FISHERIES RESEARCH BOARD OF CANADA

Translation Series No. 1690

Estimation of fish mortality in the stock of cod off west Greenland

By Albrecht Schumacher

Original title:.Bestimmung der fischereilichen Sterblichkéit beim Kabeljaubestand•vor Westgronland

From: Berichte der Deutschen Wissenschaftlichen Kommission fur Meeresforschung .(ProCeedings-of the German Scientific Commission for Oceanic Research), 21(1-4): 248.-259, 1970.

T •anslated by the Translation Bureau(MPT) Foreign Languages Division

Department of the Secretary of State of Canada

Fisheries RéS'earth -Board of Canada . Biological Station

St. John's, Nfld.

1971

20 pages typescript

CANADA

TRANSLATED FROM — TRADUCTION DE INTO — EN

GerMan English

PAGE NUMBERS IN ORIGINAL NUMÉROS DES PAGES DANS

L'ORIGINAL DATE OF PUBLICATION DATE DE PUBLICATION

PUBL ISH ER — ÉDITEUR

Paul Parey . 248 - 259

VOLUME - ISSUE NO. NUMÉRO

YEAR ANNÉE PLACE OF PUBLICATION

LIEU DE PUBLICATION NÛMBER OF TYPED PAGES

NOMBRE DE PAG,ES DACTYLOGRAPHIEES

1,4 1970 20 21 Hamburg

TRANSLATION BUREAU NO. 0763 NOTRE DOSSIER NO

TRANSLATOR (INITIALS) M.P.T. TRADUCTEUR ( ) NITIALES)

DATE ROMPLETED ACHEVE LE MAR_3_1_11171

6 9 °

DEPARTMENT OF THE SECRETARY OF STATE TRANSLATION BUREAU

FOREIGN LANGUAGES DIVISION

SECRÉTARIAT D'ÉTAT BUREAU DES TRADUCTIONS

DIVISION DES LANGUES ÉTRANGÈRES

AUTHOR — AUTEUR

Albrecht Schumacher

TITLE IN ENGLISH — TITRE ANGLAIS

'.Estimation Of fishing mdrtality in the stock Of cod off West Greenland . Title in foreign • language (tran_sliter-eto icy.redel -crturae .ters)

. bestand Bestimmung der fischereilichen Sterblichkeit beim Kabeljaevor Westgrdnland

R5FV2ENCE IN FOREIGN 17 ANGUAGE (NAME OF BOOK OR PUBLICATION) IN FULL. TRANSLITERATE FOREIGN CHAftACTERS. REFERENCE EN LANGUE ETRANGERE (NOM DU LIVRE OU PUBLICATION), AU COMPLET. TRANSCRIRE EN CARACTERES PHONÉTIQUES.

• Berichte der Deutschen Wissenschaftlichen Kommission fdr Meeresforschung Vol. 21 (1970)

REFERENCE IN ENGLISH — RÉFÉRENCE EN ANGLAIS

Proceedins of the German Scientific Commisslon for Oceanic Research

REQUESTING DEPARTMENT MIN ISTÉRE.CLIENT

. BRANCH OR DIVISION DIRECTION OU DIVISION

• PERSON etEQUESTING DEMANDE PAR

Fisheries & Forestry

Fisheries Research Board

Mr. A.Y. Pinhorn .„ Biol. Station St. John's, Nfld. •

YOUR NUMBER 769.-18-14 VOTRE DOSSIER N °

20.1.71 • DATE DE LA DEMANDE

UNEDITED DRAFT 'TRANSLATION

On!y for inforrnafiop TIIADUC.TION NON REVISÉE

Inforine.;ion seuleir.znt

DATE OF REQUEST

(REv. 2165i

CANADA

DEPARTMENT OF THE SECRETARY OF STATE

TRANSLATION BUREAU

FOREIGN LANGUAGES DIVISION

6 SECRÉTARI AT D'ÉTAT •

BUREAU DES TRADUCTIONS

DIVISION DES LANGUES ÉTRANGÈRES

CLIENT'S NO, . DEPARTMENT 't " DIVISI ON/BRANCH CITY Ne DU CLIENT MINISTERE . DIVISION/DIRECTION VILLE •

.769-15 ■ 1à ---, Fisheries & Forestry Biological Station St. John's, Ni

BUREAU NO. LANGUAGE, TRANSLATOR (INITIALS) DATE N° DU BUREAU LANGUE TRADUCTEUR (INITIALES).

