This paper ~nöt t·o be cited wi thout prior reference to the author

International Council for theExploration of the Sea . --

C.M. 1919/G:45Demersal Fish Committee

L

RELATIONSHIP BETWEEU MEAN LENGTH AND YEAR CLASS STRENGTH IN UORTH SEA HADDOCK

by

R Jones

Marine LaboratoryPO Box 101Victoria RoadAberdeen ~

ScotlandUK

Abstract

This paper reports investigations of the relationship between year classstrength and the mean size attained by a year class by the end of the firsttwo years of life. The following conclusions were reached.

1. That there has been a tendency for length at two years of age to increasefrom a minimum value for the 1928 year class to a maximum for the year classesin the period 1960 to about 1966. 'TIlis suggests a trend with aperiod of about70 years» and having a minimum for the 1928 year class.

2. When this trend is taken into account» it appears that mean length of ayear class .is s~gnificantly an4 negatively correlated with the strength of thesame year class and with the strength.of the preceding year class. Multipleregression analyses yielded the fo1lowing two equations.

~ northern area

north centra1 area

....~ ,,~

where Lt is the mean length o~·a year c1ass a~ 2 years of age

Xl is the strength of the same year c1ass

X2 is the strength·of the preceding year class

X3 is a periodi C function to a110w for tr~nd.

For each area 7 each of the three partial regression coefficients is significantat at least the 9% level.

1.

5. The variations in growth rate are not large enough to compensate completelyfor the increased food requirements ',01' a good year class throughout theremainder 01' i ts life. Variations in growth rate may however play animportant part in the stage when~a year class makes the transition frompelagic to demersal fe~ding.:,...:.... ~, ," '

6. Annual variations in leng~h·at.2·years 01' age are large enough to affectcatch predictions significantly•. " " ,.

,. ,

3. It was alsonoted that ·,the ,two outstand.i~ .Nor~h Sea,.yearclasses, tho.se·01' 1962 and-1961;·' were·spawned·ät-times "when"thEnnean'lengths-of-two' years 'oldhaddock were at the highest levels ever recorded•

.... ;~'\ ... \ '-, ~I ....) 't.-'r;.; :":'~ : r; :;: <' ~~;;'~",,' ~ .:' ....~:. ; ;... r- l;' ~..... •. ... ~,- '. ..... I .. " ~, .,

4. "The 'available evidence suggests that the differences in:·growth rate .'oocUr .primarily after fish become demersal; ie during the second rather than duririg

/ the' f~rst year of1life. "':. : ::,~:~,.L '.. ::- ;."j. ~;' ';"':'::-J ~.~,",::.'; ... :' .~:';. ~-; ~l:~::"n~~l -::-.

Extrai.t.

Ce travail rapporte des recherches pour trouver le rapport entre Itimportancede la classe dtune arm'e et l~ taille moyerme atteinte par la classedtune':ann~e ~ lafin des.deux premieres.a.rmees.de,.vie. ~On est arriv~ a des con~

.w.,...•• 1. '-'~~"'~ .t •. _ •••_ ll .._".. ' ..sJ.~""'I ~;\·.:: ~ ':;~ .• L··'" ,.,/,

clusl.ons sUl.vantes:-. '. . ....' 1'-1'; ... '.... '.~;" .. .::.... ~.~: -:... -: ...~ ~ ; .. ol" '.I ..~ ; •. ~ :;, • ~l~'~-:'

:. " ~ 'I\. .... ;... r . - i;'~,~ .. ,.I'~, - ...... 1",;' .\ • ,:-~ ~.' ~ t' ...1...... •..., ,_ .. "

1. Que 1a 10ngeur a 11age de deUx'ans"a,'tendance'a au.gmenter d ' une'ValeUr" mi?iIll.umpow:;~ la.J c;as~e ,d? L '~arme'e 1928.cl ,une .v,-aleur lmaximum pour,les '. .

