....
• •t
This paper not to bei cited without prior reference to the author
CM 1986/H:7
Pela.gic Fish Committee
Iriternationai CouncÜ for the
Exploration of the Sea
.,.
.
(
"
MACKEREL STOCK DISCRIMIN AnON USING OTOLITH MORPHOMETRICS
by
P J Hopkins
Marine Laboratory
Vietoria Road
Aberdeen
Scotland
',e
"
SUMMARY
"
The use of otolith dimensions to dlscriminate between mackerel stocks is
examined. Otoliths from pure North Sea and western stockS were measured and the
dimensions used in a discriminant 'function analysis. ,Excellent discriminatiori
between stocks was possible for the sampies taken in 1984 and 1985, ,but the same
discrhninant functions poorly classified pure western fish taken, in 198"2. and 1983.
Thereseems to be heterogeneity within. stocksand the discriminant analysis
probably emphasised sample differences ratherthan stock differences. Principal
components analyses suggested that stock differences may exist which could be
used for discriminatiori given better 'sample coverage•
.,
- -..
INTRODUCnON
"
.
•
~
There are thought to be two stocks of mackerei in European waters, one spawning in
the North Sea arid the other spawning to the west of Britain and Ireland down to the "
Ba)" of Biscay. After spawning the mackerei,. migrate northwards, and, there is
some mixing of the stockS in the late summer arid autumn. These stocks are assessed
separately, so it is important to estimate the proportion of ' North ,Sea and western
, mackerel in commercial catches. The objective of the work described in this paper is
to examine variation in otolith morphology which might be used to discrimiriate
between mackerel stocks.
The most comnion use ofotoliths for stock discrimination has been based on the
measurement of the length of the first growth zone~ If a relationship ,can be
established between otolith, length. and fish length, then the size of. the fish after one
year (the LI length) cari' be backcalculated using the length of the first growth zone.
This might ,differ between stoc:ks~ . 'For example, the peak of the mackerel spawnirig
season to the west of Britain is abouta month earlier than that in the NorthSea, so it
might be expected that the'longer growth period would .result in larger fish at one year
of age~ The first step in such an analysis is to e,nsure' that the relation between otolith.
1
.
...
,
'I •
length and fishlength iso .suitable for making backcalculations. However, ust?g,ari
analysis of covariance with the data split into subsets by year c1ass (Bartlett, et at,
1984) it was foinid that the slopes of the regressions within year c1asses were lower
than that or the ,overall regression.
Moreover, the year c1ass means deviated
significa.ntlY from a straight line. Log transformation did not improve the fit~ .
Another approach is to use the length cf the first ring on the otolith directly rather
than attempt any backcalculatiOn (eg Dawson~ ,1983). DiHerences da not necessarily
imply corresponding differences in fishlength at. one year. of age, because the
relationship between otolith length and fishlength might diHer between the ,two
stockS. Given that otolith dimensions are to be used directly, hewever, there is no
reason to limit measurements to the first ring. It may be more efficient to use several
measUrements at once.
Measurement of.the Otoliths
The coordinates cf, a set of i-eference points oneach. otolith were, recorded (Fig. 1).
This was done by using a camerä ludda attachmenton a microscope.to create a. virtual
image of, the, atolithsuperimposed with thatof a clirsoron a, digitising iablet
(Appendix). From these coordinates, five variables were calculated. Referring to
Figure 1:
•
Ü Vii :width of the
Z)
3)
4)
5)
iirst ring [j-K]
, "
LO : length to the inside of the first ring [R(O)-S(O)] ,
'
LI-LO : size of the first growth incremenf [LI: R(1)';'S(1)]. ,
LZ'::'Ll: size of the second growth increment [LZ= R(Z)-S(Z)]
L3-LZ : size cif .the third growth increment [L3= R(3)-S(3)] .