0763 German •.P.T. .MAR-3 11971 - _._

Estimation of the Fishing Mortality

in the rtoek of .:od off West Greenland

by Mbrecht Schumacher

Institut für Seefischerei •

Bv.ndesforschunsanstalt fur Seefischerei,'Hamburg

rhe "virtual ;populations" method of assessing fishine,. mortality .

is described and - applied to the stock of West Greenland cod. The

resultin .; mortality values, by a;e groups, for the years 1956-1964

are discussed and their relation to the fishing . intensity analyzed.

. Introduction , .

The estimations of the total mortality 'in the stock of Greenland .

::“)d available to date are of a rather general nature due to-the

method of estimation and' the available data, i.e. they are related

to low periods of time and to the tbtal stock regardless of the (24)

differenCes between the various age groups.. These estimations are .

based on distinctions between the sizes of - age groups as established

from catches by research vessels (Greenland Working Group) and by •

eperiments (ciorsted, 1968). For More comprehensive stock

analyse', especially in view of fishing regulaUtigns, that uill NE-1.41- LD DRAFT TRANSI-KnON

Qnly for information •

TRADUCTION. NON REVISÉE .

'Information seulement. •

• 2 .

possibly be introduced, a more detailed breàkdowb,Of the mortality.

values, by individual years apd age groupS, is desirable in order

•to better evaluate the'effect of fishing on the stock'in general

and on its iuvenile and adult constituents in particUlar, •

Method

The basis for the assessment of mortality rates in theAésired

classified form has So far been the number of fish of the same

year-class in the catches per. unit effort in consecutive. years.

The conditions under which this method can be applied are: the

catch capacity of the vessels has remained the sanie in the years

-compared, or'it is pôssible to determine changes in the catch

capaditY and fOrmulate conversion factors, WhiCh enable the con- .

version of catch capacities for a series of years to a 'coMparable

unit of measurement. Bueckmann (1963) has discUsSed these problems

in detail.

The deVelopment of fishing' fleets.sincè approxiMately 1960, however;

does not allow. either a direct. comparison of catch capacities or à

conversion to comparative values. The introduction of .fish. -

prOcessing vessels with partially different economic objectives,

e.2. freezer, refrierator or salter, as.well.as the - fresh fish

vessels fishing in the same regions, has 'made it impossible to .use

the catch pet. unit erfort as a criterion for the size of the stOck.

An equally i,mportant factor is the ext .ensive. size distribution

within the total fleet and an occasionally occurring redudtion in .

,s. ,vn , xv„

(1)

3

fishin activity because of limited processing capacities.

:onsequently, the basic condieion, comparability of the catch

capacity and the behaviour of the fishirm vessels toward the stock,

does not exist any 1om,2er. With respect to fishing off West

. -3reenland, we can add that many different methods of fishing have

always been practiced here, side by side. This is another

circumstance which Takes an assessment of the fishing intensity,

i.e. catch per unit effort, very difficult or renders it impossible.

Thel‘iirtual populations" method - developed by Fry (1949 and 1957),

modified by Gulland ( 1 1 65) and Jones (1961, 1967) - requires,

as startin values, only the total number of fish landed per year

and their ane'..1,roups. As there is no comprehensive presentation

of the latest modification of the method available, a detailed

description is given here.

Method I (250)

A prerequisite for the application of the "virtual populations"

(up) method is that the complete year-class has been subject to

fishin?„ i.e. for ',lest Greenland cod at least tfie age group of

12 year olds should be present in the year considered.

The first estimation of the survival rate in the year n is given

by the ratio of the 71-' of one year-class at the beginning and at

the end of a j_ven year (at the point n + 1).

(2 ) N„ . 1

C„

4

Qince 1- E nd consequently also V x ntl xn - Yn A n xEn+1 • xNn+1 -z

as well as N - N • e xntl x n and, at a constant mortality for consecutive years, we obtain

E • ,N„ • e 7 \S„ E \Nn

and therefore xSn = e -z or Z • —logeS.

