Appendix 3. NOTES ON THE ASSESSMENTS

In the assessments it was assumed that M. merluccius could be dealt with separately from M. senegalensis and M. cadenati, and that they could be separated by areas (M. merluccius in Divisions 34.1.1, and 34.1.2, and Merluccius spp. in Divisions 34.1.3 and 34.3.1)-see Section 5.

1. Methods of Assessment and Input Parameters Used

The relation between yield and fishing effort (mortality) was investigated using both General Production and the Beverton-Holt models.

The effect of changes in mesh size were investigated using the Beverton and Holt model. Cohort analysis of length compositions was used to determine current values of F/Z and hence, indirectly, current values of F.

1.1 Cohort Analysis (Tables 6 and 7)

Length compositions were used to determine values of F/Z, using the cohort analysis method of Jones (1974).

The following input parameters were used for these analysis:

M. merluccius (Table 6)	Merluccius spp. (Table 7)
Final F/Z = 0.8	Final F/Z = 0.5
M/K =2.8	M/K = 2.0
L¥ = 130 cm	L¥ = 90 cm

For each species cohort analysis provided a value of F/Z for each length group. For M. merluccius inspection showed no significant trend over the length range 12-72 cm. The average value of F/Z for this length range was found to be 0.74.

For Merluccius spp. values of F/Z showed no significant trend over the range 45-70 cm, and for this range the average value was 0.72. For “fish” smaller than 45 cm, smaller value of F/Z was obtained. From inspection, it was decided that the “effective” 50 percent length at first capture was about 40 cm.

1.2 Current value of fishing mortality rate (F)

Current values of F were calculated from the values of F/Z obtained from cohort analysis, by first assessing values of M and using the relationship: F = ME/(1-E) where E = F/Z.

For M. merluccius, with M = 0.2, the value of F corresponding to F = 0.74 is:

F = 0.74 (0.20)/(1-0.74) = 0.57

This provides an estimate of the current value of F for this species.

For Merluccius spp., with M = 0.28, F = 0.72 (0.28)/(1-0.72) = 0.72

1.3 Beverton and Holt Yield per Recruit Assessments

These were made using the tables provided by Beverton and Holt (1964). During the meeting tabulation for M/K = 1.75 only were available, but later more extensive tables were used. This made it possible to examine the results for a range of parameter values, and thus take some account of possible errors in the estimates. These are likely to be particularly significant in the case of M (or M/K) and also, for M. merluccius for C (because of uncertainty in the value of both 1_c and L_¥). For convenience in comparison between different assumptions, the tables give the values in the tabultation, and also the yield per recruit expressed as a percentage of the current value.

For Table 8

(a) M/K = 1.75, C = 0.11
(b) M/K = 2.00, C = 0.11 (plotted in Fig. 6, best estimate of parameters)
(c) M/K = 2.50, C = 0.11
(d) M/K = 2.50, C = 0.18 (most conservative estimate)

For Table 9

(a) M/K = 2.00, E = 0.75 (plotted in Fig. 7, best estimates of parameters)
(b) M/K = 1.75, E = 0.75
(c) M/K = 2.50, E = 0.75
(d) M/K = 2.50, E = 0.50 (most conservative estimate)

For Table 10

(a) M/K = 1.75, C = 0.44
(b) M/K = 2.00, C = 0.44 (best estimate, plotted in Fig. 8)
(c) M/K = 2.05, C = 0.44

For Table 11

(a) M/K = 1.75, E = 0.70
(b) M/K = 2.00, E = 0.70 (best estimate, plotted in Fig. 9)
(c) M/K = 2.50, E = 0.70
(d) M/K = 2.00, E = 0.60 (conservative estimate)

For both species, mesh size was related to length at first capture by the relationship: 1_c = selection factor × mesh size.

A selection factor of 3.6 was used.

Lengths at first capture were converted to ages at first capture using the growth parameters in section 2.3.

1.5 General Production Models

The relationship between yield and fishing effort was also investigated using the Schaeffer General Production Model.

Plots of catch per unit effort against total effort yielded unsatisfactory results however (Fig. 10) and it was concluded that the available data were not suitable for the application of this method.

2. Data for Information and for Use in the Assessments

2.1 Length Composition (Tables 3-5)

For M. merluccius, length compositions were derived for the Moroccan and Spanish landings from Divisions 34.1.1 and 34.1.2 (Table 4).

These were based on experimental trawling for M. merluccius in Moroccan waters (Table 3), separate length compositions being shown for different depth zones.

To represent the Moroccan fishery, an average length composition for the depths 50-200 m was used and 200 to 500 m for the Spanish fishery.

For each fishery, these length compositions were raised to correspond to the effective average landings for 1973-1975. The raising factors were each equivalent to the ratio: total weight/weight sampled.

For Merluccius spp. the length composition data provided by Portugal (Table 5) was used.

2.2 Weight/length relationship

The following weight/length relationship has been determined from samples of M. merluccius caught off the Moroccan coast (from unpublished Moroccan data):

where	W=013 L2.87
	W = weight (g)
	L = length (cm)

For both species, the following data were provided by the USSR

Length (cm):		30	35	40	45	50	55	60	65	70
weight	Merluccius spp.	150	300	430	610	800	1100	1300	1510	1000
	M. merluccius	150	300	430	700	910	1190	1410	1510	1910
Moroccan data for M. merluccius									2075	2566

2.3 Growth Data

Growth data for M. merluccius and Merluccius spp. are given by Maurin, 1954. In neither instances do the growth curves look as though they might tend to an asymptote so that these data are unsuitable for calculating Bertalanffy growth parameters.

The Bertalanffy growth parameters used for M. merluccius by the ICES Hake Working Group (Anon. 1978) are:

L¥	(cm)	K		t0
92.4		0.13	-	0.24
152.5		0.063	-	0.66

Values for the different sexes were combined and the following values were used for M. merluccius in the assessment:

L¥	130 cm
K	0.10

For Merluccius spp., USSR data (Appendix 6) were used to calculate values of L_¥ = 90 cm and K = 0.14. These values were used in the assessments for this species.

2.4 Natural Mortality

There are no estimates of mortality for hakes in the CECAF area.

Assessments were made using a value of M equal to 0.2 for M. merluccius and 0.28 for Merluccius spp. (a value of 0.3 was assumed for Merluccius spp. but later changed to 0.28 to be consistent with a ratio of M/K = 2.0 for this species).

2.5 Selectivity Data

For M. merluccius, selection factors range from 2.42 to 5.6, the large variation being due to differences in:

(a) the method of mesh measurement (by hand or by using a pressure gauge with pressures ranging from 1.5 to 5 kg);

(b) the experimental technique employed (covered cod-end technique usually give lower selection factors than the alternate haul techniques);

(c) the material used (cotton, hemp, polyamide, polyester, polyethylene, manila, sisal, or polypropylene).

No selectivity data are available for Merluccius spp. or M. cadenati. In constructing Table 11 a value of 3.6 was assumed in estimating the mesh size corresponding to a given size at first capture.

2.6 Length at First Maturity

Maurin (1954) has investigated lengths at first maturity of Moroccan hakes. He found that all hakes below 18 cm were immature and that all above 36 cm were mature.