,
ICES 1991
PAPER
C.M. 1991/G:42
AN ATTEMPT TO EXPLAIN COD GROWTH VARIABILITY
by
Bjöm JE. Steinarsson and Gunnar Stefansson
Marine Research Institute
P.O. Box 1390
Sk111agata 4
121 Reykjavfk.
Iceland
ABSTRACT
Several measures of cod growth are considered and related to environmental parameters, including capelin
biomass, using simple regression models which do not require strong underlying assumptions on growth
curves or biological relationships. It is found that the best explanatory model usually includes capelin
biomass.
'j
____________________1
Codgrowth
1. IntroductIon
Cod growth in Icelandic waters is highly variable, with the mean weight of 4 ycar old cod in the catches
ranging from 1.4 kg to 2.0 kg. This has severe effccts on prognoscs for this stock and calls for an analysis
of the causes, in order to obtain the bcst quota management for the stock. In addition, multispecies
interactions are of interest in their own right, apart from the potential need to manage the species in a
multispecies context.
For the past several years, a number of indications have appeared to support the hypothesis that cod
growth is strongly influenced by environmental parameters (measured by temperature and salinity) and
capelin stock biomass.
.
•
.
Claims about the basic effccts of the environment date back to the 1960's (J6nsson 1965), when it was
shown that cod length at age correlates with the temperature of the ses where the cod is found. This has
later been verified a number of times and it is quite obvious from looking at the raw data that cod in the
northern (colder) region has a lower mean weight at age than those in the southern region.
Substantiated claims about the effect of capelin biomass on eod growth are somewhat more rccent. A first
indication is the amount of capelin in cod stomachs (Palsson, 1983) and the results of modeling the
corresponding effccts on growth (Palsson and MagmIsson, 1989).
.
In 1981 - 1983 a severe dccrease in cod length and weight at age was observed at the same time as the
capelin stock was at a very low level and a cold aretic water mass dominated North Icelandic waters
(Malmberg, 1986). Further, simple plots of weight-at-age against capelin stock size or temperature (as
given in Anon, 1990) indicate a relationship.
All of the above has indicated that cod growth is inßueneed by environmental factors in general and by
capelin biomass in particular.
A formal analysis of the basic effccts, based on the raw data, has not bccn done to date. This paper is a first
allempt to forrnalizc same of the questions by first defining appropriate data sets and then investigating the
correlations involved.
•
One major concern is that of defining the data sets, and in this paper scveral data sets are considered. In
particular, one of the qucstions raised when the cod-capelin interactions are modeled based on
consumption rates concerns the time of sampling. Thus, thc capelin may not bc abundant in the area when
cod stomachs are sampled. As a rcsult of this, it is feit essential to verify relationships, based on the raw
data, without a strong model assumption, such as the one that occurs in a model which dircctly links
growth with stornach contents.
2. Problems In uslng lengthlwelght at age data for growth studles
For the past dccades 10 to 25.000 fish have bccn age determined and length measured annually from the
Icclandic cod stock. This has been done mainly for the purpose of stock assessment. At first glance this
seems to bc a lot of data for growth analysis. But bccause of differenees in growth bctween areas, different
selectivity of sampling gcars, varying sampling time and migrations it is not obvious how to choose a
dataset representing aetual annual changcs in mean length/weight at age. For example the difference in
mean weight at age in the relatively warm waters (battom tempo 8-9 oe) at the south coast and at the
northeast coast (bauom temp 3-4 oe) is about 30 %.
In choosing data to study actual annual changes in mean length/weight at age it is thcrefore essential to
set up some criteria in order to minimize sampling bias. The following critcria seem to bc reasonable:
A. Sampies should bc laken with the same kind of sampling gcar each ycar or at least using gcars with
similar selection pattern.
B.
SampIes must bc laken at the same time (month) cach ycar.
C.
Tbc sampling area should be kept as small as possible and should be hydrographically fairly stable.
D.
Sampies should bc laken at the time of ycar when spawning migrations do not take plaee.
.
. .
Codgrowth
E.
A minimum sampIe size requested for each age group.
In spite of large numbers of otoJiths/length sampIes taken annually from lcelandie coo, it seems 10 be
impossible to build up a dataset ranging over severaJ years (decades) fulfilIing all the above mentioned
eriteria. So one has to make some kind of a sensible compromise. e.g. combining data from severaJ
months, selecting data from larger areas and time of year than beJieved to be optimal and so on.
