.
,
-
C~H.
International Cöuncil för the
Exploratio~ of the Sea
,
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1993/D:55
G
.
,.
Departmerit. of 'Fisheries .arid :oc~ans;'; p ~ O. B~X 5,667
. St~.J~hn's, Nfld, A1C 5X1, Can~da
Much'of ~he research s~~piiri~~f'age c6mposition in comm~rciai
f'ish species 'is stratified .on· the ·basis. of, lemgth,with a 'fixed '
number of samples taken from each apriori length class~ Fot most
fish species, a given age can straddle several lencjth classes.
Further , .the .probability· of. beirig mature at a giveri age' is "
influenced by.length at that age. ,This"can result :in biases in the'
estimation of· proportion mature at age if.catch atlength is not:
.takenirito,account. We present a method to correct for the bias in
maturity at aga from a.length stratified sampling scheme arid apply
it. to cod, and American plaice in ,the Northwest Atlaritic~
In
general;' . the differences between the', corrected arid uricorrected
estimates . were small, but some comparisons showed substaritial
differences.
".
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INTRODUCTION
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The' ability ,to accurately. determine age, at maturity. is '
important to the study and management of commercially exploited
fish species. while spawning stock biomass can be.estimated using
a ,knife edge estimate of maturity (eg;,assuming all, 7+ fish are
mature), and .bioinass at age "estimates, use" of theestimated
proportion mature'at'each age will produce a more accurateestimate
of the biomass of spawning fish. T~e abilityto track changes in
.. spawning stock biomasscan be crucial to monitoring' the health.of
stocks~ Also, there are oftenchanges in.the age'atmaturity with
changing population size {eg:Beacham, 1983; 'Pitt, 1975; Templeman
et ale 1978; Shelton and Armstrong, 1983);.Thesechanges will be
more reliably detected if one has an" unbiased . estimate of the
proportion mature at ~ach age.
'.,'
.
.
Many sampling.programs forcollecting.an age sample.from fish
populations are designed on the basis of length stratification;
with a fixed' number . of samples being .takenfrom eacli apriori
length group~
ThEl, age of the sampled fish is then determined
later. Maturity atage esti~ates determined from samples collected
in this way. are" subjectto errors ifthe riumber of fish in each
.length . group is not. taken into account ~ ,.' When ari age straddles
several length classes tlie probabilityof being mature can increase
with lengtli,andtherefore, onemust account for the catch at lerigth
and the distribution of age across length. '
.
.
In this paper we show that maturity at age is affected by
length at age in two important commercial species in the Northwest
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2
Atlantic; the Americanpla~ce ,(H~ppoglosso~des platesso~des) ,and
the Atlantic' cod (Gadus morhtiä);
Maturity 'at ,age in bottithese
species is sampled using a lerigth stratified scheme~ ~Wepresent a
method to 'estimate'the'proportion mature.at age from this sampling
regime.by weighting the 'observations,fram each lerigth group bythe
aburidance of the length categorY •. "We then compare tne resülts, to
those obbiimid without 'accounting for 'length, composition in' these'
, species; ' , '
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... . MATERIALS' AND METHODS
..."
, The data', examlried were', collecte'd dliring spririgmuitispecies '.:
groundfi'sh surveys "conducted by the Canadian, Department of
Fisheries and Ocearis~ ",The surveys lare conducted ,anriually froni
April to June in NAFO Division 3L on thc northern GrandB~uik off
Newfouridlimd,using an otter, trawl with' a fine mesh' liner ~in ',the
ciodend. Intlie'surveys, ci depth' stratified design was'used where
sets iri the depth strata were chosen at random, ,with the number of,
sets , ,beincj .appr6ximately "proportional to the ,stratum är'ea
(Doubleday, ~98~) •... For Anierican .plaice, data, fram the' spring
surveys from ~97~~~992 were used and forcodthe data came from the
spring surveys in the years ~978~~992". Far both species, 6toliths
were collected for ageing using, a le'ngth stratified scheme. For
cod, 25 sampIes are collected from each 30m lerigth class.
For
American plaice, a fixed numberof fishare sampled for each 2 cm
lengthclass. The fixedriWnber ,varies.. with the size of fish, with
'fewer fish sampled at the" smallest arid largast lengths.
