Biological Journal of the Linnean Society (2001), 74: 237-253. With 6 figures
doi: l0.1006/bij1.2001.0573,available online at httpj//www.idealibrary.com on I D
E hl@
Variation patterns of bilateral characters: variation
among characters and among populations in the
White Sea herring, Clupea pallasi marisalbi (Berg)
(Clupeidae, Teleosti)
@
DMITRY L. LAJUS
Zoological Institute, Russian Academy of Sciences, Universitetskaya nab.l, 199034, St. Petersburg,
Russia
Received 13 November 2000; accepted for publication 12 J u n e 2001
Phenotypic variation in two populations of the White Sea herring Clupea pallasi marisalbi (Berg) (spring spawners
and summer spawners), based on 21 meristic and 21 morphometric bilateral characters, has been studied. Total
phenotypic variance was partitioned into a within-individual or stochastic component (fluctuating asymmetry) and
an among-individual or factorial component, reflecting heterogeneity among individuals and resulting from the
diversity of genotypes and environments. Both standardized stochastic and factorial components show clear negative
correlations with means across characters. Negative correlation of the factorial components with means is in
contradiction to the commonly accepted explanation of negative means-standardized variances association. Slopes
of regression of standardized stochastic variances on means in meristic characters was significantly higher in
summer spawners than in spring spawners, and results in discordance of stochastic variance across characters: it
is higher in spring spawners for low and average variability characters and does not differ for both populations for
high variability characters. The populations do not show notable differences in variation of morphometric characters.
Consideration of other available data on these populations, such as spawning behaviour and salinity resistance of
larvae, suggests that the lower slope of regression of stochastic variances on means is associated with the reduced
viability of spring spawners.
0 2001 The Linnean Society of London
ADDITIONAL KEYWORDS: Clupea pallasi - developmental stability
variation - population asymmetry parameter.
INTRODUCTION
Morphological (phenotypic) variation among individuals within a population consists of several components. Genotypic variation reflects the genetic
differences among individuals. Modification variation
results from differences in the environment during a
character’s formation and, thus, reflects the diversity
of the environment during the character’s formative
period. These two components together describe
heterogeneity of individuals within a population. There
is also within-individual variation, which is manifested
in the differences between genetically identical structures that have developed under the same environmental conditions. The latter was first studied
* Corresponding author. E-mail: [email protected]
00244066/01/100237 + 17 $35.00/0
-
fluctuating asymmetry - phenotypic
by Pearson (1901) and then called “stochastic variation”
by Astaurov (1930). According to Astaurov, any process
of formation in an organism has some self-dependent
variation, which cannot be reduced either to genotypic
differences o r to the direct effect of the environment.
At present, it is usually proposed that this kind of
variation results from developmental instability, which
reflects the ability of a n organism to develop the same
phenotype under the same environmental conditions.
It is considered to be a source of phenotypic variation
equivalent to genotype and environmental diversity
(Gartner, 1990; Lajus, Graham & Kozhara, in press).
It is commonly measured by fluctuating asymmetry, i.e.
variance in random deviations from perfect bilateral
symmetry (Mather, 1953; Palmer & Strobeck, 1986,
1992; Zakharov, 1987).
In a non-symmetric structure, two kinds of variation,
237
0 2001 The Linnean Society of London
heterogeneity among individuals and within-individual variation, impact the total phenotypic variance and it is impossible to separate them. Most of
the ways of partitioning total phenotypic variance
require special experimentation and are very difficult
to apply to populations of outbred species in natural
conditions. I n bilaterally symmetric structures, differences between sides, i.e. fluctuating asymmetry, are
due to stochastic variation and it is possible to divide
the total variance into stochastic and factorial (heterogeneity of individuals) components using a special
index of fluctuating asymmetry. The contribution of
asymmetry in the total variance has been measured
in different ways (Jolicoeur, 1963; Bader, 1965; Leamy,
1984: Kozhara, 1994; Klingenberg & McIntyre, 1998).
The contribution of the stochastic component varies
significantly for different kinds of characters and difierent organisms and often comprises more than half
the total variance (Lajus et al., in press). The factorial
component includes genotypic variation, environmental effccts, and their interaction; hence it can be
considered as a maximum estimate of genetic heterogeneity (Kozhara, 1994). Some studies show that the
contribution of the component caused by the diversity
of thv environment is notably smaller than the contribution of‘ the genotypic or stochastic component
{(Xrtner. 1990; Kearsey & Pooni, 1996).
In considering morphological variation, it is necessary 10 differentiate variation among characters from
\-ariation among populations.
Vuriatinr?aiiiong characters
I he negative correlation between a character’s coefficient of variation and its size was first reported
hy Pcarson & Davin (1924), then by Huestis (19251,
Koginskii (1$359), Yablokov (1966, 1974) and Yegorov
( 1969. 1973); it was then treated mathematically by
I,ande ( 1 9 7 ) . According to Soule’s (1982) hypothesis,
each morphometric character consists of many elements having their own stochastic variation. Thus, the
greater the size of a character, the more elements
it includes. Since the stochastic variations of these
c.ompoi1ent.s partly compensate each other, the effect
of such compensation increases with the number of
elements. i.e. with size of the character. Consequently,
the standardized stochastic variance negatively correlates with the size of a character. Because the total
phenotypic variance reflects the stochastic variance, it
also decreases as the character’s size increases (standardizcd indexes of variability, such as coefficient of
variation. are used). Therefore, according t o Soule’s
hypothesis. only stochastic, but not non-stochastic,
components (standardized variances are considered)
should be correlated with means. Another consequence
of the hypothesis is that the square root of means
I >
should be the best transformation t o produce linear
associations between variances and means. In this
paper I study stochastic and non-stochastic (factorial)
components of both meristic and morphometric characters.
Variation among populations across characters
One of the first questions that arises when populations
are compared is whether o r not the results of comparisons depend on the characters used. If characters
vary concordantly, then the results will not depend on
the characters used; for instance, if population A is
characterized by a higher fluctuating asymmetry than
population B for one character, there is a tendency
that population A will also be more asymmetric for
other characters. In such a case it is possible to use any
character for analysis. Otherwise, the interpretation of
results becomes more difficult.
Soule (1967) and other authors (Felley, 1980; Kat,
1982; Jagoe & Haines, 1985; Zakharov, 1987) reported
concordance across characters among populations.
Based on his results Soule proposed a ’population
asymmetry parameter’, i.e. an integrated index of
population fluctuating asymmetry. Many studies, however, reported that deviations from perfect concordance
in fluctuating asymmetry are possible (for instance,
Kozhara, 1989, 1994; Leamy, 1992; Leary, Allendorf
& Knudsen, 1992; Clarke, 1998; Campbell, Emlen &
Hershberger, 1998; Auffrey, Debat & Alibert, 1999).