3. Dsts sets used in this study
In this first analysis only two age groups (age grouvs 5 and 6) are considered since the annual changes in
lengthlweight at age of all age groups seem foughly to follow the same pattern (Fig. 1-3). Further. the age
groups 5 and 6 are weIl represented in sampIes in all years.
Four different parameters were used as indicators of cod growth:
vpaa'
Mean wcights used in vpa analysis. Age-Iength data are coIlectcd from landings throughout
the year and some 20 different age-Iength-keys are set up for each of the 4-5 main fishing
gears for two different arcas and two seasons. Using corresponding length measurements
the mean length at age for each category are caJculated. The mean weight is then found by
using length-weight relationships (a different reJationship is used in each category). Finally.
the mean weight at age over aJl categories is caJculated. by weighting with catch in weight
in each category (Fig. 1).
•
Obviously this parameter nced not reßect actual annual changes in the mean weight at age
in the stock since for example an increase in giJInct catches ofT the north coast in one year
would decrease the mean weight at age in certain age group in that year.
=Vpa(a+l,'+l) - vpaa,' (Fig. 2)
Oa"
Oa"
la'
Mean length at age. obtained by sampJirig off thc north and northcast coast (Fig. 3) during
June - September from commercial bauom trawl.
Pa'
This is the slopc of the weighted least squares linear regression of the monthly mean Jength
of age group 5. The weights are the inverse variances of the mean lengths per month (fig 4§). These are sampled from commercial baUom trawl fisheries in thc northem region, as in
lalt but monthly data are used. This is a more direct measurement of growth than those
based on differences in annual mean Jengths or weights.
Several explanatory variables are available. For this study. these were chozen to correspond to the coo
growth indicators. The following variables were considered (Fig. 7):
capelinlV, Biomass of capelin (age groups 2-5), at 1. January.
cape/inS,
Biomass of capeJin (age groups 1-4), at 1. August.
temp,
Deviations from 1961 - 1980 mean temperature at 50 m depth in May-June on standard
hydrographie stations north of Iceland (Anon. 1990).
cod,
Biomass of cod (age groups 3-9) at 1. January.
port,
port,
temp5ra,
Five years running average of temperature (temp,).
cod5ra,
Five ycars running average of coo biomass (cod,).
=
capelinW,
cod,
The eapeJin biomass estimates are preliminary. based on backca1culations from autumn and winter
acoustie abundancc cstimates. catches and a monthly natural mortality rate (Vilhjalmsson, pers. comm.).
•
Codgrowth
4. Methods
Multiple regression models were used for the analysis (with the Splus statistical package).
4.1 Model A
The first model relates the mean weight at age as obtained in the total catches to an environmental factor,
capelin biomass and a five ycar running average of cod biomass. Using the dircct measurement of mean
weight at age means that the independent variable contains an aggregation of several ycar's growth.
•
The choice of explanatory variables reßcclS the notion that the mean weight at age depends on the
temperature in several previous ycars, competition for food in previous ycars and capelin stock biomass in
the beginning of the ycar. The capelin biomasses are not available as a long enough scries to facilitate
using a running average, but a large capelin biomass indicates large ycarclasses which, therefore, have
been available for some time to the cod. Thus a capelin biomass estimate corresponds partly to a longer
'
period of growth and notjust a single ycar's growth.
The full model A bccomes:
vpa, = (X + (XlcapelinlV, + (X2temp5ra, + (X3cod5ra, + l:,
4.2 Model B
The second model relates the direct growth estimate (ß) to capelin biomass, cod biomass, capelin
availability and temperature. Since this is an estimate of growth during the ycar, an attempt has bccn made
to usc as explanatory those variab1eswhich should affcct this parameter.
It is not obvious whether the capelin biomass at the beginning or in the middlc of the ycar should bc used.
For this model the summer estimate is uscd, in order to indicate an average value for the amount of capclin
available. An integrated average might also bc considered, but that is outside thc scope ofthis study.
Ir the food resources are stable and limitcd the cod biomass should bc a measurement of overall food
availability (density dependent growth rate). Since ß reßects thc within-year growth, a simple biomass
estimate is uscd rather than a moving average.