::, ethod 2

calclation is more accurate than the previous

estimation of the total mortality if the catch of one year-class

is expresseci as a function of natural mortality and the mortality

due to fishin7 in one year, and of the population

of the year-class at the end of the year. This is done in a

manner similar to that presented by Jones (1964). If it can be

assumed that the natural mortality is constant during the life

span of the year-class considered and a certain value for fishing

mortality of the very old fish can be assumed as startinc point,

it would be possible to determine the'differing fishing mortaliti

duricv2, the life oi each year-class. This is doge by calculating

back from year to year, from the older to the yourmer fish.

If a certain a2e -:-,roup is t years old in the year n, we assume

that

r„

r,, (3)

it follows that N e –n"

(1—e '

F.M)

(4)

Vn+1 n+1 N - E and C v n+1 n n Therefore, ve obtain

(251)

(5) 1

r " Ent, (

V n-41

5

where r represents the population at the end of the year, expressed

as proportion of' the annual catch. Since

, N„e (E" _e I ■ 1

where F stands for t - n . Che factor r n consequently is a function

of t Fn and ". If the natural mortality is given, t Fn can be

determined with the aid of this function by the equation

r,,

T-t- -N71

if r n is known (see T..Sorktable Table 2).

To establish r n' it is considered that in efluation (2)

and since7n+1 =nn (see eetiation (1) ), it follows that

I S„ i -s. I

i.e. r n is a functrion of the survival rate in the year n and the

ev.ploitation rate n , l , to be applied to fish of the year-class x,

which are alive at the end of the year n (at the point n+1).

calculate 1 for consecutive years, it is necessary to calculate

the value for En' which is used when evaluating the next year, n-1,

(6)

6

instead of the initially assumed starting value for .En+1 (estimat- .

ed).

Startirr,), from the equationt(2) and (4), we obtain

e -- ( 1--"4 )

C„ ' -(F+m))

and since Cn En

Nn

—E Nnsl

(F M) and Nn÷1.

N e- n

and therefore also c -(fri- M) N e--(F 4- m)

I' — I__________ N u (En — E„ -0_...e—(F+m ) )

M

i.e.

r • m

• M ")) Eh • "'

Thus we obtain E as the sum of those portions that live at the of the yearn

beginnin;/and are landed during the year:

,E n (1—e— (tFat+M))

, NI

as well as the sum of those portions of the same year-class that

are landed later: E„ \".

Both values can be read from the Worktable (Table 2) when r n is

known. Tt is thus possible to determine En and successively

• \i') E„ — f \u, also

n-1' -n-2 etc

therefore N1 1 E n ., (1—e—zn 4-1) .

(252)

Method 3

If a vear-class has not completely been subject to fishing, the

values for the "virtual populations" (V a , Vnil etc.) cannot be

known. In this case it is possible to use the ratio of the catch

of one year-class in two consecutive years to determine r n , e.g.

•

n

and .;n+1'

The starting point of the derivations was equation (2).

ince .0 1 — e Nn

equation (2) is represented as

Cn r " E„. i (1—e— z. + 1) C„

and consideriwz equation (4), as

C fi 1 e 7 -. i) C„ E r, ( 1—e --- zri)

Therefore, at a -;iven value for M and .an estimated starting

value for En+1 (1-e-n+1 ), a value can be calculated for F as

-Zn well as for E n (1-e ) ' En-1 (1-e )etc., as -substitute for

the estimated value in the continuous calculation. It can also

be read from the Yorktable (Table 2). Examples of the calculations

for the three methods described are given in Table 1.

8 Comparison of the Methods

A comparison of the• methods is presented in Figure I,- .considering

as examples the year-classeS 1951-1954, which have been fully

subjected to fishing. The values obtained with method 2 are ùsed

as basis for the comparison. ',-;ompared to the values of method 1,

the latter shows an underestimatton of the fishing mortality,

especially within the range of the lower values up to approximately

7. •

rhe values obtained wtth method 3 show -..with certain exceptions -

fairly good areement with the comparative values of method 2.

The exceptions are due to the neceSsity of calculating .with es -

-Zn+1, tirnsted startin values for En+1' or E ), which . .n+1

tnfluences th e result of the first-estimation for the.oldest age

croup. This influence, * however, becomes negligible after the

second oldest, or at the latest after the thirdoldest age group.