Furthermore, there are often no differences in fluctuating asymmetry between samples in cases where
there are evident reasons to expect them (Siege1 &
Doyle, 1975; Ames, Felley & Smith, 1979; Felley, 1980;
Jagoe & Haines, 1985; Drover et al., 1999; Lu &
Bernatchez, 1999). Many such cases probably remain
unpublished, because positive results tend to be published more often than negative ones (see Palmer
(1999) and Simmons et al. (1999) on meta-analysis of
association between fluctuating asymmetry and sexual
selection and Vdlestad, Hindar & Mdler (1999) on
association between asymmetry and heterozygosity).
Fluctuating asymmetry, the most common measure
of developmental stability, has been proposed for assessing stress in natural populations (Zakharov, 1987,
1989; Leary & Allendorf, 1989; Parsons, 1992; Graham,
Emlen & Freeman, 1993; Graham, Freeman & Emlen,
1993a; Moller & Swaddle, 1997). Therefore, i t is important to know what characters are most likely t o be
useful for monitoring. Soule & Cuzin-Roudy (1982)
suggested that characters with high heritability,
which are less critical t o fitness, should be the most
sensitive t o stress. Alados, Escos & Emlen (1993), who
studied hake otholiths, concluded that asymmetry of
shape is more sensitive to stress than asymmetry of
simple morphometric characters. An explanation for
VARIATION PATTERNS OF BILATERAL CHARACTERS
why this may be so is proposed by Emlen, Freeman &
Graham (1993). Some convenient characters for the
analysis of developmental stability in different groups
of animals and plants are described in Graham et al.
(1993a).
The prevailing approach is to associate fluctuating
asymmetry with either genetic or environmental variation among populations or individuals. The main
point of interest in these studies is to use fluctuating
asymmetry as a measure of developmental instability.
This approach is based on studies carried out in the
1950s by Mather (1953), Tebb & Thoday (1954), Thoday
(1958), Beardmore (1960) and Reeve (1960). Another
approach treats within-individual variation and fluctuating asymmetry as the stochastic component of
total phenotypic variance. Although historically this
approach appeared earlier (Pearson, 1901; Astaurov,
1930) than the former, less attention was paid to it.
In the present study I mainly follow Pearson's and
Astaurov's approach, attempting to analyse consistent
patterns of fluctuating asymmetry by analysing it together with other manifestations of phenotypic variation.
I studied two White Sea herring (Clupea pallasi
marisalbi (Berg)) populations from Kandalaksha Bay.
These two populations may be considered genetically
close but ecologically distinct. They differ in their
life history, primarily in respect to spawning ecology.
Summer spawners spawn in June, a t a temperature
of 8-12"C, whereas spring spawners spawn in April,
at a temperature of about 0°C. The spring spawners
occupy a peculiar place among herring populations
because of the extremely low temperature of spawning
and early development. Summer spawners show a
higher resistance of embryos and larvae to low salinity
(Ivanchenko & Lajus, 1985; Dushkina, 1988). Evidence
of genetic similarity of these populations is the absence
of differences in frequency of the chromosomal Robertsonian rearrangement, although chromosomal differences occur between these two populations and other
populations of the White Sea herring (Lajus, 1989,
1996a).
In this study I analysed variation in patterns of
morphological characters in two populations of the
White Sea herring. I attempted to find general
patterns of morphological variation typical for both
populations and to determine whether morphological
differences between them depend on chosen characters. The main methodological basis for the study
is the partitioning of total phenotypic variance into
stochastic and factorial components with use of
bilateral characters. I used cranial bones, which
provide a very high diversity of characters and
are convenient for analysis. The use of numerous
characters increased the statistical power for amongcharacter comparisons.
239
MATERIAL AND METHODS
Fishes were collected in Chupa Inlet (White Sea, Kandalaksha Bay, 66"28'N, 33"30'E). All were adult and
in spawning condition. Spring spawners ( N = 60) were
obtained in April 1990 from commercial traps. Their
standard length was 12-24cm, and their age (determined by scale readings) ranged from 4 t o 9 years.
Five males and five females from each age group were
analysed. Summer spawners ( N = 32, 18 males and 14
females) were collected in June 1991 using gillnets.
Their standard length was 20-25cm, and their age
ranged from 4 to 7 years. Fresh specimens were treated
in 2% aqueous sodium hydroxide during 10-30 h a t a
temperature of 40-50°C. After treatment, soft tissues
were washed out with water and the clean bones were
dried.
Forty-two bilateral characters (21 meristic and 21
morphometric) were examined (listed in Appendix).
One of the main methodological requirements for
comparing the variation of characters is that they
must be anatomically and embryologically similar. The
meristic characters used in this study are the numbers
of holes in cranial bones. These holes form fat-filled
lacunae within the bone matrix and so decrease weight.
Thus, they can be considered anatomically and functionally similar. In this study, the set of characters
was changed from that in earlier studies (Lajus, 1991,
1996b) to avoid functional and anatomical dissimilarity. No special selection was made regarding
morphometric characters, although, all characters
used are from the cranial bones and hence can be
considered to be similar.
The standardized means were calculated as predicted values of linear regression of the characters on
standard length for length of 20 cm.
The procedure for calculation of size-standardized
indices of variation is based on Lajus & Alekseev,
2000):
(1) Calculation of the first principal component (PC1)
based on 10 log-transformed morphometric characters highly correlated ( r= 0.90-0.98) with size
(characters 26,28,29,33,36,38,39,40,41and 42);
(2) Regression of each character on PC1;
(3) Dividing residuals by predicted values.
Data obtained were size-standardized residuals.
They were used for computations of the total variance
(i') and its stochastic component (G:), based on the
factor model for bilateral traits, described by Kozhara
(1989, 1994):
G2=Z(X,-M)2/2(N- I),
04 = Z(R -L)'/2N,
where X , is the sum of the left and right manifestations
of the character, M is the mean value, R is the right
2-1-0
I). I,. I A J U S
.____-
~-
and I , is the left manifestation of the character, and
;I:is the nuniber of individuals.
Thcx factorial Component was calculated as the difference between the total variance and the stochastic
variance. The ratio of the stochastic component t o the
total phenotypic variance is the relative stochastic
\m%tion also called relative fluctuating asymmetry
(Ideamy.1992).