.c1asses .dans. la penode entre 1960 ,e~t;' 1966 ;environ:. '.'Ceci. suggere qutil ' ..' .... existe' 'une 'tendance' a.a.ns .Une perfode. dta. peu' 'pres 10 ariS,','avecun minimum' .

pour 1a CÜl.l3se'·de 1928'. ..', ,.' :.: ....'.:...., • ,;.'(." •• (..' ·.·.·,~c:·;_ .:','- u •• ~. .• .. ',0\.'.' "L.'; ," .~: _:~.tr.~ .:' :!,~ ..~- .~.t~ .~ .01" •• ' ••~~,.;

•

~ ,.2•. ) Compte tenude cette .tendance, .il parait qu'il existeune correlation•• ~. ,_ "I~ ':-'_'. :,":. ~ " .'; .. ",' '"",.' .···;·1 ",r ~"""\" "

~. significative. et,negative entre la,longeur.moyenne ·de.~a'c1asse·d'unearmee" et ·1 'importaricä, da ~ cette~meme"classe jet 'celle' de ·lci::.classe' de;1 taMee ';:"',

• 1 _ ",'. / ~ ~ . _. <". J I." "'''''' '•• '. ~ j \ ,'_. '''''. ,I";' ••••• '," .0:- I • '" .'

precedente. Des analysede, regression multiples 'ont:fourni les deux equations. t '" ),. ~ "' ..... I' .. " \ ••• , ",' tl ,: 1 • .' '" ~ ~ ., t j •• {""" ~ .' ") ~J' .' I '." P, .' ...sUJ.van os:- ..-,._.,' ' .. ,-_.. .. '.. .

La.

La

r~gion du nord, ~,., . ,~, \ ~ • :. ~. '.. :) •• f'" ", ," .;.- .,.... -

Lt

= 21.51 - 0~000150'X~' ':;O~000989'X; -t"1;406'X3(' ... /

region du centre nord:-

•

, ' - ., ..... Aou Lt est 1a longeurmoyenne:de~la'classed'une:annee a.ltac~ de,deux·ans.

Xl est L'importance de~la:classe de:la·.Iri~me::arm~e~'.·~iX~ est L1importance de Ia classe precedenteX3' est une fonction'p6riodique:en 1 tenant. compte .deda tendanc~.

Pour chaque r~gion, tous;les~trois~cöefficients~de~r~gression~partie11esont significatives au niveau d'au moins 95%.

,.·!"2! ..... ;-::.: "'J' ::.1~::1:':~}Jl·'::'~>(~"... .,,·'·-~':I~Vi··~ .. ·~;. [,:,1..~'1 '::r '~).;." '. :..:;:i~· '". :·i.J~ .. ·, ....~<.·L ... ':.':,.,

./ .3. On a constate aUS91 que les de~~ classes exceptionne11es de la Mer duNord, celles de 1962 et de 1961 ont pondu au moment ou la Iongeurmoyenne des haddocks de deux ans etai t au niveau le plus eleve qu'ona jamais enregistre.

4. L':vidence ~ notre disposition sugg~re que les diff~rences entre lestaux de croissance se produisent surtout apres les poissons deviennentdemersals; a savoir pendant ia deuxi~me plut~t que Ia premHre anneede vie.

5. Les variations dans les taux de croissance ne sont pas assex importantes,pour compenser completement les besions de nourriture plus grands d'unebonne classe pour le reste de sa vie. Des variations dans les tauxde croissance peuvent pourtant jouer un role important pendant la phasede transition d'une classe de I'alimentation p~lagique a l'alimentationd6mersale.

"-6. Des variations annuelles de longeur a l'age de deux ans sont asseximportantes pour influencer d'une facon significative des predictionssur les ~ches.

Introduction

Investigations of North Sea-haddock show that the mean size attained duringthe first 2 years of life can be related ~o a function of year class strength.