This is also evident in the second *compariSon (see Figure 2) -

where ap- ain the ae :: .roups 1951-54 are used - with values obtained

with method 3, bep,inning with differing starting values for •

-Zn+1 ), wbtch correspond to'.an F value decreased by 25%. . "n+1 (le

Apart from the oldest a?e groups (marked by e circle in. the

Tioures), which should be neglected in the application of the

values, there exists good agreeffient. .Only in the . higher age

uroups is an insinificant.deviation observed due to the influence

of the lower starting value. This deviation, however, is not

greater than 2.5.

';alculation of F for West Greenland :o0.

For the calculation of the fishing mortality with the described

9

methods, as •mentioned earlier, the number of fish landed per year.

and acre group must be known. 1 -0 obtain this basic data., the

.national cod catch was diVided hy . catch area (sùbdivision).and..

time of, catch (usually months) on the basis of the respective age -

structure (ICNAF Sampling Yearbook, also Statistical Bulletin).

Also the various operating methods were considered separately, •

Based on the age composition obtained by weighing, but expressed

in number of fish, the total trawl. catch of cod and the total. catch

by line fishin during one year•was distributed in the individual

ace groups.- Also, the catch of the few.countries that do not

publish ae distributions, was considered (see:Table.3).

Another condition . for the application of these methods . Was a

reliable estimation of the natural . mortality. An assessment of ,

the natural,mortality was 9,iven by Horsted (1968) as a - result of

his tagginp: experiments during the years 1935-1939, From the

catcr durini-1 the war years, a total mortality of .28 is calculated.

Considerin the relatively insignificant fishing activity of the -

Greenlander durin .!, these years, at anT of .08 7.7, a •

natural mortality rate of .20 Should he close to the actual value.

(2.57)

As starting values for 'the calculation of the fishing mortality

in year-classes that have been fully subjected to fishing., En+1

.80 was chosen considering earner estimations (Horsted, 1968), which

correspond to an F value of .80 andEn+1(1-e) . .506 . . If the =

calculation is'made for . year-classes that have.not been fully

10

subjected to fishin, the starting value should be changed according

to the younger startiru age grOups. Hère, the mean fishing

mortality is calculated for individual age groups of completed

fishin , years (1950 - 1954) and used as starting value for.the

youn2,- er a ,.;e ç, roups (see Table 4).

Discussion of Results

The calculated mortality values obtained with method 3, for the

years 1196 to 1964, are summarized in Table 4. In order .of

manitUde they agree With mortality values estimated earlier

on the basis of the age compositions of catches by research •

vessels, Ho'wever, an even greater agreement - exists with the

values obtained bv tagging experiments (horsted, 1969) for the -

years 1962-1964.

The difficulties in estimating - fishing intensity. have been •

pointed out earlier in this paPer. The best estimation available

originates from Horsted (1965). Table 5 . and Figure 3 show that a

sip,nificant relationship exists between the fishing intensity and

the mean fishing mortality.

(258)

An evaluation of Table 4 also shows that the fishing mortality

has .!,leatly increased .since 1960., A comparison of the mean values

for the Years 1956-61 and 1962-64.réveals the remarkable. fact that

the fishing mortality has at least doubled in all age groups. To

.display the significance of this fact, Table 6 is presented, which

11

shows the . destinv of two equally lare year-classes.- These have

grown up in.periods characteristic for the mean fishing mortality

in the years 1956-61 on.the one hand and 1962-64 oh the other,

- Since there ts no reason to .assume that the fishing mortality

has decreased in the'years after 1964, the described example

should be representative of the condition of the stock of cod off

West :Jreenland, ''.)hen comparing• the number of fish in the individual'

froups in fable 6, the following fact is of great importance,

both in viw.of maintaintng a spawn stock . and of utilizing the

growth potential:

. At the end of, the seventh year, when a year-class is just subject '

to fishin, , this a2,e ?,roup, with ita actual mortality, already

consists:Of les than 50of an originally equally large age groupi

that was subject to the fishing mortality of thè.previous period.