The stochastic variation obtained in this way is the
observed but not, the true stochastic variance. The
observed stochastic variance includes measurement
error as well. To evaluate measurement error I made
repeated measurements on 18 specimens (36 measurements from one specimen) from the summer-spawning population. Measurement error was estimated with
the same formula as for the stochastic component (see
abovi?). but using XIinstead of L and X 2 instead of
11. where X,and X 2 are values from two consequent
replicate measurements (Lajus & Alekseev, 2000).The
true stochastic component was estimated as the difference between observed stochastic component and
the ineasurement error.
Kurtosis and skewness were analysed both for the
distribution of standardized values (left and right together, kurtosis ( R , L ) and skewness (R, L ) ) and for
the distribution of the difference between left and right
standardized values (kurtosis ( R- L) and skewness
(I? 1,)).
In summary, the following parameters of characters
have bern analysed: (1) the standardized stochastic
component of total variance, (2) the standardised factorial component of t.otal variance, ( 3 )relative stochastic variation, (4) standardized mean. (5) kurtosis (R,
/,I,( 6 )kurtosis(R--L), (7)skewness(R,L),(8)skewness
( R-~ 1,). 1 also analysed measurement error.
~
RESULTS
Partitioning the total phenotypic variance into stochastic and factorial components using analysis of variance is valid only for characters exhibiting fluctuating
asymmetry, and not antisymmetry or directional asymmetry. Only one of the 42 analysed characters in spring
spawners. and two in the summer spawners (3.6%),
showed significant (P<0.0t5,or 5%)) deviations from
iluctuating asymmetry. Application of a sequential
Konferroni test for multiple characters (Rice, 1989)
indicated that this can be attributed to sampling error.
Thus. asymmetry in the present paper should be considered as fluctuating asymmetry.
MEASUREhlEKT ERROR
Kesul ts of the assessment of measurement errors are
~ h o w nin Table 1. In both meristic characters and
morphonietric characters rather high differences are
observed between characters. This can be explained
partly by the fact that measurement error is negatively
(though non-significantly) correlated with means in
the meristic characters. A similar pattern is observed
for morphometric characters. Here, however the negative correlation is higher ( r = -0.504 - 0.51 1, P<0.05).
Contribution of measurement error into observed
stochastic variation ranged from 0 to 46'% (usually
5-15%) in meristic characters and from 0.1 to 43?h
(usually 3-10%) in morphometric characters. In both
types of characters the contribution of measurement
error to the observed stochastic variation is positively
correlated with the mean, i.e. the relative nccuracy of
measuring characters with higher means is lower than
that for characters with low means.
VARIATION AMONG CHARACTERS
Ranges of variances and means
The standardized variance (both stochastic and f'actorial) of meristic characters is approximately 100-200
times higher than that of the morphometric characters
(Table 1).Within each group of characters, the range
of variance is also rather large. In the most variable
meristic characters, the stochastic component is 30-50
times higher than that in the least variable. Differences
for the factorial component are 15-20-fold. In morphometric characters, the range is greater: 300-500
times for the stochastic component and 70-170 for the
factorial component. The range in size is from 1.2 t o
27 holes for meristic characters and from 19 to 270
relative units (0.95-13.5 mm) in morphonietric ones.
Relative stochastic variation varies from 1 3 to 78%)in
meristic characters and from 5 t o 60%in morphometric
ones. Differences between characters in levels of factorial and stochastic variances and means are consistent between characters. Their ranking is very
similar for spring and summer spawners (Table 1).
Kurtosis a n d skewness
Kurtosis and skewness of R-L distributions do not
show deviations from normality over the whole set of
characters. They are equally positive and negative
L ) show
(Table 2). Kurtosis ( R , L ) and skewness (R,
similar deviations from normality for both populations.
Kurtosis (R, L ) for both meristic and morphometric
characters are frequently significantly negative (platykurtic). Skewness (R, L) is positive for nearly all
meristic characters, whereas in morphonietric characters it is equally negative and positive (Table %).
Association between para nzeters
While the association between variances and means
is not linear, I tested two different ways to achieve
linearity from the data. First. I used the square root
0.010622
0.023994
0.003744
0.001519
0.001209
0.004721
0.000397
0.002429
0.008415
0.002435
0.019343
0.028925
0.008657
0.004476
0.00517:1
0.006818
0.000615
0.002401
0.003488
0.000459
0.004904
7
8
9
10
11
12
13
14
15
I6
17
18
19
20
21
6
2
3
4
5
1
Morphomctric
22
0.007447
23
0.021018
24
0.001536
25
0.000418
26
0.000393
27
0.003756
28
0.000130
29
0.001233
30
0.004319
31
0.000870
32
0.013539
33
0.016302
34
0.002467
35
0.002611
:3c7
0.005225
37
0.000394
:I8
0.000162
:I9
0.000944
40
0.000460
$1
0.000070
.I2
0,000708
FC
0.268475
0.388489
0.253229
0.181 4 11
0.052543
0.043196
0.077 129
0.046927
0.039742
0.035426
0.478914
0.34246 I
0.064223
0.338823
0.050343
0.1 19875
0.027586
0.105888
0.097901
0.338030
0.069476
SC
~
0.143433
0.155657
0.212625
0.145612
0.043880
0.088814
0.041685
0.080552
0.031475
0.042962
0.478192
0.610913
0.037749
0.135187
0.118443
0.170809
0.070682
0.134464
0.125828
0.128120
0.022486
Meristic
Charactc>r
~
0.1:3:3
0.126
0.117
0.412
0.467
0.291
0.216
0.245
0.443
0.246
0.337
0.339
0.263
0.412
0.360
0.22'2
0.368
0.503
0.055
0.208
0.125
0.348
0.286
0.456
0.445
0.455
0.673
0.351
0.632
0.44'2
0.548
0.500
0.641
0.370
0.285
0.702
0.588
0.719
0.559
0.562
0.275
0.245
KSV
82.83
20.80
11 2.90
248.74
206.37
62.86
153.33
112.11
39.49
103.96
34.17
29.12
54.06
98.78
137.41
147.81
180.58
91.74
72.76
219.86
58.40
4.38
3.54
8.42
7.10
9.31
12.11
21.85
4.25
19.68
8.46
1.24
1.19
7.03
9.76
2.63
3.95
7.40
2.53
8.62
3.71
11.80
SM
~
~
-
-0.663
-0.545
0.498
-0.014
0.256
-0.239
-0.224
-0.308
-0.115
0.186
-0.089
0.216
--0.123
0.113
-0.530
0.650
0.063
0.284
0.019
0.186
0.246
-
--0.673
-0.463
-0.579
-0.505
0.255
-0.133
0.524
0.770
-0.155
-0.213
-0.931
-0.842
-0.023
-0.681
0.086
-0.527
- 0.072
-0.383
-0.469
-0.102
-0.201
Kit!