Sources of Da.ta

Also shown are the year class strengths for the year classes 1923 to 1931and 1945 to 1912. These are based on catches per 10 hours fishing of one­year old haddock by Scottish research vessels, standardised as far aspossible to.allow for changes in sampling vessel during the period.

Mean lengths of 2 year old haddock

Fig 1 shows» for each year class, the mean lengths attained at 2 yearsbased on samples taken from both the northern and north central areas.northern area w mean 1engths at 2 years of age varied between 21 and 34In the north central area the range was about 22 to 33 cm.

of age,In the

cm.

_, f

Elimination of Trend

Both sets of data in Figure 1 show, that there has been a tendency for meanlen~~ ~o increase. For the two areas, it appears that the meanlength atage 2 was ~ "minimum for the 1928 year class anc1 at a relatively high levelfor the 1960-1966 year'classes.

'Ib allow for this in sub~equent regression analyses p a periodic fUnction wasfitted to th~ data. A cosibe fUnction with aperiod of 70 years was foundto be appropriate. Values were chosen so that the minimum value wasassociated with the '1928 year'class. This was defined by the fUnction

-cos (2,n,(YC~1928)/10»

where YC = the year class reference year

This f'unetion has aminimum' for year class 1928, a:.d a maximum for yearclass 1963.

Relationships between mean length and year class strength

Preliminary analyses were done to investigate the correlation between meanlength and year class strength. These included correlations of the meanlength of a year class with the strength of the same year class andcorrelations of the mean length of a year class with the strength of thepreceding year class. The results as shown in Table 2. Only in one instance(correlation of mean length on strength of preceding year class in northernar~a), was the ~orrelation significant at the 9~ level.

Further analyses, in which trend was eliminated using the periodic f'unctionreferred to above, gave very different and quite significant results.For exarnple 7 Table :3 shows the resuit of using two X variates " one (the X2variate) being the per10dic fUnctioh to allow for trend. For thefPurregressions shown, the yalues of student's t' for assessing the significanceof the periodic f'unction (ie t2) are all significant at the 9~ level and(in the case of thenorth,central area) are significant at the 99% level..... \ . .

•

The values oftl are the values of,student's t for assessing the significance4ltof the'variate Xl. ,~~is relates mean length ta year class .strengt~ afterallowing for trend using the periodic f'unction:. The results show thatallowing for trend ~eads to relationships between mean length and yearclass ,~trengths that. are significa~t at the 95% level.

By using the periodic fUnction,residual'mean lengths can be determined. Asan example, Figure 2 shows the relationship between these residuals and thestreng1h of the preceding year, class using data for the ,no~thern area. Thedata a~e clearlynegatively correlated.

The most significant results were obtained using multi regression analysesin which the mean lengths were related to thre~ X variates. Thsse wererespectively:

Xl the strepgth' of tl).e year class "same

X2the strength of tlie preceding year class

;,

X3 the periodic fUnction to allow for trend (see above)

4.

'l"he mul tiple regression QqUatiohs are':

northern area

north central area

Lt = 27.29 - 0.000914 Xl

•

Values of student~ t for assessing the significance of the 3 partialregression coefficients are shown in Table 4. All but one are signifioantat the 99% level. '

Relationship between predicted and observed values

Figure 3 shows the relationships between the observed lengths and the lengthspredicted using the multiple regression equation for the north central area.The extent to which the points fall on the 45° line provides an indicationof the extent to which the multiple regression equation fits the observations.

For the northern area similar results were obtained although» since theoverall Significance was not so great as in the oase of the north centra1area, the degree of goodness of fit is not so striking.

Exceptional year classes

'For both areas the mean lengths of the 1959,1960; 1965 year c1asses wereexceptionally large in relation to other and to predicted values. Thisis clearly shown in Figures 1-3. These year classes would have been two yearsof age in the years 1961, 1962 and 1967. One implication is that for the2 years preceding 1961, 1962 and 1967» conditions for the growth of juvenilehaddock were better than they have ever been» either before or since. Itmay be coincidental, but it is interesting to note that the two outstandingyear c1asses recorded this century werethose spawned in 1962 and 1967.A possible implication is that these tW9 year classes w~re produced at timeswhen the conditions far the' growth.of juvenile haddock, were exceptionally good.