•
Onth
e oth er han d 1'f cape1"10
IS
the mam
' prey then th·C
capelin
d b'biomass or the capeI'10 b'10mass a Ione
,
co
LOmass
should explain at least some of the variations in the growth.
The temperature offthe north coast should reßcct the relatively scvere hydrographie variations in the area
(Malmberg, 1986) and was therefore chozen as an indicator of environmental conditions. These values are
mid-ycar values, which are interpreted as representing an average value throughout the ycar of growth.
The fuH model B bccomes:
ß, = (X + alcapelinS, + a2temp, + a3cod, + C1.4port, + l:,
4.3 Model C .
The third model relates the mean length at age in the northem area to the same explanatory variables as in
Model A. The mean length is a much bctter parameter than vpa (as an indicator of the condition of the
stock), with respect to sampling bias due to different catchcs in the different gcars.
Sinee this independent variable is of the same type as the one in model A, the model development follows
the same logic and the same independent variables are used.
.
Thc full model C bccomes:
-------..
Codgrowth
4.4 Model D
The fourth model uses the annual weight increase as obtained from catches, and since growth is being
considered, it is related to the same explanatory variables as in Model B.
ö,
=Cl + Cli capelinS, + Cl2temp, + Cl3cod, + f1.4port, + E,
It is noticed that there is a buHt-in autocorrelation in the Ö, values, but this is ignored the analysis.
5. Results
The analysis was conducted using backward stepwise regression, beginning with a full model, eliminating
the least significant variables at each stage. The full procedure depends somewhat on the purpose of the
analysis. For predictive purposes, one often stops and includes variables after all have a marginal P value
of under 25%. For testing significance, however, it is necessary to use spccific P-values, whcre 5% or 10%
are common, and this is the approach laken here.
5.1 Model A
Ofthe three explanatory variables, only capelin biomass is highly significanL The full model cxplains 81
% of the variability (R 2 = 0.808, P = 0.0067). The temperature is insignificant (P=0.49) in the full model as
is the running mean of the cod biomass (p=0.17).
When temperature is deleted from the model, capclin remains highly significant and the average cod
biomass is marginally so (P=0.1 0).
The regression equation becomes:
vpa5
3.70 capelinW
+ 0.44 cod5ra + 1.34
and it is no~d that the sign of the cod stock is positive.
Capelin biomass a10ne explains about 70 % ofthe variability in vpa with a significance level ofP
(Fig.8).
=0.0012
5.2· Model B
None of the independent variables bad a significant efTect in the full model (p=0.45, R 2 =0.41), nor is there
a significant relationship betwccn thc growth and capelin biomass a10ne (p=0.18, R 2 =0.19). Looking at a
scatterplot of the parameters (Fig. 9), it is obvious that the two values in 1982 and 87 are responsible for
the lack of a significant rclationship betwccn ß and capclin biomass. One way to interpret this is that 2
points out of 11 are outliers in the relationship.
Tbc regression equation bccomes:
beta
0.69 temp
-0.95 cod
-6.69 port
+ 0.63 capelinS
+
1.32
and it is noted that the signs of terms cxcept port are as cxpectcd, allhough thcy are not significant.
In 1987 a high temperature and capelin biomass but low ß is observed. In the 1988 groundfish survey it
was noticcd and reported that the mean Iength of 7 and 8 year old cod bad decreased betwccn years, for
each year class. Such anomalies are very rare (this is the only instancc in thc 6 survcy years) and at the
time it was thought to bc an indication of amigration from outside the survey area. Further, there is a drop'
.
in the mean length ofage group 5 in November and December in 1987 (Fig. 5).
There is no obvious reason to deletc the 1982 data point and this has therefore not becn done, although it
would clcarly makc a great improvement on thc regression. In 1982, therc is a similar drop in mean length
at age 5 in the last few months of thc year, indicating some sort of deviation from the simple linear
regression model used within the year to compute ß. Using a more appropriate functional form (an S-typc
curvc within thc ycar) might allcviatc thc problem.
After deleting the 1987 data point all variables turn out to bc at least marginally significant in the full
model (wbere, now, R 2 =0.90, P=O.OI). Cape/inS has thc lowcst P-value of 0.0069 in the full model and
the tempcrature is least signi ficant with P = 0.055.
•
Codgrowth
The resulting regression equation is:
beta = 1.6 ternp -1.1 cod -9.4 port + 0.90 capelinS
and it is noted that eoefftcients exeept pon have the signs that are to be expeeted.