Spring spawners
-
-0.607
-0.057
0.822
- 0.030
-0.588
-0.572
-0.415
0.482
-0.047
0.283
1.115
-0.201
-0.218
0.591
0.976
0.282
0.227
0.759
0.591
0.476
0.502
-
,
0.301
0.416
0.791
0 5 11
0.663
-0.773
0.066
-0.069
-0.118
--0.551
-0.072
-0.165
1.019
0.110
-0.454
-0.477
0.682
-0.688
0.450
0.344
-0.816
K,,
-
-0.118
0.378
-0.054
-0.081
-0.295
-0.002
-0.102
-0.095
0.332
0.169
-0.189
0.220
--0.269
-0.119
-0.167
0.078
0.246
0.027
-0.069
-0.223
0.075
0.427
0.595
0.504
0.384
0.456
0.289
0.440
0.849
0.009
0.180
0.300
0.274
0.578
0.372
0.498
0.465
0.503
0.510
0.501
0.674
0.648
Si;,
-0.031
-0.253
0.564
0.322
-0.263
0.048
0.178
-0.075
0.021
-0.101
0.661
-0.239
0.054
-0.126
0.306
-0.241
0.228
0.064
0.172
0.<'106
0.532
0.224
-0.507
0.113
0.257
0.624
0.113
0.070
-0.219
-- 0.273
-0.243
-0.292
0.391
0.232
-0.013
0.126
0.070
-0.185
-0.025
-0.091
-0.011
-0.272
S,;
0.009700
0.021527
0.001136
0.000320
0.000307
0.005053
0.000065
0.001 723
0.004451
0.00081 1
0.017550
0.009253
0.003978
0.003338
0.001576
0.000334
0.000128
0.000595
0.000424
0.000043
0.00 1853
0.137677
0.198818
0.062862
0.066457
0.026584
0.029096
0.020109
0.084404
0.010328
0.032604
0.529640
0.485243
0.045546
0.024387
0.071417
0.080372
0.05 1156
0.208947
0.048526
0.15 1647
0.010279
SC
0.024981
0.017821
0.003446
0.001537
0.000873
0.008779
0.000328
0.001141
0.004883
0.001718
0.032665
0.038276
0.005104
0.002585
0.005667
0.003834
0.000461
0.001546
0.001514
0.0002"6
0.003089
0.421781
0.119669
0.227340
0.432507
0.032246
0.067159
0.067 153
0,127001
0.047727
0.027535
0.455909
0.214260
0.071915
0.117388
0.020419
0,155886
0.056569
0.064412
0.075917
0.208930
0.065848
PC
0.280
0.547
0.248
0.172
0.260
0.365
0.166
0.602
0.477
0.321
0.349
0.195
0.438
0.564
0.218
0.080
0.217
0.278
0.219
0.162
0.375
0.246
0.624
0.217
0.133
0.452
0.302
0.230
0.399
0.178
0.542
0.537
0.694
0.388
0.172
0.778
0.340
0.475
0.764
0.390
0.421
0.135
RSV
64.23
17.40
125.28
257.40
199.80
62.07
153.31
118.03
40.51
109.67
33.94
25.82
56.27
93.08
158.76
148.92
176.60
92.20
76.15
245.74
60.88
3.46
3.01
4.04
6.35
8.59
11.32
16.92
3.07
20.40
7.41
1.24
1.07
6.91
9.46
2.65
4.12
6.98
1.65
5.62
2.42
12.22
SM
-
-0.222
-0.255
-0.469
-0.110
-0.261
1.126
0.372
-0.219
-0.515
0.065
-0.593
0.638
-0.017
-0.368
-0.316
-0.454
-0.231
-0.736
-0.749
-0.119
-0.775
-0.677
-0.503
-0.661
-0.788
-0.154
0.009
-0.721
-0.279
-0.425
-0.865
-0.629
-0.487
-0.722
- 1.008
-0.972
-0.364
0.001
-0.512
-0.081
-0.576
-0.096
Kifi
Summer spawners
i
Si,,
-0.573
-0.084
-0.191
0.638
-0.780
0.691
-0.530
0.214
-0.179
0.484
2.478
0.458
0.321
-0.637
0.465
-0.729
-0.475
0.194
0.042
0.550
0.927
0.293
0.545
-0.013
0.180
-0.321
0.979
0.370
-0.217
0.361
0.209
- 0.430
0.092
- 0.374
- 0.263
-0.051
0.326
0.123
0.049
0.161
-0.237
0.090
-0.005
0.562
0.431
0.422
-0.191
0.464
0.259
0.590
0.874 -0.269
1.362
0.574
0.950
0.164
-0.913
0.308
1.031
0.312
0.020 -0.065
-0.299
0.369
-0.834
0.181
0.047
0.280
-0.273
0.249
-0.224
0.131
0.415
0.358
0.727
0.684
0.645
1.699
0.516
-0.216
0.432
-0.862
-0.114
0.593
K,,
i
-0.179
-0.214
0.332
0.620
-0.179
0.187
-0.356
0.250
-0.132
0.525
0.057
0.61 1
-0.184
0.259
-0.182
--0.125
-0.249
0.894
0.218
0.188
0.887
0.299
0.168
0.415
-0.430
-0.268
-0.625
0.484
-0.080
0.010
0.568
-0.359
0.120
-0.415
0.212
0.175
0.338
0.192
0.419
-0.305
-0.015
0.249
Si,
0.000135
0.001097
0.000278
0.000048
0.000045
0.000323
0.000049
0.000034
0.000238
0.000048
0.000107
0.000489
0.000039
0.000020
0.000005
0.000127
0.000010
0.000129
0.000034
0.000018
0.0001 15
0.017485
0.004469
0.002625
0.000798
0.008432
0.001392
0.006827
0.008003
0.009983
0.024654
0.001065
0.000000
0.008387
0.012776
0.005446
0.021949
0.076395
0.048387
0.005871
0.003240
0.005020
ME
Table 1. Parameters of' phenotypic variation. Abbreviations: SM - standardized mean (for morphometric characters in relative units = 0.05mm); SC standardized stochastic component; FC - standardized factorial component; RSV - relative stochastic variation; KR,,,- kurtosis of R,L distributions; K,, kurtosis of' R 1, distrihutions; S , , , ,- skewness of R,L distributions; S,, ,, - skewness of R-L distributions. ME - measurement error.
Table 2. Kurtosis and skewness of R, L and R - L distributions
~~
Type of characters, population
-
KK I.