In all
surveys an attempt was made t6 spread the sampling throughöut the
entire. NAFO Division.
Maturity stages ware determined at" sea '
according to the scheme of Templeman et al. (~978). In this scheme
there are 7 mairi maturity stagesfor males arid 9 for feniales. The
first' stage' for each sex. refers to Iimniature fish arid all, öther
stages show, some evidence of maturing to späwn in.thei present year
or of having spawried ",arid are classed ,as, meiture~' During these
surveys; lerigth frequency datei were collected from every successful
fishing set to provide an estimate of the length distribution.of
the populations. ,
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. currently ,the proportion mature at age is, cil1culated. using'
oIlly data fromthe aged sampIe, dividirig the riUritber of mature fish
at an age by the number of fish at that age~
,
" .'
proportion mature at agea
I.n'·
= lJ~~ p(aIJ; p(mla;.J)
""'-~~--------
n
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i
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.}J
J=~
(~)
•
01'·"
. .
,.
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3
,where: p(älj)
P(mla,j)'
..', n
lEmgth j
'. , = I'iUmber of
length classes
. .
.
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,
....
. .'
•
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"
= probability'of age a given length j
= probability of being mature,given age a and
"'.
'.
'-.
,: F'or.. each ,'species,' the 'proportiondf mat:ure" fish' ät each age' ,
and sex' in ,each year was,calculated using the, fish from the aged"
sampIe as show above:' Also, 'the proportion' mature at each ,length "
class for each aga was also calculated for each'sex in ,each year
(ie. nosummatiori across length class). ',The,effect.of,lengthclass
onthe, proportion 'mature at age was exainined using a Kruskal";;'Wallis
test.
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The data from the aged sample'and from the length frequericy
sampIe were, combined to .correct for 'the effect of the ,length
'stratification scheme.
This estimator weights the "observations
from eacn'lengt~ cat~gory by'the aburidance of the leng~hcategory~
,n
C
l:
~ ·...J:...=...;l~
j
proportion mature at age
a
P(alj) i'(mla,j)
_
n
~
(2)
Cj p(alj)
,]=1
•
where: Ci
= number caught at length'j
P1alj)
= probability of age a given,length j
P(mla,j)' = probability of being mature'given age a arid
'length j
n
,= mrinber of length classes
,
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'The denominator is simply' the nümberof fish at age 'a whlle
the numerator is the number of mature fish ,at age a•
.,Thenumber at l~ngt:h"(C j ) • was produ?e? from rese:arch vessel
survey length frequenc1es uS1ng, Strat1f1ed Analys1s ,Programs
(STRAP) ,(Smith and Somerton;, 1981) which weight the catch in ci
stratum by the size of the stratum.
,
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,
The difference between the estimates obtained ,fromweighting,
by the abundance, of each ,length category (weighted estimates,
equation 2) and,the estiinates of percentage mature at age'from tl1.e
unweighted method (equation 1) was c:alculated by sUbtractingthe
.weighted·from the unweighted estimate foreach age,in each year~
Age at 50% maturity was produced for each species, foreach sex and
year, usirig probit, analysis assuming a normal distribution. This
was done for both the weighted and unweighted estimates.
"
RESULTS
For hcith ccid and Aierlcan plaice there was an effect of length
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on the proportion mature at age",w~th the' probab~l~ty of a fish
being mature at'a'given age increasing with increasinglength., :As
an, 'example"results for, age 9 'Anlerican plaice are presented in
.
, Figure 1and ,for age' 6, codm:Figure~.
Th~ effect of,lerigth on
': proportion mature wa's statistically significarit ,(age 9 plaice male:
, 2~43.14;.. df=:=,15,: P<0.?901i.,a~~' 9 pl~ice_'fe~~le: 2~8,~.08~ df=13"
',' P<0.0~~1, 2c:ge,'6.;,cod~male., ,,~33.6"?'j d~-15, ,p<o.o~~',:age. 6 co~
female.
-:45.93, df~12, p<0.0001) .1',
','.