+ 1.15
Although all parameters were signifieant in the full model a backwards stepwise regression analysis was
performed. Deleting first the temperature parameter results in R 2 0.765 and P-values ranging from 0.014
(capelinS) to 0.05 (port). Deleting the port-variable results in a P-value for cod of 0.332 but capelinS still
significant with P-value ofO.047. Finally deleting cod and using only capelinS as an explanatory variable
gave R 2 0.445 and P-value 0.035 (Fig. 10).
=
=
=
It is always eonsidered somewhat suspect to delete outliers. However, in this instance, anomalies were
notieed from other saurces in the given year. In My case, the resulting regressions, after dcleting the
.
anomalous point, are presented mainly for informative purposes.
5.3 Model C
The full model gave no significant rclationship. The highest P-values was for temperature (temp 5ra) so
this variable was deleted. The resulting regression on capelin biomass and average cod biomass was still
not significant (p=0.16), but now the capelin biomass was marginally significant (p=0.089). The signs of
the eoefftcient of eod biomass and capelin biomass are positive in both cases. A regression on only capelin
.
biomass yielded a marginally significant rcsult with P=0.08 and R 2 =0.30.
Here again outliers (1980 and 1988) are observed. The 1988 outlier corresponds to the 1987 outlier in
model B. (The anomaly as obscrved in the surveys shows up betwecn the surveys in March 1987 and
March 1988. The drop in mcan lengths at the end of the year 1987 indieates that migration may have laken
place that fall, resulting in an anomalous value for mean length in 1988). When delcting the 1988
datapoint, using same arguments as in Model B, a backwards stepwise regression ends in only capelinlV,
and the eapelin biomass turns out to be significant at the 5 % level (p = 0.04) with R 2 = 0.42. As before,
this regression is done mainly for informative purposcs.
5.4 Model 0
•
The full model was highly significant (P=O.006 and R 2 =O.88). A scatterplot of these variables is shown in
Fig. 13. Only the temperature is significant in the fuH model. The first variable to be delcted from the
model is the eapelin biomass. In the resulting regression, the cod biomass is not significanl, but both port
and temp are signifieant (P=0.OOO8 and 0.001, respcctively).
A final regression on port and temp shows both variables to be highly significant, so it would scem that for
this independent variable, the main efTect of the biomasses comes in through the ratio bctwecn them. The
overall R 2 for this final model is 0.84.
The rcsulting final regression equation bccomes in this instance:
delta
-1.468 ternp + 2.575 port
+
1.0909
It must be noted that the temperaturc variable in this instance comes into the model with' a negative
eoefftcient, and this is not casily explained.
To see more explicitly the relationship with eapelin biomass, a simple linear regression was performed
against this variable only (Fig. 12). This resulted in an R 2 -value of23% and a P-value of0.14.
6. Discussion
Several indieators of eod growth have becn considered and related to external parameters such as
temperaturc, cod biomass and capclin biomass. In most instances at least an indication is found that
capelin biomass afTects eod growth. A summary of the results is given in the following text table:
Codgrowth
Model
Full model
R2
A
0.81
B
B w/out '87'
C
0.90
D
0.88
P
<0.01
N.S.
0.01
N.S
<0.01
Final model
(all P-values ~ 0.1)
capelin+cod biomass
constant
fuH
capeJin
port+temp
CapeJin only
R2
P
0.70
<0.01
0.18
0.67
0.44
0.04
0.30
0.08
0.23
0.14
It is feIt that the most reasonable and promising independent variable is ß. where seasonal efTects have
been removed and a direct growth measure is obtained, independently for each year. The constraints
imposed by available data are reduced by using this variable, since the problem of missing data in some
'
months is alleviated by performing a regression across the months.
Future work should incIude an attempt to diminish the region under consideration and this may weIl be
possible by using the ß parameter. It is also tempting to attempt to use more age groups, either in a single
model or separately.
Another item of interest is to use a nonlinear function to describe the growth within a given year (since the
growth is not expected to be the same in winter-spring and fall as during summer). .
•
Work on capeJin biomass backcalculations is underway and these data may be revised in the near future,
resulting in estimates of capelin biomass for eaeh month. When those data are available, it is tempting to
associate the eod growth to "available" capelin. The problem is twofold, on the one hand the total capelin
.
biomass at each point in time and on the other the spatial overJap' between the two species.
