8.28 EXAMINATION - WRITTEN TEST (LISBON, DEC. 1997)

TRAINING COURSE ON FISH STOCK ASSESSMENT
INSTITUTO DE INVESTIGAÇÃO DAS PESCAS E DO MAR
(LISBON, 3 NOV. -10 DEC. 1997)

QUESTION 1

Consider a certain stock with the following parameters:

Natural Mortality Coefficient:	M = 0.20 year^-1

Fishing mortality in 1996:	F₉₆ = 1.08 year^-1

Exploitation pattern:

Age	1	2	3	4	5	6	7+
s_I	0.07	0.23	0.33	0.49	0.97	1.00	1.00

Mean weight (kg) in the catch and in the stock:

Age	1	2	3	4	5	6	7+
	0.053	0.076	0.111	0.125	0.158	0.204	0.337

Maturity ogive (percent):

Age (year)	1	2	3	4	5	6	7+
% matures_i	34	90	100	100	100	100	100

The estimated recruitments and the spawning biomasses between 1986 and 1996 are presented in the following table:

Table 1

Year	N (age 1) (thousands)	Spawning biomass (t)
1986	8751	1957
1987	8305	1591
1988	7123	1956
1989	7596	2073
1990	6013	2287
1991	5054	1506
1992	9713	1400
1993	5520	1275
1994	6000	980
1995	7329	675
1996	6840	917

1. Calculate the biological reference point F_0.1. Indicate the value of the virgin biomass that you estimated and calculate the percentage B_0.1/B_virgin..

2. Calculate the biological reference point F_max.

3. Calculate the biological reference point F_med

4. Estimate the parameters of the S-R Ricker model and indicate what the value of the spawning biomass/recruit is, corresponding to F_crash.

5. Comment on the present state of the stock and its exploitation.

QUESTION 2

Consider a stock where the length compositions of the catches during 1986-1995 are known (Table 2).

The following parameters were estimated from this stock:

Natural mortality coefficient = 1.2 year^-1Asymptotic length = 39.8 cm
Growth coefficient = 0.8 year^-1

Table 2 - Catch Matrix (thousand individuals)

Length classes (cm)	Year
Length classes (cm)	1986	1987	1988	1989	1990	1991	1992	1993	1994	1995
14-	10	9	8	9	7	18	13	12	15	8
15-	20	17	15	18	13	35	26	23	29	16
16-	29	25	23	26	19	52	39	34	42	24
17-	47	41	37	43	31	84	63	56	69	39
18-	92	80	72	83	60	164	122	108	134	76
19-	224	194	175	202	146	398	297	263	325	185
20-	261	226	203	234	169	461	343	305	376	214
21-	420	363	326	376	271	736	547	488	601	342
22-	335	525	603	506	511	365	983	571	657	741
23-	345	540	618	516	520	370	995	581	666	752
24-	422	661	751	622	625	444	1189	699	799	902
25-	442	693	781	642	643	454	1212	718	818	923
26-	415	650	726	592	590	415	1102	659	747	843
27-	388	607	672	542	537	376	995	601	677	765
28-	360	564	617	493	486	339	890	543	609	688
29-	332	520	563	444	435	301	788	487	543	613
30-	304	475	508	396	386	265	689	431	478	539
31-	275	430	453	348	337	230	594	377	414	468
32-	272	246	509	494	330	314	212	428	351	353
33-	239	216	439	419	277	261	174	359	292	294
34-	206	186	369	345	226	211	139	293	235	237
35-	171	155	300	273	176	162	106	228	181	182
36-	136	123	230	202	129	117	75	167	130	131
37-	82	99	116	196	147	91	80	40	117	83
38-	49	60	66	103	75	45	38	21	58	41
39-	0	0	0	0	0	0	0	0	0	0

1. Estimate the values of the fishing mortality coefficient in each length class of the cohort of 1987 (to simplify, adopt F_terminal = 0.5 year^-1).

2. Estimate the corresponding values of the number of survivors at the beginning of each class.

3. Say what the recruitment of this cohort is.

QUESTION 3

The Fox Production model was adjusted to a certain stock and the following parameters were obtained:

K = 300 thousand tons
r = 0.50 year^-1

1. Determine the biological reference points F_MSY and F_0.1.

2. Knowing that in recent years the biomass of this stock is about 30 percent of the virgin biomass, comment on the present state of the stock and its exploitation, based on the adopted model.