lengths and corresponding assigned ages were then used, with a modification of the von Bertalanffy plot as described in Sanders (in press), to estimate the von Bertalanffy growth constants. The values obtained are given below:
L_{¥ } = 61.7 cm., K = 0.100 per year, and t_{0} = 0.708 years.
A plot of the growth curve described by these constants is shown in Figure 2.
Figure 2. Plot of mean lengths at assigned ages and the growth curve based on the estimated von Bertalanffy constants.
The length converted catch curve and Jones and van Zalinge methods, both described in Sparre (1987), were applied to the sum of all the quarterly length frequencies. The von Bertalanffy growth constants (L_{¥ } and K) used in these analyses are those presented above. Figure 3 shows a plot of the log (C/dt) values against estimated ages and the fitted regression line.
The total mortality coefficients (Z) obtained are given below.
Method 
Est. of Z 
95 % Confidence Interval 
Comments 
Length Converted Catch Curve 
0.434 
0.4150.453 
for fish > 29cm. 
Jones and van Zalinge 
0.465 
0.4580.472 
for fish > 29cm. 
An estimate of the mean value for the total mortality coefficient is thus Z = 0.449.
Figure 3. Plot of log (C/dt) values against estimated ages and fitted regression line.
The length at first capture (the length at which 50 % of the fish of that size are available/vulnerable to capture) was estimated as a components of the length converted catch curve analysis, again as described in Sparre (1987). The value obtained is L50% = 29.5 cm., which corresponds to an age of 5.8 years when using the previously presented von Bertalanffy growth constants.
The length at which 75 percent of the fish at that size are available/vulnerable to capture was estimated as L75% = 31.2 cm., and corresponds to an age of 6.34 years.
These were estimated iteratively through a process involving the application of the length converted cohort analysis of Jones (1984). Trial values for the natural mortality coefficient (M) were applied separately with the length frequencies summed over all quarters. The growth parameters used were those presented earlier. In all cases the "terminal F/Z" was given the value of 0.7, where F is the symbol for the fishing mortality coefficient
The output of interest from each analysis was the estimate of the mean fishing mortality coefficient for fish of lengths exceeding 29 cm. The "best choice" combination of mean F and trial M were taken as those whose sum was equal to the estimate of mean Z (ie. Z = 0.449 given earlier). The estimates obtained from this iterative process are mean F = 0.23 and M = 0.22; see Table 3.
Table 3. Determination of the "best choice" mean F and trial M when applying the following results of the Jones length converted cohort analysis.
Trial M 
Est. Mean F 
(a) + (b) 
Comment 
0.33 
0.149 
0.479 

0.25 
0.206 
0.457 

0.22 
0.230 
0.4501 
("best choice" combination) 
0.20 
0.246 
0.446 

Table 4. Estimates of yield per recruit and biomass per recruit from the application of the Thompson and Bell Model.
Multiples of Contemporary F values 
Yield per Recruit 
Biomass per Recruit 
0.0 
0 
15,061 
0.2 
554 
10,965 
0.4 
777 
8,818 
0.6 
887 
7,460 
0.8 
948 
6,515 
1.0 
983 
5,818 
1.2 
1,003 
5,283 
1.4 
1,015 
4,861 
1.6 
1,020 
4,519 
1.8 
1,022 
4,238 
2.0 
1,022 
4,002 
2.2 
1,020 
3,802 
2.4 
1,016 
3,630 
Note: MSY = 1,022 gm./10 recruits, and Biomass at MSY = 4,191 gm./10 recruits; both when X = 1.8.
The length converted Thompson and Bell yield per recruit analysis as described in Sparre (1987) was undertaken using the output of the length converted cohort analysis. This analysis allows a relative prediction of the long term (equilibrium) catch weights and stock biomass for alternative assumptions on the future fishing pattern. In this case the fishing pattern found by the cohort analysis was assumed to remain, whereas the level of the fishing mortality (assumed proportional to fishing effort) was varied.
The results of the length converted Thompson and Bell analysis are shown in Table 4. The number of recruits used in the analysis was 10 fish. The results indicate that the contemporary catches are at about the maximum sustainable yield, and that the contemporary biomass is some 40 percent of the preexploitation biomass.
The results presented above are generally in agreement with those reported in Bertrand et al (1986) for the stock inhabiting the Saya de Malha bank. The estimates for the growth constants obtained by the latter author are:
L_{¥ } = 60 cm., K = 0.1, T_{0} = 1.05 yr. (sexes combined, Nov. 1984).
They also report estimates for the natural mortality coefficient of M = 0.2 for fish younger than 8.5 years and M = 0.7 for older fish; and F = 0.41 (1982/83) and F = 0.31 (1983/84) for the fishing mortality coefficient. The latter are higher than obtained here for the Nazareth bank, which presumably reflects higher levels of fishing effort (relative to the magnitude of the stock).
In respect to the management implications of the assessment, the results of the Thompson and Bell yield per recruit analysis indicate that additional fishing effort would provide very little additional catch. Having in mind the relatively high costs associated with this type of fishing, there is likely to be no economic justification for seeking to harvest this small unrealised potential. On the contrary, particularly if the fishery were to be managed more in the direction of maximising profits, reducing the fishing effort would seem the preferable option.
Battacharya, C.C., (1967)  A simple method of resolution of a distribution into Gaussian component. Biometrics 23: 115135.
Bertrand, (1986)  J., Données concernant la reproduction de Lethrinus mahsena sur les bancs de Saya de Malha (Océan Indien). Cybium 10 (1): 1529.
Bertrand, J. et al, (1986)  Rapport du groupe de travail pour une évaluation des ressources en capitaine/dame berri des bancs de Saya de Malha. Publication IFREMER., 40p.
Lebeau, A. et J.C. CUEFF, (1976)  Biologie et pêche des Lethrinidés sur les haut fonds de Saya de Malha. Trav. et documents ORSTOM 47: 333348.
Sanders, M.J., (1987)  A simple method for estimating the von Bertalanffy growth constants for determining length from age and age from length, p. 299303. In D. Pauly and G.R. Morgan (eds.) Length based methods in fisheries research. ICLARM Conference Proceedings 13, 468 p. International Centre for Living Aquatic Resources Management, Manila, Philippines, and Kuwait Institute for Scientific Research, Safat, Kuwait.
Sparre, P., (1987)  Computer programs for fish stock assessment. Length based fish stock assessment for Apple 2 computer. F.A.O. Fish. Tech. Pap. No. 101 Suppl. 2: 218p.
Wheeler, J.F.G. et F.D.P. Ommanney, (1953)  Report on the 1953 MauritiusSeychelles Fisheries Survey 194849. Colonial Office Fishery Publ., 154 p.