Appendix 8: ALTERNATIVE APPROACHES TO ESTIMATING THE EFFECT OF CHANGES IN MESH SIZE1

¹This Appendix was prepared in FAO HQ, Rome, after the working party meeting, to illustrate the application of alternative methods of assessment. It has not been discussed by the working group as a whole.

The importance of this to the hake fishery is shown by the differences between the sizes of hake apparently taken by Moroccan and Spanish fishermen. The greater part of the Moroccan catch is of fish less than 30 cm, which could be released by a 70 mm mesh. The fish caught by Spain are much larger, and most of the catch (at least in terms of weight) would be obtained by a 70 mm mesh. The effects of a larger mesh would therefore bear very unequally on the two fisheries, the benefits being much greater for the Spanish than for the Moroccan fishermen, and an analysis treating the fishery as a whole could be quite misleading.

The steps involved in calculating the immediate and long-term effects of a mesh-change, using the alternative method are as follows:

(i) Estimate the proportion of the present catch in each length-group which will be released if the mesh-size is increased (= P. say).

(ii) Estimate (for each section of the fishery) the numbers N_R and weight Y_R of fish released

(N_R = S P_i N_i; Y = S P_i N_i W_i),

where N_i is the number of fish caught of length i, and W_i is the average weight of fish of that size.

= S N_R, summing over all sections of the fishery), and the total numbers retained = S N_K, where N_K = C - N_R, and C is the number caught at present with the original mesh-size).

(iv) Estimate the numbers of the fish released which will ultimately be caught, taking account of (a) natural mortality between the time at release, and the time at which they will have grown big enough to be retained by the new larger mesh, and (b) the proportion of those reaching the latter size that will ultimately be caught (= E). That is, the numbers caught will be equal to N_A, where

N_A = E e^-Mt

and	M = natural mortality coefficient
	t = time between release and reaching the selection size of the larger mesh

(v) Calculate the proportion, Q, by which, in the long-run, the catches immediately after the change in mesh size, will be increased as a result of the capture of fish released by the larger mesh; this will be equal to the ratio of N_A, the additional numbers caught, to , the numbers caught immediately after the change i.e.

(vi) Calculate, for each element of the fishery separately, the immediate loss _jL, and the long-term effects _jG

where 1-_jL = _jY_K/j/Y

(_jY = initial weight caught by the _jth element of the fishery = _jY_K + _jY_R)

and 1 + _jG = (1 + Q)(1 - _jL)

This has been done for data for the northern (M. merluccius) fishery, treating the Spanish and Moroccan catches as two distinct elements, and for the southern fishery, treating it as a homogeneous unit, with a size composition the same as that of the Portuguese fishery. The results were. as set out below:

A. Northern Stocks (M. merluccius fishery) (Changes in percent)

	Mesh Change from 30 mm to:	Immediate Loss	Long-Term Gain
			E = .5	E = .7	E = .9
Total Fishery	40 mm	1.6	5.4	8.1	10.9
	50 mm	8.0	16.1	25.7	35.3
	60 mm	17.6	34.3	55.1	75.8
	70 mm	26.9	59.5	94.1	128.7
Morocco	40 mm	2.6	4.3	7.1	9.8
	50 mm	17.3	4.2	12.9	21.5
	60 mm	40.1	-2.4	12.7	27.7
	70 mm	60.8	-14.4	4.2	22.8
Spain	40 mm	1.0	6.0	8.8	11.6
	50 mm	2.0	23.6	33.9	44.1
	60 mm	3.3	57.6	82.0	106.2
	70 mm	5.4	106.4	156.9	202.7

B. Southern Stocks (M. spp.)

Mesh Change from 60 mm to:	Immediate Loss	Long-Term Gain
		E = .5	E = .7	E = .9
70 mm	2.3	1.8	3.5	5.2
80 mm	6.3	3.1	7.2	11.4

Too much attention should not be paid to the precise figures, which depend on the length compositions used in the calculations. The true length compositions are not well known. In terms of the total catches there will be very considerable gains in the northern area, even if the stock is moderately exploited (E = 0.5, fishing mortality is equal to natural mortality; in fact the estimates determined by the group were F = 0.6, M = 0.2, E implying E = 0.75). However the immediate loss in going in one step is high (over 25 percent), and intermediate steps would be needed.