Otoliths from the 1979, 1980 and j 981 year classes were avail~ble from both North Sea
and western stocks in 1984and 1985. These were taken on, the spa\vning grounds and
were therefore kriown to be pure stocks~ Numbers ",?ere suHicient to perform the
analyses provided the sämples from the two years were combiried~ Iri addition, sampies
of otoliths ,were availa.ble from the Bay of Biscay. in 198Z arid trom south west of
Ireland in 1983. Thenumbers of otoliths in each of the groups are given in Table 1~
Positions of the sampies are shown in Figure Z~
Larger mackerel tend to spawn earlier in the season thari smaller mackerei, so that the
fishon the spawning ground at any one·timeneednot be representative orthe whole
population.. Thüs", compariiig otoliths, from North Sea arid western spawning stocks
could be misleading if the mean fish sizes in the respective sampies
very dirrerent~
. There were no significant differences between themean lengths of fish in the, North
Sea sampies arid these in the western sampies for the 1979 and 1981 year c1asses. For
the 1980. year c1ass the meän length of fish in the North Sea sampies was 35.5 cm
cempared with 34~5 cm in" the western sampies. However, the correlations of the
variables with fishlength were rather weak (Table 2.) so this is unlikely tc influence the
results to any great extent~
are
Linear Discrlminarit Analysis
Linear· eUscriri11nant analysis is a niethOd in which a weighted Imear cembinatlon of
variables (the discriininant ftinction) is fOUnd which maximises the ratio of between
group to. within group sums of squares. The most probable group to which any
iIidividuäl belangs can then be found by calculating its score on the discriminant
runction~
•
,
I
I
....
,
,
.'
Discriminarit functions were calculated between North Sea and Western fish ror each
of the 1979, 1980 and 1981 year classes, using the sampies collected in 1984 and 1985.
Variable means arid the discrirriinant funciion coefficients are shown in Tables 3 to 5~
The succeSs, of the. discriminant functions can 'Oe assessed by construcHng, ,a
contingency table of correct and. incorrect alloeations of individuals to groups~
However, the analysis is done on predefined groups and if the ability of afunctiOn to
discriminate between groupsis tested using, the same iridividuals as those used to
calculate the function the result will be biased; individuals cif a riew sampie would be
unlikely to be allocated to their correct groups with aS much success~ To avoid this
bias, each otolith was removed in turn from the data set and allocated to the North
Sea or Western stock using the, discriminant funcHon calCulated On the remainder of
the data set (Hills, , 1966). The results are Shown in Tables 6 to '8. Box arid whisker
plots of the discriminant scores are shown in Figures'3 ta 5.
Thereis ciearly very goOd discrimlnation between North Sea. and western' otoliths for
all three year classes. From the discriminant fUnctien coefficiimts in Tables 3 to 5,
the grawth increment LI-LO seems the mostconsistent difference between the groups.
In North Sea fish, the size of this increment is 50-60% of that of western fish~
Desplte the consisten6y of, tbe diffe~ences betwee~ North Sea änd western otoÜths for
the three year classes, the discriminant fwictions could not correctly, c1assify fish
caught iri the Bay of Biscay in 1982 and those caught on the spawning ground in 1983
(Table .9)." . For the 1979 year cla.ss iIi the latter group only 9 fish out of 40 were
correctly allocated, and for the 1980 year. c1ass 13. out of 42 werecorrect1y allocated.
The inerement L3-L2 was not properly defiiled in 1981 year c1ass fisb taken in 1983 so
the discriminant functions were not applicable. ,The. reason far, the. high level of
misc1assificatian is that the. L l-LO increments of the, fish sampled in 1983 are much
more similar to those of the North Sea fish sampled in 1984 and 1985 than thaseof the
western fish sampled in thase years(Table9). For the 1979 year class of the Bay of
Biscay, fish caught in 1982; all 20 fish from the more southerly haut were,wrongly
classified aS North Sea stock whereas all 10 fishfrom tbe more northerly haul were
correct1y dassified aS, ,western stock. These results imply that there is significant
heterogeneity within the western stock.
'Priricipal Components Analysis
c
.,
:'
.
,
.
.
,
,
'
.
..,.
i
....
'
.
. . . . . . "
One of the limitations of usirig·ä discriminant function to allocate individuals to /irciups
is that every individual is assumed to belong to one or ather group; there is no way of
dealing, with individuals, which belong to neither. ,A principal: components analysis
uSing the covariarice matrix was therefore carried out far each year class to examine
the possibility that the western otoliths takeln in 1983 differed from bath North Sea
and western otoliths taken in 1984 aiid 1985.