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,:When, theweighted, percent:,matu're' at age calculated :using
equatiori 2 was comparedtothe unwedghte'd ,percerit, 'mature at 'age
where lengthwas nottaken. into, acciount (equation 1), all ages for
which tlie fish ware neither all,matüre nor all immature,showed a
difference l:ietween thetwo estimates: ,This was true' in all yeai:'s •
The differences were sometimes negative arid sometimespositive and
for a,qivenage they varied from yearlto yearboth inmagriitudeand'
direction cif the difference ~ .: However, for' both sexes cf both
'species approximately one-thii:'d cf the differences were less than'
1%;
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. 'For male American, plaice (Figure 3, top), 26.2% of the'.
c6mparisons ,hild a differerice ,of less than 1%.
,There' was, a
difference of greater than, 5% in 28; 9% of the comparisons, and the
largest difference was 49.3%.' For American plaice feniales ,(Fiqure
3, bottom) " 32 ~7% of the compai:'isons differed by lass than 1%;
15.7%Of ,thecomparisons differed by;more than 5%, arid the largest
difference between unweighted and weighted estimates was 25;7% •
. ,Formale cod ,(Figure ,,4; top)'" 27.6% ,of 'the comparisons
differed.by lass than 1%, 16;2% differed by more than,5% and the
largest difference was 16~2%.' For.female cod (Figure 4, l:iottom),
29.5% of the, comparisons differed jby less than1% ,with 22.8%
differingby more than 5% arid,the largest difference being '15.0%.
For both speeies, there were only, small differences (less. thari
orie' year) in,the estimatas, of, age at 50% maturity, from ,the two
methods (Table 1& 2). Tha magnitude of the differences between
the. two estimates was not consisterit over years ·nor was the
dii:'eciticin of the difference consistent.
'.'
DISCUSSION
I
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" Forboth cod and AlUerican pläice the probabllity' of being
mature at a given age increased' with. size., ,This mearis, that
estimates of maturity atage based on a length stratified sampling
scheme will be biased if ,the distribution of size at. age,is, not
accountedfor properly.' This potential bias can be easilywEdghted
. for as presanted here; accountirig for. tliEi effect of lerigth on the
. probability ,of.being mature at a.given aga, the distribution ofa
. given age across length classas, and the length frequency~of the
populat~on:
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The d~fferences between the we~ghted and unweightedestimates
of the percent mature at age were generally small ~ However, '. there
was a difference for all ages wherethe fish were neither all
mature nor all iminature; Also", some large differences did occur,
up to 49% for male American plaice.
The differences were not
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consl.stent l.n magnl.tude or . dl.rectl.on across ages, or for a ,given
age across years.'
Therefore, a constant emp~rical corre~tion
factor. cari not .. be applied. "
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" There was also little' difference in,the estimate of age 'at 50%
'maturity between the two methods.'However, even asmall difference
in ',the aga 'at ~aturity can' be, 'have a signiflcarit impact ori the
'estimation, o'f , expecte'd" yfeld ~of a"fishery (Welch and'Foucher, '
J.988) ~·Again·the magnitude ,and directioriof the 'differences were '
not corisistent,'precluding the application of a coristant empirical'
correctiori factor..'
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Althoughdifferences in the weighted'and unweighted estimates
were generally:small, the method presented is simple tö apply. It
will resultiri a more accurate estimate of proportion mature at
age~
ACKNOWLEDGEMENTS:, ,We: thank N. payton for extensive' help with
programming. The 'staff of th~' gro,undfish division at the Northwest
Atlaritic, FisheriEis Centi'e collected, and processed, the research
vessel data. E., Murphy compiled'the cod data;
,
,
,REFERENCES
•
Beacham, T.D. 1983. Variability in median'size and age at seXual
, maturity of Atlantic cod, Gadus morhua, on the Scotian Shelf
in the Northwest Atlantic Ocean~ Fish. Bull. 8J.: 303~321;
Doubleday,., W.G •. 1981. Manuäl. ori . groundfish. surveys in the
Northwest Atlantic. NAFO Sei. c6uri~ Studies. No. 2; 55pp.
Pitt, T.K. ,1975. Changes in abundance arid certain biological
characteristics of Grand Bank American plaice, Hipp,?glossoides
.' platessoides. ,J. ,Fish. Res., Bd. Cariada ,32: ,1383-139.8 •. '"
.