KR-I
s, I
si; I
3:18**
2:19**
10:ll
11:lO
21:00**
19:20**
5:16*
3:18**
12:90
9:12
13:80
11:lO
12:90
~~
Meristic, spring spawners
Meristic, summer spawners
Morphometric, spring spawners
Morphometric, summer spawners
9:12
7:14
13:80
Table 3. Coefficients of correlation for association between parameters. For abbreviations see Table 1
~~~
~
Meristic
Pa-ameters to be correlated
Morphometric
~
Spring
spawners
Summer
spawners
Spring
spawners
-0.587**
-0.702**
-0.954**
-0.415
-0.442*
-0.452*
0.573**
0.584**
- 0.598**
flSV-S(’
-0.550**
-0.660*“
-0.799**
- 0.476*
-0.536**
-0.541**
0.746**
0.320
[.is V-[>(
-0.326
-0.268
RSV-SYI
-0.377
-0.643**
_
Summt,r
spawnc~s
.___-
SC-SM (untran sformed)
Sc‘-SM (sq. root transformed)
Sc‘-SZI (log-transformed)
K - S l l (untransformed)
FC‘-SlI (sq root transformed)
FC-S%l (log-tumsformed)
,SP-H‘
transformation of the mean (recommended by Pearson
& Davin (1924). Lande (1977), and Soule (1982)).Second, I used the log-transformation of both variances
and means. As a measure of the success of t h e transformation, I used a coefficient of correlation - a greater
coefficient of correlation indicates a more nearly linear
association. The results of these data transformations,
together with the untransformed data, are shown in
Table 3. The results are very consistent for spring
and summer spawners, and for both meristic and
niorphometric characters. The square-root transformation of means leads to a higher correlation with
variances than untransformed means, but log-transformation of means and variances provides for a n even
higher correlation in all cases. Thus I used log-logt.ransformation in further computations.
The correlation between stochastic and factorial components of the same character is positive and usually
high ( r ranges from 0.57 to 0.92) for both meristic
and morphometric characters, higher in morphometric
ones (Table 3. Fig. 1).
Both stochastic and factorial components show a
high and significant negative correlation with means
(Table 3 > Fig. 2). The stochastic component usually
-0.688**
-0.802**
-0.660**
-0.744**
-0.845**
0.909**
0.798**
0.484”
-0.442*
O,fi4(;*”
- 0,73:;i;*-
-~0,8j:$**
0,58t{**
0.65:l**
--0.790**
0.91!1* *
0.60!j*;’;
0.248
-~o.j0:3*
-
-
shows a higher correlation ( T = -0.80-( 0.95)) than
t h e factorial component ( r = ( - 0.45)-( - 0.84)).
The slope of linear regression of‘ stochastic components on means (Table 4) is notably higher for morphometric characters t h a n for meristic. The slope of
regression between components of variance and means
is higher for t h e stochastic component t h a n for the
factorial in all cases (the difference between slopes is
significant (P<O.Ol) for meristic characters of summer
spawners). Because of this, the contribution of the
stochastic component to total variance (sum of stochastic and factorial components), decreases with a n
increase in means (i.e. correlation of relative stochastic
variations with means is negative) (Table 3). The relative stochastic variation is positively correlated with
the stochastic component. Association of the relative
stochastic variation with the factorial component is not
so consistent. In meristic characters it shows negative
correlation with the factorial component, whereas in
morphometric characters the correlation is positive
(Table 3).
Kurtosis ( R , L ) and kurtosis (R-L)are not associated with each other. Nor are skewness ( R ,L ) and
skewness (R-L). Kurtosis ( R - L ) and skewness ( R - L )
~
_
VARIATION PATTERNS OF BILATERAL CHAMCTERS
0.0,
I
c)
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
-4.0 t
-4.5
0.0
-
-2.0 -
'
l
*
u
-4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 -0.0
6
a -2.5
a
.-
2
I
I
I**
/ I
-1.5
243
I
B
I
I
I
I
I
I
0.5
1.0
1.5
2.0
2.5
I
I
3.0
3.5
42
E
0.0
I
-3.5 -
Ld
a
5
-4.5 -
65
-5.5
-
-8.5 I
-10
I
I
I
I
I
-9
-8
-7
-6
-5
I
-4
-3
Standardized stochastic component
Figure 1. Plot of factorial components on stochastic components (log-transformed values based on natural logarithms) for spring spawners: (A) meristic and (B)
morphometric characters.
a
9 -4.01
v)
0.0
I
0.5
I
1.0
I
1.5
I
1
2.0
2.5
I
3.5
3.0
Standardized mean (log-transformed)
Figure 2. Plot of components of variance on standardized
means (log-transformedvalues) for spring spawners: (A)
stochastic and (B) factorial components.
do not show clear associations with other parameters
(except some positive correlation with each other).
Kurtosis (R,L ) shows a negative correlation with both
the stochastic and the factorial component (significant
(P<0.01)for meristic characters in spring spawners).
Skewness (R,I,) is positively associated with the factorial component (significantly, PC0.05, in the case of
meristic characters in summer spawners. However,
none of the correlations for kurtosis and skewness
are significant after application of the appropriate
Bonferroni tests.
Table 4. Linear regression of stochastic and factorial
components of variance on means. For abbreviations see
Table 1
VARIATION AMONG POPULATIONS ACROSS
CHARACTERS
the standardised means of meristic characters between
populations. In 18 cases the standardised means are
higher in spring spawners than in summer spawners
(P<0.01).No significant differences in kurtosis o r skewness of both (R, L ) and (R-L) distributions are observed.
Morphometric characters do not show notable differences between populations in either the level of
stochastic and factorial components or kurtosis and
skewness of character distributions (Tables 1 and 2).
Associations of differences between the populations
in means and variances with the means and variances
Table 1 allows comparisons of analysed parameters
for each character between populations. For meristic
characters, spring spawners have a higher stochastic
component and a lower factorial component (in 15 and
13 cases respectively) than summer spawners. The
first value is significant (critical values for a 21 paired
comparison by sign criterion are: 6 (or 15) for R 0 . 0 5
and 4 (or 17) for P<0.01) (Lehmann, 1975)). Relative
stochastic variation is significantly higher in spring
spawners (17 cases). There are notable differences in
v p e of characters, population
Meristic, spring spawners
Meristic, summer spawners
Morphometric, spring spawners
Morphometric, summer spawners
Slope
SC-SM
Slope
FC-SM
-0.862
-0.637
-0.493
- 1.276
1.883
-2.048
-
- 1.451
-
1.546
244
I). 1,. LAJUS
- 0.0
- I
Table 5 . Coefficients of correlation of association of differences between the populations with averaged values.