Mean 1ength at the beginning of the dernersai stage

To investigate the stage at which differences in growth rate b~corne evidentit is appropriate to examinemeari lengths at the beginning of the demersalstage.

Table 5 shows the mean lengths of haddock sampled with a bottorn trawl fromJuly/September of the first year of life to October/necember of the secondyear. Values are given for two year classes that were small for their ageat 2 years of age (1963 and 1968 year classes), and for three year classesthai were large for their age at 2 years of age (1959» 1960 and 1965 yearclasses). "

..... , .. ~ , ~- ­." • I

I ~ .•~t ' ~ •

.":'

.. The results suggest that for all fi:v:ef"ye~r~ cla.ss.e~'l*~ome.·~n..di"'!?-1Ö:.~1.S,l:~~amedemersal in July/September when they were about 12cm in length. Differencesin length at age on1y became rea1ly apparent from about January/March ..onwardshowever. The evidence suggel3~therefore, that the differenöes observed' inthe gro\rth rate o~cur!Od pr~Ina:ri!-y.:\a"t:~.er_the: fi~~~b~pame ß.e~~!~a~"~eie duringthe second rather 'than the first year of life).

LMp1ications for population regulation

Density dependent growth has" beEH1':reported in :the":";yolÜl.g s'tages'of otherspecies eg in Herring (lIes, 1961; Lett and Kohler j 1916). Pacific sardine(lIes, 1913) and cockles (Hancock, 1913) •

.r ..~. ~ i .....; :- ..1 :," ~'._ ...... ~ ~1..:~'·..!·: ~ : .... ·... i;,~: ...~,~.~~>.~.:'j ":0'r ! '1.~·~~~}f·~; ..::~ ;0 -:;:";"'1"":

.:'~'he:ya~iati?~~ .?:~ B"l:?wth.. ~ep.C?r~ed)le::~ '~~.:~~e~~~i~e~YJ .l_a:z:~e,ari~,,~r:te:r,:·~..,allmnng for trend, the corre1ations with year class strength are, statisticallysignificant. One interpretation io that individuals cor:ipete 'l'1i th' meinbers ofthe same year class and a1so,with.members of~heimmediatelypreceding year

• ' • ... ~ > ..,.'. _. ....'~ .. "_ .., I, .... I , ..... .~ .. _... ... '.. ( . I I' • ,-l ' ',:, '

class. Compehtion uith-members·of'an*"immediately·preceding·year·class-t1ay, • .! .•• ,be, direct •. Alternatively i t may .be ,indirect., Forexamp1e t ,grazing.by ... e'"~' :"a;; 1.ci~g~'Y,e~~:·.~läs~·!.~ight ;~'~~~;~?JI~~4ii~~: .th·(~.~~~ ~f.oP. ~~;.~öod.:e.vap.~ble

.,for .the. iIIlI:lediat.ely, fo11m'ling year .c1ass .when i~ first..becomes .demersal.;~ *., ~~ " ' ..- .1,,' J •. '. (",,' ••• ' ' •• ' _ f -1 '.,_ ·.l_

.. "J/."~'.' ...,~~ ~~ :- f~ :~~ ~·1 ':~." .."" ., '.,i·~·:.. ·!.,,·.;.~·~:',~!·~,r;r- "_~';J :I·jt;:~·: (t,r r·~, .._:', ; '1'"