Shelton, P.A. and M.;J.Armstrong. 1983. Variations in parent stock
arid recruitment cif pilchard arid anchovy popUlations in the
southern,Benguela system. pp 1113-1132~ IN,G.D. sharp and J~
Csirke Eds. proceedings,of the Expert Consultation to'Examine
Change in.Abundance and species composition,of Neritic Fish
Resources, sari Jose,' Costa' Rica, 18-29 April 1983 ~ FAO
, Fisheries Report 291(3).
'"
Smith, S.J. and G~D. Somerton; 1981. STRAP: a, user':'orierited
computer analysis system for groundfish research trawl survey
.
,data. Can. Tech. Rep. Fish. Aquat~ Sci. 1030: iv +,66 p.
Templemani W~ ,V .M~ HOdder, and R. Wells. 1978., Sexual mäturitY,'arid
spawning in:haddock Melanogrammus,aeglefinüs of the southern
,
Grand Bank ~ ICNAF Research, .BulL 13: 53 ;';'65. ,.' "
"
.
Welch, D~W., and R.P~ Foucher. 1988. A maxiinum ',likelihood
. meth6dology for, estimating length';;;'at-maturity with applicati6n
'to Pacific cod (Gadus macrocephalus) popUlation dynamies. Can~
J. Fish; Aquat. Sci; 45: 333- 343.
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Table i. Estimates' of ' age at 50% matur!t:y, in Americari plaice
using '. weighted .arid uriwiüghted estimates. of proportion " ' ,
mature tlt age.
. .
I ...... "............
'
• ' ..,
,
.
.
Year.'
. . ' . '.
"
.'.
I
.
. . .
.
..... , . I ....,.... '~. ",.,::. Females ,: " ' .
Males
I···'·" , - •..: .. '.
.... 1971 .
6.15 .
.'
.1 .. ,.
,6.41
' ..... ', ... 6.14,
5~90
1. 1972
...
:
1973
,1974
1
.•
5.53
..
..' ..... 5.47.:
5.67_ .
I·'"
.
........ 6.88.,':.,
1975
"
'1976
......
'.
.
6~
..
..
1977
,
I
6.69
'.'
. I
5;51
..
'..
.6; 10.
...
. 1980
6.25
10~
'.
e
68"
6.78
.....
..
11.17
10~93
...... 10 .15
9~79
10.00
,.~.... 9; 68
..
I
I
6.25
.6.54
... 1981 '.
10.99
..
10.79
"
....
"0
10~82
11; 61 .....
5.72 ......... 1
..
.1979
9;78
.11;09.,.
.\
.'
1978
9.81'
1
. 6.35' '..
.
.
,
i
.i
,
10';52,
10.83
I
78:'
.
"
,I
'
7~23
>
6.46,
.6.29
10.61',
I
.>
.1
_
I
~ 10~
.,. I
73
.
...
. . 10;56.
..
6;62
.
.. 7.34.
~r
10.42 .. '.
I
"'
1984 ..... .. ,
.'
5; 06.
.5.38
.
. 1985 '.'
.
.... 4.86 .
I.
I
.. 5.44 ..... 1
8.40
8;47
8.43
8~53'
.
1986
.1987
..... :
,
.
.
.7;99
. . . . . 4.s:L.J
3.76
.
1989
..3.98 ..
.
1990 .....
:
,
4~47
.....
1991
.
1992
5~63
, ...... :... 5.62
1988 . .
,
. 8.,50
.J
. ".
.
4.03 ..".
'.'
..... H
.
.
.
7.78
7.92
7.89 ....
"
..
4.78. ..1
5.461
I,
4.73
.,!
I
I
. . , · ... 7
.
~90
.
. ..... ~ _.,7.75 .
8.71..
,',
..8.64
.
7'.95 ..... · ,. .•
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...
7.92,.,,...
•
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---
-- ---
--------- - - -
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Table 2.- Estimates of age·at 50% maturity for cod using'
weighted ,and unweighted estimates of proportion mature ,at.-.age.
,
Year,_
,
',-
Males'
Weighted·
Unwe'ighted,
.
,Weighted
,unweighted
6.07'
6.05
4.-85
'5.91
5.59
4.96, .
5.63
'5.58
'
1978:
5.10
1979
4.82'·
1980
5.00 '
.-.