Summary

As a Consequence of the changes in the structure of fishing

fleets in the course of the last several years, the catch Per

unit effort cannot be used as the basis for tha calculation of

mortality because the basic prerequisites, a comparable catch a comparable

capacity, andjapprOach of the fishing fleets to the stock, no.

lon2or !owever, us in the "virtual populations" method

and its modern modifications, • it is possible to çalculate . the

ft.shinc mortality for individual ae groups' and year-classes

when the natural mortality is given. As a startin2 valUe, the

number of fish.landed per year, by age group, is required.

(259)

12.

The results of the calculations for West Greenland cod show that

the fishing mortality in all age groups during .the period

1q62-19 .64 is twice as high as dùring the.previous period .1956-1961. -

In the fully recruited age groups, the fishing mortality reached a

• value of

e,

13

The following symbols are used: (249)

xCn = Catch in number of,fish of the year-class x in the year n.

V = Total number of fish of the year-class x, which are x n landed in the year n or later

(V=C+C +C + C xn xn xn+1 xn+2 'x n(max.) ) '

XN = Total number of fish of the year-class which live at

the beginning of the year n.

xEn = Exploitation ratio, the portion of fish of the year-class x,

which lives at the beginning of the year n and is landed

-later.

(E 7 F F+M

F = t n Coefficient of the mortality due to fishing, of t-year-

old fish in the year n.

M = Coefficient of natural mortality (assumed as constant).

= Coefficient of the total mortality of t-year- old fish

in the year n (2 = F + M).

S = Survival rate of fish of the year-class x.in the year n. x n

14 '

(252)

Figure 1

Methods 1 and 3 Iffletodelu3 • (6 .0 40

(E=.80)

09

011

0

36

0.5

04

03

02

01

/ 11

e•

/ e

° 2

/.

• r4,0,•ch Method, 2u 3

• 94,11.40, Methed• 7 ut O Ge•c4•141. Antanqswer64 9enutit

,e41 02 03 04 0. 06 07 01 09 10 11 12 41•14•4e7 (E • 010)

F Method 2 (E=.80)

• Comparison of methods 2 and 3

x Comparison of methods 1 and 2

o Estimated starting values used

(0)

12

1.1

10

01

07

0.6

05

04

03

02

01

0i , 63 61 é

071 1/42 4

061

051

04

031

024

0'4

15

Figure 2 (257)

el 0.2 03 04 05 06 0 7 06 09 10 ■ : 12 (111

Method 3. Comparison of F at differing starting values. ()F 0,80 r 3,80 . 0,5:6; (1 ) 1. - 0, 7 5 •• F 0,5 9 • hl ---c 0,41:

if m 2.22

Figure 3 (258)

59 Si

57 1 60 Si 4

Fishin. intensity . ...... 2 4 i 8 10 4 4 4 4 U

West Greenland cod. Relationship between the mean fishing mortality in the years 1956 - 1963 and the fishing intensity (Y = .0124 + .0243 X; S = 005) Sb . .

• • 16

Year - class

• rgang .95 i

Alter

Year Age

1956 5 1957 6 1958 7 1959 8 1960 9 1961 10 1962 11 1963 12 1964 13

13'

.1•); VI I

1F,, e-Z En 12- 1

Table 1

West Greenland Cod

Calculation of fishing mortality (estimated M = .20)

(253)

Method 3 Methed Methodi 1 _ A I A E - G • H B - 1) C II I I ■ I K I. - - I . K

Ntet bode 2

L - loge S F Z-M

U1'.)

Vn Cn

n(

Sl

(1°°( max) Vn , 1 I -Sn v C - Stud)

4 996 34 270 0,854 0,146 5,849 0,583 10,032 0,09 1,873 0,187 10,016 0,09 0,16 - 0,04

9 362 29 274 0.680 0,320 2,125 0,609 3,489 0,23 0,651 0,187 0,396 0,801 0,229 3,498 0,23 0,39 0,19 7 501 19 912 0,623 0,377 1,653 0,620 2,666 0,29 0,613 0,229 0,380 0,517 0,194 2,664 0,29 0,47 0,27 3 881 12 411 0,687 0,313 2,195 0,661 3,320 0,24 0,644 0,194 0,426 0,707 0,215 3,283 0,24 0,38 0,18 2 743 8 ''.3 0,678 0,322 2,106 0, 7 14 2,950 0,27 0,625 0,215 0,446 0,850 0,295 2,881 0,27 0,39 0,19 2 333 s '87 0,597 0,403 1,481 0,761 1,946 0,3S 0.560 0,288 0.426 0,732 0,392 1,867 0,39 0,51 0,31 1 709 3 454 0,505 0,49i 1 ,32C 0,798 1,278 0,53 0,482 0,376 C.385 0,676 0,572 1,182 0,56 0,68 0,48 1 156 1 745 0,338 0,662 0,511 0,77 5 0,659 0,86 0,346 0,530 0,268 0,277 0,506 0,547 0,97 1,08 0,88