Looking at the individual countries, Spanish catches would be increased very considerably, for all values of E, and their immediate losses are comparatively small. Moroccan fishermen would gain less, and if the rate of fishing is lower than expected, they might even lose in the long term. In any case the mesh-size that would give them the largest catch (but at the expense of reduced total catch) are less than 70 mm. These are, as underlined in the table, 40 mm if E = 0.5, 50 mm if E = 0.7 and 60 mm if E = 0.9.

Reference

Gulland, J.A., The estimation of the effect on catches of changes in gear selectivity. 1961 J. Cons. CIEM, 26(2): 204-14

Table 1: MERLUCCIUS MERLUCCIUS: CATCH (IN METRIC TONS) CATCH PER UNIT EFFORT AND TOTAL EFFORT DATA FOR THE NORTHERN ZONE OF CECAF

Year	C1	C2	C3	E1	E2	CPUE1	CPUE2	CPUE3	C1+C2+C3
1970	1 714	4 802	4 916	5 852	5 450	.29	.88	.57	11 432	39 421	12 991	20 056
1971	1 455	2 724	4 616	5 002	5 200	.29	.52	.41	8 795	30 328	16 913	21 451
1972	1 356	2 606	4 515	4 589	5 500	.30	.47	.39	8 477	28 257	18 036	21 736
1973	1 426	2 850	3 575	4 589	6 800	.31	.42	.38	7 861	25 326	18 693	20 661
1974	2 421	5 020	5 650	4 100	8 100	.64	.62	.63	13 094	20 459	16 526	20 784
1975	1 796	4 412	5 843	4 194	9 600	.44	.46	.45	12 059	27 389	22 722	26 780
1976	1 142	2 757	3 846	4 912	12 300	.23	.22	.23	7 739	33 648	35 177	33 648

C₁= Spanish catches (bakas)
C₂ = Moroccan catches
C₃ = Spanish catches (trios)
E₁ = Spanish effort (bakas) GRT
E₂ = Moroccan effort GRT

^1/Includes small quantities of M. cadenati

C₁ = Portuguese catch (tons)
C₂ = Spanish catches (tons)
C₃ = Soviet catches (tons)
E₁ = Portuguese effort (thousands of fishing hours)
C₁/E₁ = CPUE of the Portuguese fleet (kg/hour fishing)

^2/Total catch of 1964 not available. From 1965 to 1969 - Stat. Bul. CECAF, Catches from 1973-1975 - Scientific estimations

^3/Spanish catches not included.

Table 4: M. MERLUCCIUS: ESTIMATES OF THE LENGTH COMPOSITION OF MOROCCAN AND SPANISH CATCHES, BASED ON TABLE 3 (Numbers in 000’)

cm	Morocco	Spain	Totals
6-7		143	143
8-9	62	300	362
10-11	362	956	1 318	1823
12-13	1 557	1 539	3 096
14-15	1 896	1 459	3 355
16-17	7 298	714	8 012	14463
18-19	9 575	712	10 287
20-21	8 625	333	8 958
22-23	5 310	672	5 982	25227
24-25	3 240	649	3 889
26-27	1 962	527	2 489
28-29	1 234	522	1 756	8134
30-31	600	665	1 265
32-33	539	890	1 429
34-35	361	834	1 195	3889
36-37	247	981	1 228
38-39	109	693	802
40-41	53	876	929	2959
42-43	47	796	843
44-45	23	586	609
46-47	23	396	419	1871
48-49	22	288	310
50-51	14	159	173
52-53	11	159	170	653
54-55	5	108	113
56-57	5	98	103
58-59	8	98	106	322
60-61	2	63	65
62-63	8	82	90
64-65	5	68	73	228
66-67	3	54	57
68-69	-	75	75
70-71	-	49	49	181
72-73	3	54	57
74-75	-	23	23
76-77	2	14	16	96
78-79		9	9
80-81		5	5
82-83		2	2	16
84-85		-	- )
86-87		7	7 )
88-89		35	35)	46
94-95		2	2 )
104-105		2	2 )
No.	43 211	16 697	59 908
Weight kg	4 095	5 422	9 517