For abbreviations see Table 1. d =difference between
populations (spring- summer spawners). a = average for
populations.
f'arameters to
be correlated
Meristic
Morphometi-ic
-0.614**
0.206
0.194
0.446*
-0.135
- 0.2.54
0.12'7
0.035
0.230
-0.377
-0.246
0.404
0.259
0.507"
-0.376
0.228
0.516"
0.380
-
-
65
-4.5
"."
1
0.0
i
0.5
1.0
1.5
2.0
2.5
Standardized mean
i
3.0
3.5
Figure 3. Vectors of difference in stochastic and factorial
components (log-transformed values) for summer and
spring spawners (meristic characters). Arrows are directed from spring spawners to summer spawriers.
-
tiveraged for the two populations are shown in Table
Tt. There is a significant negative correlation of dif-
l'erences in stochastic components between populations
with averaged means. Characters with higher numbers
of holes have higher stochastic variation in spring
spawners, and characters with lower number of holes
do not differ in their stochastic variation between the
populations. This is evidence of discordance across
characters in fluctuating asymmetry. Also, there is
significant correlation between the difference in the
factorial Components of the morphometric characters
with the level of variance (both stochastic and factorial). This, again, demonstrates discordance of factorial components across characters: for high
variability characters the factorial variation is higher
in summer spawners, whereas in low variability characters it tends to be higher in spring spawners.
To illustrate the changes graphically in measures of
variation across characters when two populations are
compared, I plotted the stochastic components versus
means for spring spawners (Fig. l),together with the
points for summer spawners. Joining the points with
arrows simultaneously indicated the direction and
magnitude of the difference between populations in
stochastic components and means (Fig. 3). To show a
tendency in changes of means and variances more
clearly, I used the averaged values. The data were
averaged by calculating the slope and intercept of the
regression of differences in the stochastic component
between populations on means (averaged for the two
populations). Then, on the base of slope and intercept,
I found the predicted values of differences in stochastic
component between the populations for several
averaged means (0.0; 0.5; 1.0; 1.5; 2.0; 2.5; 3.0). In the
samc way I found the predicted values of differences in
means between the populations for the same averaged
means. For each value of averaged mean I drew an
arrow reflecting the magnitude of differences in stochastic components and means and direction from spring
to summer spawning population. Arrows for different
means reflect transformations between populations for
a whole range of characters. Graphs for the factorial
component and the mean and for the stochastic and
factorial components were drawn in the same way
(Fig. 4). Figure 4A-C contains three projections of
a three-dimensional graph where the axes are the
stochastic component, the factorial component and the
mean. These graphs clearly illustrate changes in variation between the two populations. Moreover, they
show association of character parameters within each
population.
It is evident that changes in the level of stochastic
variance are associated with the means (Fig. 4). In
characters with low means, stochastic variation of
spring spawners is slightly lower than that of summer
spawners, whereas in 'large' characters stochastic variance is notably larger (Figs 3 , 4). It is seen also from
Table 5 that the differences between stochastic components are significantly correlated with the means
(see above). Differences in factorial component between
populations are not prominent and do not associate
with the means significantly (Fig. 4B, Table 5). When
considering the stochastic variances-factorial variances association (Fig. 4C) (this figure is a consequence
of two previous ones), it is seen that stochastic variance
notably changes in low variability characters (or in
characters with high means, as seen from Fig. 4A). In
morphometric characters, differences between populations are fewer (Fig. 5). Here there are no changes in
the stochastic component, but changes in the factorial
component, observed in low variability characters still
VARIATION PATTERNS OF BILATERAL CHARACTERS
-3
0.0
-1.0
-1.5
I
- 4 p
A
-0.5
245
h
-
f
-
-2.0
-
-2.5
-
-3.0
-
-3.5
-
k
1
c
-'%ij
$
-7
-8
-9
1
-4.0
-0.5
0.0
I
0.5
1
1.0
I
1.5
I
2.0
2.5
3.0
3.5
4.0
310
315
410
4!5
5:O
5;s
J.0
Standardized mean
-3
V
:rl
~
J
I
*
5
T
-7
w
Q
I
0.0
I
0.5
I
1.0
I
1.5
I
2.0
I
2.5
I
3.0
I
3.5
4.0
-0.5
<
3(
-8'
2.5
Standardized mean
0.0 I
E -1.0
e
.- -1.5
V
4
-3.5
?i-4.01-0.5
V
-6 .-
5
U
I
3.0
g
-3
8
-5 -
I
3.5
I
4.0
I
4.5
I
5.0
5.5
I
I
I
6.0
C
4V
.3
1
2
d
%
3
-6 -7 -
)c-
h
k!
-8-
W
5
c
2
-3.5
g
3;
I
I
I
-4.0
-4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5
I
I
I
I
I
1
I
I
I
0.0
Standardized stochastic component (log-transformed)
Figure 4. Averaged vectors of difference between spring
and summer spawners based on 21 meristic characters
(log-transformed data): (A) in means and stochastic components, (B) in means and factorial components and (C) in
stochastic and factorial components. Arrows are directed
from spring spawners to summer spawners.
exist (Fig. 5B,C, Table 5). Statistical comparison of
slopes of regression (Sokal & Rohlf, 1981) of stochastic
variances on means shows t h a t summer spawners are
characterized by higher slopes for meristic characters
(Pc0.05).
DISCUSSION
MEASUREMENT ERROR
Recent studies have found, that measurement error
can be rather large when analysing fluctuating
Figure 5. Averaged vectors of difference between spring
and summer spawners based on 21 morphometric characters (log-transformed data): (A) in means and stochastic
components, (B) in means and factorial components and
(C) in stochastic and factorial components. Arrows are
directed from spring spawners t o summer spawners.
asymmetry (up to 50% or even more of measured
variance between left and right structures) (Merila &
Bjorklund, 1995; M ~ l l e &
r Swaddle, 1997; Van Dongen,
1999; Lajus & Alekseev, 2000). Therefore, it is clear
that assessment of measurement error is very important in fluctuating asymmetry studies. In this work,
I assessed measurement error by repeated observations on some specimens and then expressed it
as a part of the total variance. As measurement error
influences observed stochastic variation, true stochastic variance may be found by subtracting measurement error from observed stochastic variation.
246
L). I,. I A J U S
Pat terns o f variation of measurement error have
an interest in their own right. Like components of
phenotypic variance, standardized measurement errors show negative correlations with means. Computations based on data from table 1 in Lajus &
Alekscev (2000) also demonstrate negative correlation
of measurement error with means. This negative correlation is caused by observer and instrument error
and so is more or less independent of the structure
nwasured. Standardization of measurement error by
mean then results in lower values for large characters.
I t was found also that the contribution of measurement
error to the stochastic variance in both meristic and
niorphometric characters is negatively correlated with
the level of character variation. Thus, assessment of
fluctuating asymmetry in high variability characters
ii relatively more accurate than in low variability ones.