321 589 0,455 0,545 0,834 0,8C0 1,042 0,62 0,440 0,423 0,352 0,79 C,59

268 268 • From From

From Table 2 Aids Tabelle 7 Tated22 Tatàg22

c. IL; wg

Table 2

Worktable (M = .20)

(254-255

. c-z ) c-z E(1-e-z) e-z E(1-e-z)

17

Iu

3,01 0,21 0,811 0,009 90,1

0,02 , 0,22 0,833 0,018 44,6

0,03 0,23 0,795 0,027 29,4

0,04 0,24 0,787 0,036 21.9

3,05 0,25 0,779 0,044 17,7

0,46 0,66 0,517 0,337 1,534 0,91 1,11 0,330 0,550 0,600 0,47 0,67 0,512 0,343 1,493 0,92 1,12 0,326 0,553 0,590 0,48 0,68 0,507 0,348 1,457 0,93 1,13 0,323 0,557 0,580 0,49 0,69 0,502 0,354 1,418 0,94 1,14 0,320 0,561 0,570 0,50 0,70 0,497 0,360 1,381 0,95 1,15 0,317 0,565 0,561

0,06 0,26 0,771 ' - 53 I 1 , 0.51 0, 7 1 0,492 0,365 1.348 3,96 1.16 C.313 0,568 0,551

0,27 - '63 .hi 12 - 0,52 0.72 0,487 0,371 1,313 0.97 1,17 0,310 0,572 0,542 0.214 0,28 0,7;0, 0,073 1,-... 0,53 0,73 0,482 0,376 1,282 0,98 1,18 0,30 7 0,575 0,534 " :9 • 0,29 0 ..4 '■ 3,078 t).59 0,54 0,74 0,477 0,382 1.249 0,99 1,19 0,304 0,579 0,525

: 0,33 2.086 11.61. 0,55 0,75 3,472 0,387 1,220 1,00 1,20 0,301 0,582 0,517

:1 0,31 2," 0.295 - ,72 0,56 0.76 0,468 0,392 1,194 1,01 1,21 0,298 0,586 0.509

12 0,32 0,726 0.103 -,05 0,57 0,77 0,463 0,398 1,163 1.02 1,22 0,295 0,589 0,501

3 0,33 3,719 0 !I! 6,48 0,58 0,78 0.458 0,403 1,136 1.03 1,23 0,292 0,593 0,492

2.14 0,34 0,712 0,119 5,98 0,59 0,79 0,454 0,408 1,113 1,34 1,24 0,289 0,596 0,485

0,15 035 3,705 0,127 5,55 0.60 0,80 0,449 0,413 1,087 1,05 1,25 0,287 0,599 0,479

0,16 0.36 0,698 0,134 5,21 0,61 0,81 0,445 0,418 1,065 1,06 1,26 0,284 0,603 0,471

0,17 0,37 0,69 ' 0.142 4,87 0.62 0,82 0,440 0,423 1,040 1,07 1,27 0,281 0,606 0,464

0.18 0,38 0,684 0.150 4,56 0,63 0,83 0,436 0,428 1,019 1,08 1,28 0,278 3.609 0,456

C,1 9 0,39 0,677 0,157 4,31 0,64 0,84 0,432 0,433 0,998 1,09 1,29 0,275 0.612 0,449

0,20 0,40 0,670 0,16', 4 06 0,65 0,85 0,427 0,438 0,975 1,10 1,30 0,273 I: hit, 0,443