Tables ici toll. show the correlations between the first three component a:xes arid· the
otolith variables far each of the year classes; The similarities between the tables are
notable: Component 1 is highly correlated with LO arid less highly so with Wl iri each
year class, components 2 and 3 are highly correIa.ted with the increments L2-Ll arid
L3';"LZ respectively.
Secltter diagrams of the positions of the otoliths along ccimponent axes i and 2 are
shown in Figtires 6 to 8. The boxes on these diagrams are the projections of the
interquartiles alcing axes 1 and 2 for each group; since tbe axes are Uncarrelated the
3
...
r
boxes represent the area in which tha central 25% of observations are expected~ The
boxes give some measUre of the degree of segregation of the groups in component
space. From the figures it can be seen that while there is considerable overlap
between North Sea and Western otoliths, there is also some degree of segregation;
Moreover the relative positions of the interquartile boxes are reasonably consistent;
though there 1s no segregation. along component 1 for the 1981' year class. .For the
1979 year class the interquartile box for the western' otoliths taken in 1983 is almost
coincident with that of the other western otoliths (Fig. 6).
DISCUSSION
The mean length of the first ring on the otoliths has been found to differ between
mackerel taken in different areas, but' the distributions about the means overlap a
great deal (Dawson, 1983). While these overlaps will almost certainly be reduced when
sufficient numbers have beeIl measUred to treat year classes separately, the uSe of
more thari one otolith dimension c·cin only improve the ability to disci-iminate between
groüps. This means thatyear classes can be. treated separately even with small
sampies. However, a discriminant analysis will heavily weight any variable for which
there are consistent differences between groups, even if these differences, are
themselves small. Great care must therefore be taken to ensure 'that the sampies on
which the functions are calculated äie reilrE~sentative of their respective groups~
In the present anaiyses; the discriminaIit fuiiction weighted the iIicrement LI-LO
almost to the exclusion ofany other dimension~ This is the, first' wiIlter growth
mcrement, and m tne sampies from the North Sea was 50.;.60% the size of that iD. the
sampies from the western stoc:k~, This might be explained by harsher overwmtering
conditions in the North Sea~' However, sampies from the western stock taken in 1983
arid from Southern Biscay in 1982 were Classified aS North Sea stock on the basis of
the L1-LO increments. Sampies from northem Biscay in 1982 were. classified as
western stock. Evidemtly there is a grea~ deal of variation in the L1-LO mcrement
withiri thewestem stock. This might itsel! be related to different.overwintering
conditions for different components of the western stock~ A curious featUre of the
results, however, is the tendenc}r for the mean L1~LO increments to be, either about
0.8-0.9 mm or about 1.5 mm; there seem to be no intermediates. This is difficult to
explain, and at this stage difficulties ~ measurement when rings are poorly defined
cannot be ruled out as a source öf error, though the sharpness of the winter rings may
itself reflect overwintering conditions.
'Ön the ,basis of the present results the discriminant anaiyses cannot be regarded ciS
. having done ariy more than highlight sampIe differences rather than stock differences.
The principal components analyses, however; suggest that stock differences may exist,
though they eire not sharply defined. This implies that with more extensive sampling
of otoliths it. should be possible to calculate more robust discriminant functions but
with less power than that suggested in Tables 6 to 8~ It might be that different
variables. would be better able to' discriminate between stocks. For example, the
dimensions used in this paper are related to growth patterns which are probably
variable within stocks,' wh'ereas measurements describing otolith shape may be more
consistent.
Inconciusion, the results suggest that there is sufficient variabÜity in the otolith
dimensions to warrant niore extensive sampling. The objectives would be to stratify
the sampling by area arid time to examine patterns of variation. With larger and' more
comprehensive sampies it should be possible to recognise pattems of variation within
stocks and to i~entify those most able to discriminate between tliem.
4
e
'.",
-----
---- - - - - - - - - 1
.,
I
ACKNOWLEDGEMENTS
I would like to thank I Leaver for help with the collection of data. I am also grateful
to Mrs H Gill, E Bakken and A Eltink for supplying otoliths and catch data, and to
Mr M Walsh and Mr J A Pope for helpful comments on an earlier draft.
REFERENCES
Bartlett, J.R., Randerson, P.F., Williams, R. and Ellis, D.M. (1984) The use of
analysis of covariance in the back-calculation of growth in fish. J. Fish Biol. 24:
201-213.