}lhatever the process~ .it does not appear that the Changes observed'in growthr~t~. c~u1d, ?;r.I~.~~msel~e~,,;"1?,e.s~~~~~~en~.::.t.o,.c:~rn~e~,:,~e.~e~tirely.,f~r the..,feffects of 1arge variations, in year class .strength•. The.1962:and 1967 yearöiiiss'; for lexB.mple 1,took a'bout··3 'years' .to.va.tt'ain~ii:,1~ngth,o-f:~:b6ut 28"~;. .A poor year class i:1:iy 'a.tt'ciin tMä Ümith in ab-öüt "2 years·.·· :A··1.arge 'year' classmay therefore be reduced in nuLlerical abundance by,an additional yearts .•• . J \,. • , .... ' .........._'. .' .( , _~ :." I ~ ']

rnortalltYJ before lt attains marketable size. This;-howeveri"uas-not'enough,to .. prevent ..the 1962 and ,1967 yeo.r classes .froni. causing ,n. significant increase'in, ,the bi'()mass"Qf marketable hadciockduring·~tlie·:la.iit19(Qs~·.::(Towära.s .the

: .:::.': epjf öf.t~e':.1960si,~~~do·c~:.1?i~~äs,i;i~.<?~~ea:s.~d:~a.1?~u;'1:~~~eR7f~tg.{~i#o~~~ed.:V:i~lli·thepr.e.196O_~e.ve1_·)to;-t,-;·i::~.'j :,\(tO ,Y0~:"r I, ..; ':';)'~r tlt.l·~! r;'i,:i0'~ ~::t .. ~ '."J "';

.. ~.~ ;..:.) ....;..1. :c \; ... ~:-~.\ I ...!,~ ~~'i ~~~,c!.~lü·f~f:~ ,;l~l'.i ~:;)~ ~~(~[ ; ..C:·,·.l( ~.....;J,~;\'G:'::'!t: \: .. , ~~

,I,t app~a.rp ,l;tkely, :th~~~t:or~" ,,-t~at.:,v:a.r~o:~i~~l?:n J g:c:~'vt_~ ,r.ö7te ;..a.r.~: I?-?t",l.,:,;:ge'. enough to ,comp1etely, cornpensate for .variations in,.year. .c1ass.strength.... It

<' ' ·is•..stjii.~e~~~·sarY;· ~o,_~~pt:a~.ni .~.her~:f~~e ..,)~?}l. 'i~;;i.s· ~P..~~_~?:-'bl,e :~4r.~a:,~'a~g~.·'. p.year. class.,to find., the. necessary ,.food..tc· sustain ,it once ,it.,reaches.. adult •.' ':..s_i~'~.:~j~~reftheF. :~~e,·;i9§fn?r. ~?~. ,1961. 'y~a.~:~c.1~~~:ri"t:fo'~,~~xMip~'e;1 's~ow~~:J~. retardation in grolrrth rate once they ha.d. attained about 28 -6m lerigth iti spite ofihc

seve n -fo1d increase ,;in .totalbiomass. ",Thore ,appear"to .be .several . ,_,possibilities: ~~~~_..~~:'..~~~~":""':'~:"''''';':';~.~' ... ,,~''._....'''::'-''..'''.:. .....:..:~:.:~;,:, ~l~

~...~ ",f:,l:":', "~t':t.)·· '.. ,{ ",', -"f ~: '·I.'(~ ,'l :"r .... ,. ..• -.....').. ... ; .......,; ,'lH ~ ....i~~\·t·.... J l .... ~lj""'-,;' '-." "";' ... ('1

.<;.":.~~~ :~.' ~.:·\.Thi, ~~f2~kt',·?,f; e~l~~tä.~tori.~L1D.y)i~'fe.:P.:~e:;·}C?· ,r~du~e ..;~~ommer6~n.ilyimportant stoc s» such as that- of had.d.ock, to a level where al1.:of:.the food norma11y eaten by the adult stage is not fully uti1is'ed:~ -

