# 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+ sI 0.07 0.23 0.33 0.49 0.97 1 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+ % maturesi 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 F0.1. Indicate the value of the virgin biomass that you estimated and calculate the percentage B0.1/Bvirgin..

2. Calculate the biological reference point Fmax.

3. Calculate the biological reference point Fmed

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

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-1
Asymptotic length = 39.8 cm
Growth coefficient = 0.8 year-1

Table 2 - Catch Matrix (thousand individuals)

 Length classes (cm) Year 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 Fterminal = 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 FMSY and F0.1.

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.