Dawson, W.A. (1983) A preliminary analysis of mackerel (Scomber scombrus L.)
otolith (LI) measurements. ICES CM 1983/H:29.
•
Hills, M. (1966) Allocation rules and their error rates. J. R. Statist. Soc. (B), 28: 131•
•
5
.
• t
..
I
Appendix
A SIMPLE DIGITISING SYSTEM FOR MORPHOMETRIC MEASUREMENTS
by
P J Hopkins and P A Kunzlik
INTRODUCTION
•
Many applications require a large number of measurements to be made from images
seen through a microscope, for example size frequency distributions of eggs or larvae
and the measurement of otolith or scale increments. These measurements could in
principle be automated using an image analysis system, but the expense of such
systems and the extent of programming involved to discriminate between components
of the image are often prohibitive. A stage micrometer is often used for manual
measurements, but this is slow and requires the object to be set firmly enough to be
moved about the stage without disturbance.
This may be unsuitable for such
applications aS the measurement of organisms in plankton sampIes. In addition, stage
micrometer measurements usually comprise linear distances only; measurements of
curves and of areas are generaily approximated or neglected.
A SIMPLE DIGITISING SYSTEM
•
Winters (1981) used a camera-Iucida attachment on a microscope to enable him to
draw sandeel otoliths, from microscope images and subsequently measure increments
from the drawing. The system described here uses the same principle, but replaces
the drawing paper with a digitising tablet and a cursor. In this case, rather than
projecting an image of the object the camera-Iucida superimposes a laterally correct
and erect virtual image cf the tablet and cursor upon that of the object. A
microcomputer is used to process and store the co-ordinates or measurements from
the digitising tablet.
The system used at the Marine Laboratory comprises a
Summagraphics MM1201 data tablet with a four-button cursor, a BBC microcomputer
with dual disc drives and a Nikon SM2-10 stereo-microscope with camera-Iucida
attachment. (The use of trade names does not imply eridorsement of the products.)
APPLICATIONS
The system has successfully been used for a number of applications. These include
the measurement of larvae from herring larval surveys with automatic recording of
size frequency distributions.
This application is also being evaluated at other
laboratories. The system has also been used to measure mackerelotolith size, shape
arid growth increments for stock discrimination (this paper) and for the measuremEmt
of cell areas in slide preparations.
REFERENCES
Winters, G.H. (1981) Growth patterns in sand lance, Ammodytes dubius, from the
Grand Bank. Can. J. Fish. Aquat. Sei. 38: 841-846.
• I
...
Table 1
Numbers of otoliths used in the analyses. The third ring was undefined for
1981 year dass fish taken in 1982 and 1983. The second ring was undefined
for 1980 year dass fish taken in 1982.
Year dass
1980
1981
Area
Year
Month
1979
Central North Sea
SW of Ireland
1985
1985
April
April/May
17
13
23
25
6
41
Central North Sea
SW of Ireland
1984
1984
June
April/May
18
20
19
35
23
41
SW of Ireland
1983
May/June
40
-42
Biscay
1982
April
30
•
Table 2
Correlations coefficients between otolith variables and fishlength.
Year dasses:
1979
Wl
LO
LI-LO
L2-Ll
L3-L2
0.150
0.236
-0.230
0.155
0.017 .
North Sea
1980
0.281
0.405
0.046
-0.277
-0.245
1981
1979
-0.089
-0.196
-0.388
0.458
0.242
0.567
0.475
-0.051
-0.237
0.107
.
•
Western
1980
0.285
0.179
0.074
-0.006
-0.143
1981
0.140
0.100
0.128
-0.132
0.191
, "
,
.
,
Table 3
Variable means and discriminant function coefficients.
1984 and 1985 samples combined.
. Variable Means
Western
N orth Sea
Wl
LO
LI-LO
L2-Ll
L3-L2
Table 4
0.920
2.351
0.142
0.769
0.353
1.020
2.547
0.086
0.827
0.374
Wl
LO
LI-LO
L2-Ll
L3-L2
Table 5
0.927
2.340
0.143
0.820
0.425
0.999
2.561
0.085
0.865
0.388
-6.82
-3.58
51.84
-3.36
-9.01
1.001
2.629
0.153
0.737
0.371
1.103
2.643
0.079
0.834
0.408
1980 year dass,
Discriminant Function Coefficients
-12.00
-3.81
55.52
-5.52
-2.19
Variable means and discriminant function coefficients.