0,21 0,41 0,664 0,172 3.86 0,66 0,86 0,423 C,443 0,955 1,11 1,31 0,270 0,619 0,-1 36 0,22 0,42 2' 6 5 - 0,180 3,6; 0,67 0,87 0,419 0,447 0,937 1,12 1,32 0.267 0,622 0,429 0,23 0,43 0,651 0,187 3,48 2,68 '.S 0,415 0,452 0,918 1,13 1,33 0,264 0,625 0,422 0,24 0,44 0,644 0,194 3,32 0,69 0,89 0,411 0,457 0,899 1,14 1,34 0,262 3.6 2 11 0,417 0,25 0.45 0.6111 0 201 "1" 3 70 0,90 0,407 0.462 0,891 1.15 1,35 0,259 0,631 0,410

_46 ,;,208 3.03 0,71 0,91 0.403 0,466 0,865 1,16 0,634 0,405 3,27 0,47 0,625 0,215 2,91 - 1 0,847 1,17 1,37 0,254 0,637 0,399 . 0,28 0,48 0,619 0,222 2,79 0,73 0,93 0,395 0,475 0,832 1,18 1.3 9 0' 2ç2. 0.640 0,394 0,29 0,49 0,613 0,229 2,68 0.74 0,'4 0,391 0,460 0,815 1,19 1,19 0,2r 0,643 0,387 0.10 ̂, Sr, 0 60" 236 7 ; 7 075 0,95 0.187 0484 0 51r10 " 1 44(. ̂

0,31 0,51 0,630 0,243 2,47 0,76 0,96 0,383 0,489 0,783 1,21 1,41 0,244 0449 0,376 0,32 0,52 ; 95 0,250 2,38 0,77 0,97 0,379 0,493 0,769 1,22 1,42 0,242 0.651 0.372 0,33 0,D3 _ 0,256 2,30 0,78 0,98 0,375 0,497 0,755 1,23 1,43 0,239 C.654 • 0,365 0,34 0,54 3,583 0.263 2,22 0,79 0,99 0,372 0,501 0,743 1,24 1,44 0,237 0,657 0,361 0,35 0,55 0,577 3,269 2,14 0,80 1,00 0,368 0,506 0,727 1,25 1,45 0,235 0,659 0,357

0,36 0,56 0,571 0,276 2,07 0,81 1,01 0,364 0,510 0,714 1,26 1,46 0,232 0,663 0,350

0,37 0,57 0,566 0,282 2,01 0,82 1,02 0,361 0,514 0,702 1,27 1,47 0,230 0,665 0,346

0,38 0,58 0,560 0,288 1,94 0,83 1,03 0,357 0,518 0,689 1,28 1,48 0,228 0,668 0,341

0,39 0,59 0,554 0,295 1,88 0,84 1,04 0,353 0,522 0,676 1,29 1,49 0,225 0,761 0,335

3,40 0,60 0,549 0,301 1.82 0,85 1,05 0,350 0,526 0,665 1,30 1,50 0,223 0,674 0,331

0,41 0,61 0,543 0,307 1,77 0,86 1,06 0,346 0,530 0,653 0,42 0,62 0,538 0,313 1,72 0,87 1,07 0,343 0,534 •0,642 0,43 0.63 0,533 0,319 1,67 C,88 1,08 0,340 0,538 0,632 0,44 0,64 0,527 0,325 1,62 0,89 1,09 0,336 0,542 0,620 0,45 0,65 0,522 3,331 1,58 C,90 1,10 0,333 0,546 0,610

Table 4 (256)

West Greenland Cod Fishing mortality

(255) Table 3

West Greenland Cod

Number of fish landed per year and age group (in 1000's)

f.1/49e ...

(.s._)__ ,,.,-.:

-

1•0e.: pee-, 1.4,5 I ghee

2 544 488 24 1 96 4 2 752 88 3 20 9 1 177 348 8 7 8 435 2 '046 869 7 612 s 655 14 718 I 294 4 1 758 19 353 1 772 2 tie d, 6 186 22 958 11 423 6 589 27 181 58 619 7 738 5 4 996 12 493 15 136 54e,4 5 168 19 756 7031? 19 301 11 407 53 331 59 987 6 1790? 9 362 6 751 27 411 4 652 8 055 29 344 48 418 18 264 8 994 . 40 726 7 6 622 17.367 7 501 6 622 20 250 6 980 7 816 22 517 30 864 9 152 5 791 8 6 400 3 967 17 177 3 881 4 492 23 126 5050 3 973 11 355 15 125 4 403 9 24 418 4 061 3 181 5 996 2 743 4 359 13 772 1 708 2 543 25 95 6 667