VAKIAT1C)N AMONG CHARACTERS
I n this paper I did not observe any tendency for R - L
distributions to be leptokurtic, although it is considered
t o be ti rather common phenomenon in fluctuating
asymmetry studies, resulting from difference among
individuals in symmetry (Gangestad & Thornhill,
1999: nloller, 1999; Graham, Emlen & Freeman, in
press). The set of 42 characters for two populations
demonstrated equal numbers of leptokurtic and platykurtic distributions. Thus, analysis of distributions
does not provide evidence of differences between individuals in asymmetry.
High positive correlations between factorial and
stochastic components of total variance were observed
in my data. When one character has a higher factorial
component than another, it is most likely that it also
has a higher stochastic component. This is evidence of
a similarity of underlying mechanisms responsible for
phenotypic variation, either among individuals (reflected by the factorial component) or within individuals (reflected by the stochastic component).
In this study, two findings which contradict the
previous explanation of negative correlation between
stantlardised variances and means (Pearson & Davin,
1924; Lande. 1977 and Soule, 1982) have been noted.
The first is a strong negative correlation between factorial (non-stochastic) components and means (Table
3 , Fig. 24) (Lajus, 1997). According t o earlier predictions, the non-stochastic component of total variance should be uncorrelated with the mean value of a
character (see Introduction). Second, a square-root
transformation of means is not the best transformation
for producing linear associations with standardised
variances. Log-transformations of both means and
variances provide more nearly linear relations. Therefore, the mechanisms responsible for negative associations of standardized variances with means
suggested previously do not explain satisfactory data
obtained in this study.
To explain the discrepancies between the predictions
of the Pearson-Lande-Soule hypothesis and my observations of White Sea herring, I suggest a new model.
According t o this model, the magnitude of phenotypic
variation is determined by two kinds of processes.
First, the increase of the variances with the means
fits a simple linear mathemat.ica1 function with multiplicative errors. When the standard deviation from a
sample mean increases proportionally with that mean,
then the variance increases proportionally with the
squared mean. Then the standardized Variances which
are measured, e.g. by the coefficient of Variation (CV),
are independent of the means, i.e. for multiplicative
errors alone the slope of variances vs means is equal
to zero.
Second, non-linear feedback processes may equalize
the absolute variation of different structures, independently of their means (i.e. size in the case of
morphometric characters, or number of elements in
the case of meristic characters), so that errors are
additive. It is possible that such feedback mechanisms
are not character-specific. Such lack of specificity is
needed to make diverse structures compatible - functioning as parts of a single system (for instance, the
cranium can be considered such a system:I. Additive
errors ensure that absolute variances are uncorrelated
with the means, and therefore standardized variances
decrease with means. For instance, when the mean
increases twofold, the standardized variance decreases
fourfold. Thus the slope of log-log-transformed variance and means is equal to --2 for the additive errors
alone. The importance of the feedback interactions in
the origin of fluctuating asymmetry has been stressed
by many authors (Emlen et al,, 1993; Graham et a/..
199313, in press; Van Dongen, Sprengers & Lofstedt,
1999).
The interaction of processes involving both multiplicative and additive errors produces an intermediate
slope of standardized variances-means regression. The
presence of a negative slope indicates processes that
maintain the similarity of absolute variances in different structures, i.e. characterized by additive error.
At the same time, this slope is lower than it would be
possible with additive errors alone, due to processes
leading to a proportional increase of absolute variance
with means (and thus t o an absence of standardizedmeans associations), i.e. characterized by multiplicative error. Multiplicative error will tend t o make
the slope closer to zero, so the negative slope would
not be as extremely negative. This conclusion is in
accordance with that of John Graham (pers. comm.)
who, on the basis of analysis of R - L distributions,
involves both processes with additive and multiplicative errors in determining fluctuating asymmetry.
VARIATION PATTERNS OF BILATERAL CHARACTERS
Thus, the slope of the variances-means regression can
be considered a measure of the relative importance
of feedback processes. More extreme negative slopes
indicate higher efficiency of feedback.
Stochastic variances demonstrate higher slopes of
regression with means than factorial variances (Table
4), i.e. stochastic variances decrease more rapidly as
means increase. I believe that the difference is due
t o direct interactions between structures within an
organism in the case of stochastic variation. At the
same time, negative association between standardized
factorial variances and means reveals that there are
other mechanisms leading to negative association between standardized phenotypic variance and means,
apart from direct interaction between symmetrical
structures due to feedback mechanisms. Differences
in slopes for the stochastic and factorial components
result in the dependence of the contribution of the
different components on the means. In ‘large’ characters (size for morphometric and number of countable
elements for meristic characters), the contribution of
the stochastic component is lower than in ‘small’characters. A consequence of this, for instance, could be
higher heritability of large characters, which was discussed by Soule (1982); because the non-stochastic,
or factorial component, is due mostly to genotypic
variation, the contribution of genotypic variation to
the total variation (i.e. the heritability) is also higher
in large characters (Lajus, 1998).
VARIATION AMONG POPULATIONS ACROSS
CHARACTERS
Clear departures from the concordance of fluctuating
asymmetry across characters were observed in this
study. I consider two types of such departure: first a
difference between meristic and morphometric characters and, second, a difference between meristic characters themselves.
The presence of differences between populations in
fluctuating asymmetry in meristic, but not morphometric, characters is probably due to a difference
in the feedback control of deviations from perfect symmetry. This control presumably is more powerful in
morphometric characters, because deviation from symmetry in morphometric characters results in the asymmetry of the whole structure, whereas deviations from
perfect symmetry in a number of elements, such as
holes, do not effect symmetry of the whole structure.
Because of this, meristic characters are not so canalized. Thus, one should find (1) lower variability of
morphometric characters, (2) higher slope of variances-means regression for morphometric characters,
and (3) fewer between-population differences in morphometric characters. Meristic characters, in fact, have
247
higher levels of variability, lower slopes of both stochastic and factorial variances with means (in morphometric characters of summer spawners the slope is
equal - 2.048 (Table 4), i.e. slightly exceeds theoretical
maximum of 2, probably due to sampling error), and
more clearly describe differences between populations
in phenotypic variance and, in particular, fluctuating
asymmetry. We found similar relationships in bleak
Alburnus alburnus (Cyprinidae) from two locations
within the Chernobyl region with different levels of
activity (Lajus & Arshavskii, unpublished data).
Thus, I believe meristic characters to be more sensitive
to changes in developmental instability than morphometric characters. If this is the case, meristic characters should be more informative than morphometric
characters when differences in developmental instability between populations are small. However, the
data presented here show that there are differences
not only between meristic and morphometric characters, but also among different meristic characters.