1984 and 1985 samples combined.
Variable Means
Western
N orth Sea
Wl
LO
L1-LO
L2-L1
L3-L2
Discriminant Function Coefficients
Variable means and discriminant function coefficients.
1984 and 1985 samples combined.
Variable Means
Western
N orth Sea
1979 year dass,
1981 year dass,
Discriminant Function Coefficients
-15.15
0.79
69.26
-5.89
-2.78
,
.
~
..
Allocation of fish to groups. 1979 year dass.
Table 6
Western
Predicted Group
N orth Sea
29
4
33
North Sea
7
28
35
All
36
32
68
Western
True
Group
= 28.7 with 1 df
Chi-square
•
All
Allocation of fish to groups. 1980 year dass.
Table 7
Western
Western
Predicted Group
North Sea
52
8
60
4
38
42
56
45
102
True
Group
North Sea
All
All
Chi-square = 56.3 with 1 df
Table 8
Allocation of fish to groups. 1981 year dass.
Western
Western
Predicted Group
North Sea
70
12
82
2
23
25
72
35
107
True
Group
North Sea
All
All
Chi-square
=48.6 with 1 df
____ - - - - - - - - - -
1
,
. ..'
Table 9
Mean values of the otolith dimensions for sampies taken in 198Z and 1983.
Sampie
L3-L2
Proportion
Correct1y Classified
W1
LO
Mean Values
L2-L1
L1-LO
0.902
0.955
2.380
2.440
0.079
0.087
0.811
0.784
0.344
0.412
9/40
13/42
0.981
1.059
2.547
2.757
0.146
0.059
0.673
0.627
0.247
0.298
10/10
0/20
SW Ireland 1983
1979 year dass
1980 year dass
Biscay 198Z
1979 year dass
1979 year dass
•
...
..
~
Table 10 to 12
Correlations between component axes and otolith variables.
1979 year dass
Wl
LO
LI-LO
L2-LI
L3-L2
I
Component
2
3
0.517
0.974
-0.039
-0.461
0.034
-0.001
0.210
-0.259
0.886
-0.098
-0.495
0.049
0.223
0.011
0.850
•
1980 year dass
W1
LO
LI-LO
L2-L1
L3-L2
1
Component
2
3
0.664
0.973
-0.211
-0.498
-0.217
-0.053
0.217
-0.166
0.865
-0.200
-0.171
0.066
0.085
0.049
0.951
1981 year dass
Component
W1
LO
. L1-LO
L2-L1
L3-L2
1
2
3
0.369
0.996
0.014
-0.125
0.057
-0.147
0.082
-0.200
0.989
0.173
-0.101
-0.016
-0.148
-0.078
0.982
...
., .
.
•
I
,
.
..
'.·
·R(···)
...........
,
c
FIGURE 1
~itions
of the reference points recorded
on each otolith.
,.
07 08 OS EO Ei E2 E3' E4 E5 E6 E7 ES ES FO Fl F2 F3 F4 F~ F6
44
44
43
.,
0
42
.. '
•
41
43
42
-
41
0
40
40
39
39
..
38
38,
37
37
36
35
34
•
33
33
32
32
31
31
30
.
29
29
" 28
27
26
o •
~
~
d-'~I\
\
l--+---l....l2..l..4-0~--+---+--+--+-+ltr-+VV--=~lJ,.
',~~
A
1----+--+---I--+-+---+---+---+a.....
."
24
v
23
22
-
V
r
:~
, .
1985
'
N~.
o
1984
tl..
A
1983
V
1982
'" 1\
0
"
27
.
"SamPleS taken in
•
.
2 er-
/7
o
.~
'-"--+--f~-+--+--+--+--+---+--f--+----fi
25
•
30
'2 6
-
-25
24
23
22
,
21
21
20
.
.
20
.
19
19
18
18
....
17
17
16
.I~
.-..-+--+---+--+-.... ~
V
I';'
...'