:'::.>':'l 1~~~1.i~,ß?·fficu~~ir .howev~ri' ~~.,r~c~mc.i:~e},~~~,yi ~h,:c~~cul_a:~~o?~ ");' ;,,"j':~00'j:~ r",~p.or;.~~~,.})y.!~~~~)~918).~.o !~.he~ e~fec.t,.,~~t: .f~s~1,:,foRd ,r.::,~~~.e~~~t.~;;,~i'~" ': i:-~ .1?e J.~~~. aC?PPU!1~,C~ •.fOI>_..~1.t? .;L~~t~e,~J.f~t:~;v?:~ep._q~ ~o~: t7 •.surp1us,.. ~""'(' j,a.nyuhere., ,r Also, 0.1thougn.variations,-in adult ·gr.owth rate :are .small,t,_. _ J._~, "".' " I' ,~I'~".·· ';'1,.''9.'" .1_ \ _I ;." t.l' '~;"".,_. ~ ,.f

·':n~..: i.c~tlp~t:~dl\~ith .~~~l var~~~i.on,i;r:. jUV~:llrlJ~,,~owt~; rate;,' ,th,e, ,indicationsare that haddock" 28 cm :Ln length' grew more slowly -during the' 1930s ~thanduring the 1960s. A.1'1 implica.tion is that food linitation for·-ri.d.til t" haddockwas more severe during the 1930s than during the 1960s and yet the biomasso~ the adult stock appeo.rs to have been sma11er in the 19308.

6.....~

2. An alternative explanation is that the food available for.adult haddock tends to vary periodically. In that oase there"would·appear:to: be .. two·possibilities: .;(.,. ., -~~ .

~: ;: ,: \ .....

a. that wnen a good year class appears, it causes stoCk size. ·to :increase, leading to anincrease in food,.consumption at the·

: '.' '. expense of some other species·"":'';' .. ",:' i '.

... ,. ...:. .~

L

•

b. Alternatively.there may. be.a eorrelation between the faetorsthat influence year elass strength and adult food availabilitYi1e perhaps a good year .elass 'isonly produeed .at a time whe.n.there .is going to' be .sufficient .food to maintain i t during the

. subsequent adult stage."In that ease$ density dependent growth. ·.··in the intermediatejuvenile .stage eould be seen as an adaptation

for adjusting the food requirements of a year class during the·~<.transition from one feeding regime to another.

ImElicationsforeatehgredietio~>''' •• ,-'.',. .. .~ ... "

The variations' in. juvenilegrowth ratereported in this paper are largeenough to eause weighis at age·i;o"v?orY significantly from year to year.

This source of variation could.bereducedby using regression equations topredict lengthsat age when making catch predictions •

. i

" :....• "" I ...~

7.

... ,.... ; ....". " "-~', ,,-'·.~,\··:n ..:~"·. -~_, ,''':', .... :"

-.."'.. :-",. ~-; '~" '~~".' ..•' - :.",.;...• ~ .

Report ,of .the North,Sea':Roundfish WorkingGroup lCES CM/6:7 ,: '

" ":' :". \ .1, i.' ".i- .::" ::~~ ..:." :._ :~~: ~. r;The:relationship.between stock,andrecruitmentin'exploited invertebrates.Rapp. Proc. Verb. Reun. Cons. lnt. Explor•

. Mer,: 164:-11~131.~.". . . ,:c''-. -

:-.. < f~i , :...

"".' f'"

1978

"1913. ;."

Anon

Hancock, D.A~·'·

References .. '~-. .....

lIes, T~D~

,"

lIes, T.D.

~ , .- ..~ r',< ,--.

.... : .• ,._l

,": .•.' .!:.:.

: , Growth studies . on North Sea herring I.': The .second"year's growth· (l....group) of, East Anglian herring 1939-1963•.