The temperature parameter is only in two instances in the final models (model B without 1987 and model
D) and is only once found highly significant This is somewhat surprising and is possibly due to an
inadequate measure of temperature. For example the eod may move to more favorable environments when
the temperature in the referenee area is low.
REFERENCES
Anon. 1990. State 0/ stocks and environmental eonditions in Ieelandie waters 1990. Fishing prospeets
1991. (in Ieelandie with english summary). Marine Research Institute, Reykjavfk.
Mimeograph Series 21,145 pp.
J6nsson, J., 1965. Temperature and Growth 0/ Cod in Ieelandie Waters. ICNAF, Spec. Pul., Vol. 6,537539.
Malmberg, S.A.,'1986. Eeologieal impact 0/ hydrographie eonditions in Ieelandie waters. InLsymp.
. '
Leng Term Changes Mar. Fish Pop., Vigo 1986.
Magnusson, Kjartan G., Palsson, 61afur K., 1989 Predator-Prey Interactions 0/ Cod and Capelin in
Icelandie waters. ICES Symposium on Multispecies ModcIs Relevant to Management of
Living Resources. The Hague 1989.
Palsson, 61afur K., 1983. The Feeding lIabits 0/ Demersal Fish Species in Ieelandie Waters. Rit
Fiskideildar, Val. VII. No. 1.
•
Fig. 1. Mean weight of age groups 4 to 9 In· catches
9
age9
8
7
L-
Q)
.
+-'
..c
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6
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c 5
co
(l)
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....
•
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,", ••••••••.•
~."
age5
I'
2
78
79
80
81
82
83
84
year
85
86
87
88
89
!
1600
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1400
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1200
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78
79
80
81
82
83
84
85
86
year
Fig. 2. Annual increase in weight of age groups 4 to 6 in catches.
87
88
85
80
age7
75
......
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.........................../.....
'
•.
~.
/0" •••.••••.•••.•:••••
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45 - f - - - - , - - - - , - - - - , - - - , - - - , - - - , - - - - , - - - , - - - , - - - - , - - - - ,
78
79
80
81
82
83
84
85
86
87
88
89
Year
Fig. 3. Mean length of cad in age groups 4 ta 7
in commercial battom trawl, NE-Icelandic waters, June - September.
-
r
75~-----------------------,
7~
E
Beta = 1.37
p= 0.004
70
E
Öl
r::
70
(.)
(.)
.J::.
Beta = 0.21
P = 0.347
•
6S
==Cl
~
~
ca
Cl.l
E
ca
r::
r::
•
65
r::
•
60
• •
Cl.l
55
E
1978
50
1
10
6
tl
1981
50
12
9
1
Öl
r::
~
r::
70
E
•
65
.
• •
60
•
65
r::
~
r::
60
ca
Cl.l
55
E
1979
50
1
10
11
55
12
1982
•
50
1
3
•
r::
70
•
. .
65
•
E
-
=:Cl
70
65
r::
~
60
r::
ca
Cl.l
~
Cl.l
55
E
1980
50
1
10
. Beta = 0.58
P= 0
(.)
ca
E
12
75
Beta = 0.42
P= 0.018
u
~
tl
Month
75
Öl
c:
10
6
Month
.J::.
12
Beta = 1.04
P = 0.023
70
(.)
=:Cl
Cl.l
E
tl
75
Beta = 0.36
P = 0.016
ca
E
10
Month
75
.J::.
•
55
Month
E
(.)
•
•
11
~
55
•
•
- •
•
1983
50
12
1
7
Month
Month
Fig.4.
•
•
Mean length by manth and year (1978 - 1983) af ead, NE
Icelandic waters, eommer11 bottom trawl.
e
10
11
12
75,---------'
Beta = 0.16
75,------------------'
Beta = 1.12
E
E
P= 0
70
(J
(J
J::
oE
0,65
~
C
150
CIS
~
c
55
'L----------••:------+-----....-j
•
eo
(I)
1984.