10 2 345 8 893 3 652 I 124 5 363 2 333 2 433 6 764 I 027 539 1 166 11 4 106 1 271 12 981 1 477 805 4 724 1709 1 124 4 138 472 276 12 1 014 I 499 1 691 4 327 1 438 528 2 599 . I 156 591 1 864 122 13 1 363 485 2 168 999 5 195 1 138 720 2 325 321 73 981 4 2 893 436 725 836 741 5 052 1 219 189 933 34 137 14' 1 194 1383 3 271 960 1 859 2 383 ' 2 897 3 718 747 265 234

•

Year-drhrse ,-: 1951

Age Years !.,„ 1 T ,,malues Tor atiteeragri (Y -

ârs) ,-- - ,,, ,.., : 46: 19 96 ( I 6 6

tanting r9ue

6! 1962 1 , 1 ,1+4 ! : 9..0, 61 19 64 195 4

‘ ' 3,21 0.32 •-. 0.01 <-. 2,01 <0,31 0,02 0,01 0,02 0,02 0,01 0,02 0,01

4 2, 3 2 2.24 3,04 0,35 0,04 0,08 0,11 0,11 0,09 0,05 0,1C 0,06 0,41 0,14 0,119 ,

0 ,...9 0.21 0,08 0,15 0,13 0,18 0,35 0,28 0,27 0,14 0,30 0,20 0,49 0,19 0,157

6 0,16 0,23 0,19 0,21 0,18 0.30 0,43 0,44 0,47 0,21 0,45 0,29 0,59 0,29 0,228

7 0,30 0,22 0,29 0.28 0,23 0,45 0.5.5 0,70 0,55 0,30 j0,60 0.40 0,67 0,41 0,306

8 0,22 0,30 0,36 2.24 0.31 0,44 0,70 C,61 0,96 0,31 0,76 0,46 0,68 0,42 0,314

9 0,29 0,21 0,42 - ' - „ _ 2,27 0,55 0,52 0,55 1,03 0,32 0,70 0,45 0,73 0,53 0,378

13 0,24 0,16 0,29 .: », ...,27 0,39 3.69 0,52 0,76 0,27 0,66 0,40 0,75 0,59 0,410

11 0,40 0,20 0,37 0I 0,30 0,40 0,56 0,79 0,70 0,31 0,68 0,43 0,80 0,80 0,506

12 0,34 0.33 0,43 0 . 20 0,27 0,33 0,40 0,97 1,04 0,32 C,80 0,48 0,80 0,80 0,506

1 "; 0.27 0,78 0,48 0,38 0.35 1.00 0,75 0,45 0,88 0,50 0,80 0,80 0,506

Years 1956 1957 1958 1959 1960 1961 1962 1963 1964

• 3-7 years .16 .18 .20 .16 .17 .29 .38 .39 .48 (not fully recruited)

›--7 years .33 .24 .47 .28 .31 .37 .66 .76 .83 (fully recruited)

All age groups .21 .20 .30 .21 .22 .32 .48 .52 .59

Fishing intensityl) 5.94 7.99 11.01 9.79 10.50 16.95 17.31.18.04

1)From Horsted (1965)

F e7z F e-z Age (Years)

1956-1961 Number of fish at the end of the year

1962-1964 Number of fish of at the end of 1956-1961

the year

Table 5 . (257)

West Greenland Cod

Mean fishing mortality in various age groups .

Table 6 (258)

Compârison of numerical development of equally large age groups in periods with differing fishing mortality

(M = .20)

2 1,000,000 - 1,000,000 100

3 .01 .811 811,000 .02 .803 803,000 99

4 .05 .779 631,769 .10 .741 595,023 94

5 .15 .712 449,819 .30 .607 361,179 80

6 .21 .664 298,680 .45 .522 188,535 63

7 .30 .607 181,298 .60 .449 84,652 47

8 .31 .500 108,779 .76 .383 32,421 30

9 .32 .595 64,723 . 70 .407 13,195 20

10 .27 .625 40,451 • .66 .423 - 5,581 14.

11 .31 .600 24,271 .68. .415 2,316 9

12 .32 .595 14,441 .80 . .368 852 6

13 .45 .522 7,538 .88 .340 290 3 __

20

•

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