Table 5: MERLUCCIUS spp.: ESTIMATES OF THE LENGTH COMPOSITION OF MERLUCCIUS spp. FOR SPANISH, PORTUGUESE AND USSR CATCHES FOR THE YEARS 1970-1976, BASED ON SAMPLES FROM PORTUGUESE VESSELS (SEE APPENDIX 4). (Nos. in 000)

Length cm	1970	1971	1972	1973	1974	1975	1976
16-17	1	0	-	-	-	-	-
18-19	27	39	2	-	731	-	-
20-21	536	200	33	-	6 107	1 271	-
22-23	1 991	966	105	164	16 499	2 442	-
24-25	5 094	1 302	221	3 876	16 307	11 787	4
26-27	7 068	2 632	503	19 590	8 275	17 245	132
28-29	9 263	4 354	1 051	26 061	7 044	17 643	849
30-31	10 056	5 798	2 317	17 268	9 186	14 728	2 829
32-33	6 832	6 483	3 462	14 301	18 475	14 528	9 675
34-35	4 856	6 841	4 369	22 426	33 794	13 382	19 501
36-37	4 566	5 588	4 446	37 153	44 546	13 706	20 746
38-39	4 804	4 577	6 354	40 187	40 864	21 680	19 369
40-41	5 280	5 158	7 587	33 168	27 520	29 455	20 407
42-43	3 993	4 661	7 609	19 119	18 488	24 945	18 917
44-45	3 021	3 165	8 041	11 684	13 561	14 503	16 238
46-47	2 014	2 229	6 144	7 545	11 598	13 058	11 995
48-49	1 433	1 660	4 363	4 084	7 813	11 837	9 128
50-51	1 089	1 466	2 511	2 343	4 375	10 118	7 073
52-53	702	985	1 200	1 445	1 925	6 753	5 149
54-55	437	672	647	865	821	3 140	3 979
56-57	236	439	525	613	475	1 620	2 339
58-59	124	262	382	503	462	573	962
60-61	89	242	276	515	346	374	792
62-63	67	120	249	263	218	299	321
64-65	37	110	77	120	154	199	321
66-67	37	116	17	11	103	50	207
68-69	25	113	66	33	90	100	75
70-71	10	87	77		38	50	75
72-73	15	84	28		38	50	38
74-75	2	29	11		38	2	38
76-77	1	32	44		26	25	19
78-79	5	6	11		13	-	-
80-81	1	3	17		-		19
82-83	2	0	-		13		-
Total number	73 763	60 420	62 745	263 340	289 945	245 564	171 196
Catch tons	23 682	23 540	37 947	101 623	112 066	99 322	88 643
g	320	390	600	390	390	400	520

Table 6: M. MERLUCCIUS: WORKSHEET FOR COHORT ANALYSIS OF LENGTH COMPOSITION

Length group (6 cm)	Catch in numbers × 103	Estimated numbers × 103	Exploitation rate E = F/Z
6-12	1823	79431	(.33)
12-18	14463	73826	.70	)
18-24	25227	53309	.85	)
24-30	8134	23722	.79	)
30-36	3889	13482	.76	)
36-42	2959	8357	.78	)
42-48	1871	4553	.81	)
48-54	653	2238	.70	)
54-60	322	1310	.64	)
60-66	228	806	.67	)
66-72	181	468	.74	)
72-78	96	223	.73	)
78-84	16	92	(.47)
84 +	46	58	(.80)

Table 7: MERLUCCIUS spp.: WORKSHEET FOR COHORT ANALYSIS OF LENGTH COMPOSITION

Length group	Average numbers (1973, 1974, 1975)	Average numbers 6 cm classes	Numbers at sea	Rate of exploitation E = F/Z
18-19	244		539 756.8
20-21	2 459
22-23	6 368	9 071		(.10)
24-25	10 657
26-27	15 037
28-29	16 916	42 610	445 230.6
30-31	13 794			.37
32-33	15 768
34-35	23 201	52 763	329 222.8
36-37	31 802			.48
38-39	34 244
40-41	30 048	96 094	219 183.8
42-43	20 851			.73
44-45	13 249
46-47	10 734	44 834	87 765.3
48-49	7 911			.75
50-51	5 612
52-53	3 374	16 897	27 965.6
54-55	1 609			.77
56-57	903
58-59	513	3 025	6 063.0
60-61	412			.69
62-63	260
64-65	158	830	1 689.6
66-67	55			.65
68-69	63
70-71	29	147	417.3
72-73	29			.50
74-75	13
76-77	17	59	124.5
78-79	4			.54
80-81	0	8	16
82-83	4