J
}~
.15
07 08 09 EO Ei E2 E3 E4 E5 E6 E7 E8 E9 FO F1 F2 F3 F4 F5 F6
FIGURE 2
Sampling positions in each year.
16
.15
.. ...
;.
- 1 + ] - western
----f_+
------ North
o
-4
-8
FIGURE 3
Sen
8
4
1979 year class
---western
+
North Sea
o
-4
FIGURE 4
1980 year class
+
e
North Sea
0
-4
western
I.
+ .~
FIGURE 5
12
8
4
8
1981 year class
FIGURES 3, 4, 5
Box and whisker plots showing the medians, quartiles
and extremes of the discriminant scores for North Sea
and Western fish. There is good discrimination
between stocks for all three year classes.
_=="" __·'·__ ·c"""'~~_
.. "'=-. - - __ - - - - . - - - - _ . - .. ~--
.
ex
r'
\Je.tern 1983
\J•• te,.n t084
\J•• te,.n t986
Nodh Sea 1984
No,.th S.a 1086
o
D
+
A
PCA 1979
y~arclass
-.
otoliths
2.00
c
0
-f-
o
d
l-
x
d
>
4-
0
~
+
x
X
C\I
Ql
c
X A
+
1. 75
°iC"Jn
....C
+
X
western
1.50
0
0E
0
0
0
0
n
h
0
X
I
I
~
~D-,
X
n
I
X
~X
A
0
Ii
X
+
~
CJ
X
1\
)<.X
+
+
North
<
:~
+:
x:
1~.o-v_9___ - --'
Ok
0
Sea
A
+
+
+
o
+
0
A
X
o
1 .25 -
+ "
X~
X
,
X
U
A
X
0:J XIX ~
....1
western 19 83
o
+
/!)
.L
>
X
+
X
o
o n
o
X
o
1 .00 -;1'-,- - - - - - - - - ' - - - - - - - - - ' ' - - - - - - - - 1.5
1.8
2.1
2.4
FIGURE 6
Component
(59
%
1
of variation)
2.7
3.0
·"
x
o
\J•• tern 1083
,
.,
Y•• t..rn 1084
Y•• t.ern 1986
Nort.n Sea 1984
Nortn S.a 1886
o
+
A
PCA 1980 yearc/ass oto/iths
2.00
c:
0
°
4-
d
fot
"d
>
X
X
~
0
1. 75
~
0
..:t
r:J
-
("..l
Q}
c
X
X
+
+
A
0+
h.
[]
+
+
A
~
N
....c
!'.
AOh.
+X
+
0
tJ.
1.50
r:J
0
ox+
0
E
Xl
r:J
0
ü
~
western
0
°0
0
A 0
1 .25
0
X
~
X x·
X
++
X
X tJ.
tJ.
western 1983
Q - _!.
0
A
A
A
X
r:J
n I<
+
Sea
X
a.
North
0
X
r:J
X
0
0
'R
0
(1
0
1.00
.
._.:.
1.5
.L.-.
1.B
FIGURE 7
L-....
..
._.•
I-
2.4
2.1
Component
(62 %
1
of variation)
_
1 -------_ _ _ .1-
2.7
3.0
o
"
A
\J• .t.,.n 1084
\oI•• t.,." 1086
North S.es 1084
North S.es 1086
PCA /98/ yearclass otollths
1.65
c
o
13
C-
d
>
'l-
o
1.40
°
o~
<:>
+
m
D
....
C
Ql
C
Ä+
o
CI.
E
o
fJ
0
o
°
-
°
q.
°
o
0.65-+,--2.2
FIGURE 8
_ L.
2.4
.
CJ
0
.....
pOo
""v
.-
o
0
t.°
ro
'0
1\
1"'"
W
0
I,
~<
CJ
IJ
North Sea..
+
Western
Cb
°
.
•.L-1_ _.
2.8
2.6
Component
(49%
lJ
o
°
OD
fJ
..._ _ .. L
o
I
+I,
°
+
n
lJ
°
+
o rJ
CJf]
.Fit
11
+
'0
n
0
°
°
D
+
CJ
?,
+
° °
°+0fJ D
0""
~
°
o.so
0
0
(J
()
CJ
o
1. 15
o
°
+
°
1
of variation)
.L
3.0·