E
so.l---..,.....---.....--.....-------.------.------1
7
1
10
11
55
5O.j---~-..._-_-....._-_-
12
1
3
Month
E
(J
-=
Cl
75
Beta = 1.17
P= 0
E
(J
J::
65
Öl
~
C
CIS
C
CIS
E
•
E
1985
10
1
65
• •
eo
70
==Cl
11
12
•
•
•
• •
1988
1
2
10
3
11
12
Month
75,--------------------------,
•
E
Beta = 0.85
P = 0.017
70
(J
•
J::
65
Cl
C
65
C
~
~
C
CIS
Cl>
(I)
E
12
50
75,---------------------------,
Beta= 0.94
P = 0.001
10
55
Month
(J
7
(I)
55
so
E
-_._--.--__..-_-____l
Beta = 0.45
P = 0.057
70
C
C
~
(I)
1987
__
Month
75
70
,.
55
CIS
•
(I)
E
g'
•
C
P = 0.243
70
C
CIS
55
E
1986
5O.I---------.....-------.--------~
10
11
1
55
5O.j---~-_-_-_-....._-_-
12
1
Month
Fig.5.
Mean length by rnonth and year (1984 - 1989) of cod, NE Icelandic waters, commercial bottorn trawl.
7
Month
1989
__
-_._-_._-_...-_l
10
11
12
v..----------------------------:---1
,.....
,.....
,......
0
LO
Q)
0> CO
ro 0 .
,
CU
.......
~~
0
V
0
•
.
C\J
o
78
80
82
84
86
·88
Year
Fig 6.
Growth, as measured by slopes (ß) in regression - cm per
month.
l
R-Square
=0.7044, p-value = 0.0012
86 •
•
80
•
87
•
•
•
89
85
•
•
88
-l-'
..c
0)
._~
OJ
•
•
~0J
c
cu
OJC')
~.
0J
• 83
•
0.05
81
0.10
0.15
0.20
Capelin biomass, winter
Fig. 8. Mean weight of age group 5 in catches versus capelin biomass at
the beginning of the year.
•
•
I-
•
•
0-
E
(])
• •
+-'
•
•
•
·•
•
~
•
"0
o
()
+-'
'-
0
0-
•
1-.
•
•
•
•
-
•••
•
-
•
• •
•
.
•
c
0-
..
•
•
••
.
••
.
•
•
• •
•
•
•
•
•
•
• I
~"'
..
beta
Fig.9.
•
••
•
•
•
•
•
• ~,;o(
..
•
Ie
~.
•
•
\
•
-(])
•
• •
•
• •
f;"' t-
Cf)
~
()
•
•
•
••
~
• •
~
••
•
•
•
•
•
•
•
temp
•
.
•
cod
Scatterplot of a11 variables in model B.
•
R-Square = 0.4445, p-value = 0.0352
..q78 •
~
N
85
~
•
•
0
.c~
~
0
0)00
•
84
82
......
•
86
.
.
~
>'0
..c
......
c
0
~~
0
•
.
0
..q-
•
•
80
•
1.0
•
88
•
N
0
83
79
81
1.5
2.0
2.5
3.0
Capelin biomass,summer
Fig. 10. Monthly growth versus capelin biomass, after deleting the 1987
data point.
I
I
I
R-Square
= 0.2978, p-value = 0.0825
• 80
86
•
<.0 .
<.0
Ln
<.0
Ln~
c:<.o
cu
Q)
E('I")
<.0
C\I
<.0
•
0.05
81
•
0.10
83
0.15
capelinW
0.20
Fig. 11. Mean length of cod caught m commercial bottom trawl vs
capelin biomass.
.
R-Square
= 0.2266, p-value = 0.1389
•
•
83
.
C\J
• 88
•
79
o
(0'
L{)'r-
CO
.........
Q)
-0
CX)
o
• 82
(0
o
. ' 80
1.0
Fig. 12.
1.5
2.0
capelinS
Weight increments vs capelin biomass
2.5
3.0
•
a.
E
Q)
•
••
•
+-'
•
•
•
,
o
o
••
•
+-'
~
o
a.
-
• •
••
..
•
.
•
(f)
c
-
••
••
•
a.
CU
•
•
•
.,
•
••
•
••
•
,
...
•
•
• I
--
•
•
•
••
•
•
• ••
•
•
••
· temp
•
•
•
•
...
Fig. 13.
•
•
•
delta56
•
•
...
•
- ...
•
••
I-
•
•
• •
•
•
• •
•
Q)
•
•
•
lJ
o
~
•
I-
•
...
•
...
•
cod
Scatterplot of all variables in model D.
•
•
•
•
•
port