Table 8: M. MERLUCCIUS: WORKSHEET FOR YIELD PER RECRUIT CALCULATIONS-VARIATIONS IN EFFORT

		Y’/R (from tables)				Y’/R (as % of E = 0.75)
E	F	a	b	c	d	a	b	c	d
.10	.02	10.7	8.6	5.9	6.0	95	97	98	64
.15	.04	14.8	12.0	8.1	8.4	131	135	135	89
.20	.05	18.2	14.6	9.9	10.4	161	164	165	111
.25	.07	20.8	16.6	11.2	11.9	184	187	187	127
.30	.09	22.7	18.1	12.1	13.1	201	203	202	139
.35	.11	23.7	18.9	12.5	13.8	210	212	208	147
.40	.13	24.1	19.1	12.7	14.3	213	215	212	152
.45	.16	23.9	18.7	12.5	14.3	212	210	208	152
.50	.20	22.8	17.9	11.9	14.1	202	201	198	150
.55	.24	21.3	16.7	11.0	13.5	188	188	183	144
.60	.30	19.3	15.1	9.9	12.8	171	170	165	136
.65	.37	17.0	13.0	8.7	11.8	150	146	145	126
.70	.47	14.2	11.1	7.4	10.6	13	125	123	113
.75	.60	11.3	8.9	6.0	9.4	100	100	100	100
.80	.80	8.5	6.8	4.6	8.1	75	76	77	86
.85	1.13	5.9	4.8	3.4	6.8	52	54	57	72
.90	1.80	3.8	3.2	2.4	5.5	34	36	40	50

Parameters values used:

M = .20

1c = 14 cm

Present value of E = 0.70

(a) M/K = 1.75 c = 0.11
(b) M/K = 2.00 c = 0.11
(c) M/K = 2.50 c = 0.11
(d) M/K = 2.50 c = 0.18

c	1c	Mesh size	tc	Y’/R (from tables)				Y’/R in %
				a	b	c	d	a	b	c	d
10	13	36	.54	8.4	10.7	5.6	11.6	79	81	77	91
12	16	44	.90	9.4	11.9	6.4	12.2	89	90	88	95
141/	18	50	1.10	10.6	13.2	7.3	12.8	100	100	100	100
16	21	58	1.40	11.8	14.6	8.3	13.4	111	111	114	105
18	23	64	1.70	13.2	16.1	9.4	14.1	125	122	129	110
20	26	72	2.00	14.5	17.7	10.4	14.7	137	134	142	115
30	39	108	3.70	22.0	26.4	16.6	17.6	208	200	227	138
40	52	144	5.60	28.9	34.9	20.4	19.0	273	264	279	148
50	65	181	7.80	33.0	40.9	21.9	18.3	311	310	300	143
58	75	208	10.00	33.7	42.3	20.5	16.1	317	320	281	126
60	78	217	10.70	32.5	42.0	19.7	15.3	307	318	270	120
70	91	253	14.30	26.7	36.8	14.3	10.5	252	279	196	82
80	104	289	19.30	16.7	25.2	7.4	5.2	158	191	101	41
90	117	325	28.00	5.7	10.1	1.8	1.2	54	77	25	9

^1/Present level

M = .20

F = .60

Selection factor =3.6

Present value of c = 14

(a) E = 0.75 M/K = 2.00
(b) E = 0.75 M/K = 1.75
(c) E = 0.75 M/K = 2.50
(d) E = 0.50 M/K = 2.50