: '", '~'J.- Cons ... lnt. :Explor. }:ier 31: 56-76.-:~~; _:...~ . ..-."'.' ... ,.~'~ .),r' '.:' ..' ',-,., Interactions of environment and parent

stock size in determining recruitment inPacific Sardineas revealed by' analysis,··of dens1ty-de'pendent ~iröup growth'. ."Rapp.Proc. Verb. ,Reun. Gons. Int.,Explor.-Meri 164 228-240 1· .

Jones, R~' .. < 1971 Someinterrelations'.between North Seafish species. ICES ~I/F:36 ".\

Jones R. 1978 Further observations on the energy flowto the major fish species in the North SeaICES mi/GEN: 6 (Symp)

Jones, R. andHislop, J.R.G.

1978 Changes in North Sea haddock.and whiting.Rapp. Proc. Verb. Reun. Cons. Int. Explor.'Mer, 112: 58-71-

Lett, P.F. andKohler, A.C.

1976 Recruitment: a problem of multispeciesinteraction and environmental perturbations,with special reference to Gulf of St LawrenceAtlantic Herring (Clupea harenws harengus)J. Fish. Res. Bd. Can• .ll: 1353-1311. •

.--------------~----- - - -

...,,',

, .Ta5r ~lu~ Strs. Gd _m l~tm ~ 2 f'el~ of 88'& fel:'. @~ä 71~.t" oia"

,

..

I" .

'fGBr 1) '1&811 ~h" roar I· . Maan LcJ1ß1iholMs lmmbG%o II area :wo area olmel3 Imtib&" 11' crsa 1m ~n&

...

.1S23 100 .- .' . '- 1950 .. 170 26 ..1 %-6.11 600 . 26.9. 25.7

1924 ·'MO· 26;4 2J~1 2 370 '26.1 2;GiO.. " 280 .25...8 2300 ' 3 400 21.9 28.5.' 6 ·500 24.2 2400 4' 450 25;9 21.6

7 110 . 26.2 23.5 S '. 500 25.7 26 ..5.8 'soo 22.7 22e>4 ,6 50 28.7 28 ..29 230 24.7 . 23.9 1 75 28 ..8 28..8

a 368 29.0 29.41930 160 25 ..6 25.5 5) 234 32.1 31.6

1 500 .25.2 24.72 170 27.4 25.3 1950 152 32.0 3106:3 250 27.6 G5.8 1 638 28.0 28.94 140 28.3' 21.4 2 3203 25.0 27.5

'5 600 25.8 24~6 3 70 22.9 26.16 140 24.8 24.4 4 115 28.1 30.2

.. 7 120 29.9 21.3 5, 147 34.1 .33.06 761 27.1 30.87 6296 24.1 23 ..08 ' 385, 24.1 2304-

1945 600 25.1 ~.7 -. 9 109 27Q1 26 ..4 ...'6 60, 24.4 25;.4

.. ' ,

l' 120 27.0 28.6, 1910 974 21.1 26 ..08 210 ~.4 26.1 1 1510 25.4 25.6 .

" 9 180 . 26 ..4 27.0 2 273 26.1 ,25 ..2.'. t.. .- !-. <" •

-"""

. '." .... ,

......... .

. .-..'. "

.' ,..

': .

...•......., .

. :.' '.' .

.........•.'", .

.' .

"....

.:. ~ '...:'. ' ..-.: "..

. . ,

.~ .. ~

'.

'. '.' ", 1) '~lUw:m of 1~groUp 'fiB~ .... baG~~ o'-n 'Bcottisb Nae~ch ve~~~ ~a'tchem: : . ". pSl".10houi-a f1ohing-nQrlhema.rea'from·J"onee (1971) : ,

. : :

, ... . .

',' .

~ . .... , ",.,

,'. ~ .

> •. '~.

;;. '.

.. . ~

~. .:

;--

",: ..: "

'...

_....., ,.

:..

". \.; ... .•.... :.'. .

'.J ..