,
5-.04
"
.
1981
5.02
5.08'
'5.64 .
'5 '-61-
1982
4.74
4.63
5.42
5.35
1985
5.18
5.10
6.21
6.11
,.
5.04_
5.01
. 6.04,
1987'
5.22
5.29
5.98
6.00
1988
4.78
4.96
5.93
5.93
1989
5.74
5.'70
6.00
6.00
1990
5.03
4.98
5.27
5.25
1991
5.48
5.35 ..
6.07
5.89
1992
4.06
4.24
5.08
. 4.93
1986
•
Females
..
..
5.88'
.
PLAICE AGE 9
1.5
1.4
1.3
1.2
Q)
''1. 1
;:)
0
1.0
:::2
e 0.9
0
0.8
'0
a. 0.7"
0
0.6
'0e 0.5
0
Q)
0.4
:::2
0.3
0.2
. 0.1
0.0
8
9
2
12
+J
29
t
+J
Q)
'-
;:).
+J
1.5
1.4
1.3
1.2
.
\ '.
Males
.3
16
32
73
149
!
1
!
,
92
171
232
42
54
211
248
280
75
199
12
8
2
! • • • • • •
•
251
264
1.1
196
Females
12
5
96
•
0
1.0
e 0.9
0
~
0.8
'0
a. 0.7
0
'0.6
0e 0.5
0
0.4
Q)
:::2
0.3
0.2
0.1
0.0
:::2
•
•
e· .
20.522.524.526.528.530.532.534.536.538.540.5
42.5 .44.5 46.5 48.5 50.5 52.5
,"
Length Class
Figure 1.
Mean
(+ 1· Std. dev.) proportion mature for age 9 American ploice moles and
females at each length class. The means are over the years 1971 to 1992.
The numbers above the points are the number of fish examined.
COO AGE 6.
9
1.5
Males
1.4
3
1.3
12
27
.....:;
1J
0,9
c
o
..... 0.8
~
O.
~
0...
0.7.
0.6
c
0.5
2
0.4
0.3
0.2
0.1
O. 0
86
82
31
22
11
5
1.
,
..
• • • • • •
!
1. 1
°1.0
:;2.
:::2
103 .115
1.2'
(I)
.0
0...
62
-+--4I--+---T--__r-_y_-r--__r-~__r-_y_-~__r-~__r-___r_-r____,
1.5
Females
1.4
4
1.3
14
26
54
81
98
85
64
38
17
8
9
2
1.2
1.1
e
1.0
0.9
0.8
0.7
0.6
c
0.5
c
o
.....
~
8..
0..
o(I)
:::::E
• •
I
f
I
0.4
0.3
0.2
0.1
O. 0
-+-~~__--+----=r_--r--.----,r__._-_.____r-__r_-.____r-__r_-.____r-....,
40
4.3
46
49
52
55
58
61
64
67... 70
~
7.3
76
79
82
85
Length Class
Figure 2.
Mean (+ 1 Std. dev.) proportion mature for age 6 cod males and
females at each length dass. The means are over' the years 1978
to 1992. The numbers above the points are the number of fish .
examined.
35
\ •.
~o
30
Males
n=103
>-
<.J
25
c
V
~
v'
--....
20
~
c
v
15
<.J
~
v
C-
,10
•
5
0
35
30
Females
n=104
>.
25
<.J
c
Q)
:J
0-
-
20
Q)
~
.....
c
Q)
15
u
~
Q)
a..
10
5
0
0
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 .40 42 44 46 48 50
Oifference in percentages
Figure 3.
Percent frequency of occurrence of difference between weighted
and unweighted percentage mature at eact1 age in, each year
for male and female American plaice. n = total number of
age X year combinations compared.
35
30
>u
c
25
:J
CT
20
c:
15
Femoles
n=44
Q)
-.....
Q)
I-
•
Q)
u
IQ)
a..
10
5
0
0
2
3
4
5
6
7
8
9
10 11
...
12 13 14. 15 16 17· 18
19 20
Difference in percentages
• Figure 4.
Per·cent frequency of occurrence of difference between· weighted
and unweighted percentage mature at each age in each year
for male and female cod. n = total ·number of age X year.
combinations compared.