E	F	Y’/R (from tables)			Y’/R (as % of E = 0.70)
		a	b	c	a	b	c
.10	.03	10.3	8.2	5.3	27	26	25
.15	.05	15.0	11.9	7.7	39	38	36
.20	.07	19.2	15.2	9.9	50	49	46
.25	.09	23.0	18.3	11.9	60	59	56
.30	.12	26.4	21.0	13.7	69	68	64
.35	1.50	29.4	23.4	15.4	77	75	72
.40	.19	32.0	25.5	16.8	84	82	79
.45	.23	34.1	27.2	18.0	89	87	85
.50	.28	35.8	28.7	19.0	94	92	89
.55	.34	37.0	29.8	19.9	97	96	93
.60	.42	37.9	30.5	20.5	99	98	96
.65	.52	38.2	31.0	21.0	100	100	99
.701/	.65	38.2	31.1	21.3	100	100	100
.75	.84	37.7	30.9	21.4	99	99	100
.80	1.12	36.9	30.5	21.4	97	98	100
.85	1.59	35.8	29.8	21.2	94	96	100
.90	2.52	34.3	28.9	20.9	90	93	98

^1/Present level

M = .28

(a) M/K = 1.75 c = 0.44
(b) M/K = 2.00 c = 0.44
(c) M/K = 2.50 c = 0.44

c	1c	Mesh size	tc	Y’/R (from tables)				Y’/R as %
				a	b	c	d	a	b	c	d
10	9	25	.80	13.6	10.6	7.0	9.6	36	34	33	47
20	18	50	1.60	20.3	16.5	11.6	13.6	53	53	54	66
30	27	75	2.50	28.3	23.4	16.7	17.6	74	75	78	86
40	36	100	3.60	35.8	29.4	20.5	20.2	94	95	96	99
44	40	111	4.20	38.2	31.1	21.3	20.5	100	100	100	100
50	45	125	5.00	40.7	32.6	21.5	20.2	107	105	101	99
60	54	150	6.50	41.0	31.5	19.0	17.4	107	101	89	85
70	63	175	8.60	35.3	25.6	13.6	12.1	92	82	64	59
80	72	200	11.50	23.9	15.8	7.0	6.1	63	51	33	30
90	81	225	16.40	9.5	5.3	1.7	1.4	25	17	8	7

Parameters values used:

Present value of c ⁼ 0.44

(a) E = 0.70 M/K = 1.75
(b) E = 0.70 M/K = 2.00
(c) E = 0.70 M/K = 2.50
(d) E = 0.60 M/K = 2.50

Figure 2: DISTRIBUTION OF HAKES IN THE NORTHERN ZONE OF CECAF (From Bravo de Laguna, in press)

Figure 3: M. MERLUCCIUS - TOTAL CATCHES AND INDICES OF TOTAL FISHING EFFORT IN UNITS OF SPANISH “BAKAS”, MOROCCAN VESSELS AND BOTH CLASSES OF VESSELS COMBINED

Figure 4: M. MERLUCCIUS - INDICES OF ABUNDANCE BASED ON CATCHES PER UNIT EFFORT BY SPANISH “BAKAS” AND MOROCCAN VESSELS

Figure 5: MERLUCCIUS spp. - TOTAL CATCH IN NORTHERN ZONE OF CECAF AND INDEX OF TOTAL EFFORT

Figure 6: M. MERLUCCIUS - RELATIONSHIP BETWEEN YIELD PER RECRUIT AND FISHING MORTALITY RATE (F)

Figure 7: M. MERLUCCIUS - RELATIONSHIP BETWEEN YIELD PER RECRUIT, AGE AT FIRST CAPTURE (t_c) AND MESH SIZE

Figure 8: MERLUCCIUS spp. - RELATIONSHIP BETWEEN YIELD PER RECRUIT AND FISHING MORTALITY RATE (F)

Figure 9: MERLUCCIUS spp. - RELATIONSHIP BETWEEN YIELD PER RECRUIT AND AGE AT FIRST CAPTURE (t_c)

Figure 10: M. MERLUCCIUS - RELATIONSHIP BETWEEN CATCH PER UNIT EFFORT BY SPANISH “BAKAS” AND TOTAL EFFORT IN UNITS OF MOROCCAN TRAWLERS