....... --

Table 2

RESULFJ:S OF SIMPLE REGRESSION ANALYSIS

Regression Intercept I Slope Corre1ation Significance level 1)coefficient.,

1:,..-

Northern Area-Lt on Yt 21.09 -0.00054 -0.24 NS

Lt on Yt-l 21.24 -0.00019 -0.36 P < 0.05

N Centra1 Area.Lt on Yt 26.93 -0.00054 -0.23 NS

Lt on Yt-1 21.03 -0.00010 -0.29 NS

Lt = mean length of 2 year old fish for year class t

Yt = year class strength for year class t

1) Significance level

NS = Not significant

_. ~

Table 3

RESULTS OF REGRESSION USING TWO X VARIATES, ONE BEIl'ID A PERIODIC WNCTIOl?-) TO ALLOW FOR TRE:ND

Regression IInterceptRegression coefficientsXl X2

t va1uestl t2

MultiplecorrelaUoncoeffident

Uorthern Area• pe. -

Lt on Yt ~~d periodic functionLt on Y-[;-l and periodic funetion

N CentTal AreaikL ......

Lt on Yl al1d periodic functionLt on Y-1 and periodic function

26.1226.81

-0.00013-0.00091

-0.00089-0.00102

1.131.18

2.072.09

-2.2-3.1

-3.0-3.7

2.62.8

0.450.53

0.680.71

1) Variate X2= -cos (2 TI (yo-1928/10)

~~-~--- ~---- -~ ._- ~-~----- -~-------

Table 4

VALUES OF STUDENTS t FüR ASSESSING THE SIGUIFICANCEOF THE THREE MULTIPLE REGRESSION COEFFICIENTS

I

Area tl t2 t3

Northern Area -2.6 -3.4 3.6

North Central Area -3.9 -4.4 1.4

ti = value of t for variate Xi

where Xl is the strength of the same year class

X2 tt " fI ff ff 11 11 ff

X3 is the periodic fUnction -cos 2 TI (YC-1928)/10»

where YC is the reference year class.

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l'car J~/:) .. ,riati Jenl !:prUI :July! Oe't!C1ass Sspt' , ])~O ~ June Sopt D$c'

., ., .

1959 - 13.1 18.7 23.7 25.8 -41960 11.3 - 21.7 23.) 28.7. -.."196; - 13.7 - : 19.2 24.0 . 26.9

~

- ;1963 - 15.2 16.5 - - 21.2D 1968 1600 11.2 -- - . - ---, 2)

12.0 15.0 11.7 19..5 23.3 25.2t?VQrage ,, '

J'orth Central Ares

1959 - .13.5 18.0 21.6 26.3 -J. 1960 12.8 - 18.9 23.0 21.6 -1965 - 12.9 - 20.2 25.1- 26 ..6, '

:B 1963 - 12.8 14..9 - - 21.519~8 - 15.5 16.8 16.5 - ~-: ';', 2)

12.0..

1503 170' 19 ..9 24.0 25.2average. .<0:

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2) AV8~' for &11 ,-.sur class~s 1948-1968

. i) b~ed 011 rel.e;Uval:' amall numbers sinoßt tew haddock iU'9damsi"sal at this stage.... '

, A 7esr oluBee that were ltIrgs tor thei.1" ag9 'b,. 2 ~srs

cf e.&'O.

B JTe&r clasaes thS't vers small for thsir Sße by 2 yaars,~f ago

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Figura 1 North Ssa hä~doek.mean le~ths .at .2 years of. a8~~

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-4 ·3 -2...1 0 1 2 3 4Residuals fram regression of lt on periodic function

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Figure 2 Relationship between mean length of a year elaas and strength 01".pree,eding year elas8 after al.1owil18 tor trend..

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e' 65

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21 22 23 24 ..·..25 26 27 28 29 30 31 32Predicted

Figure 3 Relationship between o~served.and predicted mean lengths tor thenorth central are~. Predicted values determined from theexpression.. . .

"Lt = 2:1.29 - 0.000914 ~ - 0.00104 X2 + 203~3 X,