Thus, the response of the meristic characters is less
‘predictable’.
Soule & Cuzin-Roudy (1982) and Emlen et al. (1993)
predicted that high variability characters should be
more sensitive to between-population differences in
developmental stability (but for opposing view see
Leung &Forbes, 1996).This prediction is not supported
by the data on the White Sea herring. The meristic
characters in the two populations contradict this prediction, i.e. differences between the populations are
manifested more clearly in low variability characters.
Therefore, on the basis of these results, it would be
possible t o say that characters with higher means (low
variability) would be the best for discriminating these
two populations by fluctuating asymmetry. However,
the observed pattern, that of higher discriminatory
capacity of characters with high means, can describe
the situation only for these two particular populations
and does not allow the prediction that it is true for
any other populations. Thus, I would not consider these
results in terms of higher or lower efficiency of some
characters for discrimination of populations by the
level of fluctuating asymmetry, although it is accepted
in the literature on developmental stability (see, for
instance, Campbell et al., 1998; Clarke, 1998; Auffray
et al., 1999).
I propose an alternative model to describe fluctuating
asymmetry and, more generally, phenotypic variation
for comparing populations. According to this model,
phenotypic variance may be described with two parameters, the first is the slope of regression of the standardized variances on the means, and the second is the
average variance for the set of characters used (Lajus,
1998). The two populations differ in both these parameters: spring spawners are characterized by a lower
regression slope and a higher average variance (Table
248
D. L. LAJUS
-1). Another example of differences between populations
was in the slope of the regression of variances-means
regression lines in the study on the copepod Acanthocyclops signifer (Lajus & Alekseev, 2000). Data
presented in Table 2 of this paper, after log-transformation of both means and stochastic variances,
show significant differences in slopes between the third
population and the first (P<O.Ol) and between this and
the second ( R 0 . 0 5 )populations.
It should be stressed that average variance is a
function of the set of characters analysed. If I had
selected other characters on herring for analysis, for
instance, with a lower means (on average), the differences between populations would be fewer. The
slope of the regression should be independent of the
characters used.
How can the data be interpreted from the point of
view of population biology of the White Sea herring?
Taking into consideration other data available on the
populations studied, the following hypothesis of interrelationships between spring- and summer spawners of
the White Sea herring populations from Kandalaksha
Bay was suggested (Lajus, 1996b).Due to early spawning (in April), the critical period of larval development
(in the first month after spawning (Ivanchenko, 1983))
of spring spawners is coincident with the maximum
abundance of plankton, which usually occurs in June
(Prygunkova, 1982).It seems quite possible that early
spawning and, consequently, favourable feeding conditions for larvae, result in an increased abundance of
spring spawners relative t o summer spawners. However, the cost of this adaptation is a decline in viability.
Indirect evidence of this decline is a decrease in salinity
resistance (Ivanchenko & Lajus, 1985). Decreased
growth rate in spring spawners can also be considered
as evidence of their decreased viability. Other evidence
for decreased viability is the increased fluctuating
asymmetry, reported previously (Lajus, 199613). The
more comprehensive study of fluctuating asymmetry
reported here shows that populations are characterized
by different slopes of the regression of fluctuating
asymmetries on means. Therefore, there are reasons
to think that a small regression slope is evidence for
decreased viability of the spring spawning population
of the White Sea herring.
CONCLUSION
In two populations of the White Sea herring and in
two different types of characters - meristic and morphometric - I observed similar relationships between
within-individual variances (stochastic variance, fluctuating asymmetry), inter-individual variances (factorial variance) and means of different characters.
Standardized variances consistently showed negative
vorreiations with means. 1 suggest that this negative
correlation is due to feedback interactions, and the
relative role of such interactions is higher in structures
with greater mean values. The slope of the variancesmeans regression was consistently higher for stochastic than for factorial variance; this causes a decrease
in the contribution of stochastic variance t o the total
variance of larger (in terms of means) Characters.
Although relationships among variances and means
were principally similar in different populations, slopes
of regression of means in stochastic variances were not
the same. Thus, the magnitude of differences between
populations depended on the particular characters
chosen for study. Differences in fluctuating asymmetry
between two White Sea herring populations were manifested more clearly in meristic characters having
greater means. This does not mean, however, that
this would be the case for comparison of any other
populations. Thus I propose t o compare slopes of variances-means regression prior to the comparing the
magnitude of the variances; comparisons by means are
valid only when slopes do not differ. The summerspawning population of the White Sea herring, which
is characterized by a greater slope of the stochastic
variances-means regression was characterized also
with by higher growth and higher salinity resistance.
This suggests that the slope of the regression may be
related to fitness.
ACKNOWLEDGEMENTS
I would like to thank John Graham for his valuable
advice at all stages of my study. Vladimir Zakharov,
Alexander Kozhara, and Nikolai Glotov provided useful discussions of results. I also would like to acknowledge helpful comments of Adam Wilkins and two
anonymous referees. Rosalind Marsden, Nigel Merret
and Lloyd Ackert helped improve the English of this
paper.
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VARIATION PATTERNS OF BILATERAL CHARACTERS
APPENDIX
LIST OF CHARACTERS
(Fig. 6)
Meristic characters
1. Number of holes in the external surface of the
Nasale.
2. Number of holes in the lateral surface of the Vomer.
3. Number of holes in the dorsal surface of the Mesethmoideum.
4. Number of holes in the lateral surface of crest of
the Mesethmoideum.
5. Number of holes in the ventral external surface on
the anterior part of the Maxillare.
6. Number of holes through the anterior part of external surface of the Dentale.
7. Number of holes in the external surface of the
posterioventral part of the Articulare.
8. Number of holes in the external surface of the
posterior part of the Articulare.
9. Number of holes in the external surface of the
anterior part of the Quadratum.
10. Number of holes just dorsal to the articular process
of the Hyomandibulare.
11. Number of holes on the dorsal part of anterior
surface of the Supraoccipitale.
12. Number of holes on the dorsal part of posterior
surface of the Supraoccipitale.
13. Number of holes in the inner surface of the Frontale.
14. Number of holes in the part of the external surface
of the Alisphenoideum.
15. Number of small foramina through the external
wall of the sensory canal of the Supraoperculum.
16. Number of holes through the middle part of the
Parashenoideum.
17. Number of holes in the inner surface of the anterioventral part of the Quadratum.
18. Number of holes just ventral t o the tooth in the
external surface of the Dentale.
19. Number of holes in the posterioventral surface of
the Sphenoticum.
20. Number of holes in the inner internal surface on
the anterior part of the Maxillare.
21. Number of holes just ventral to the articular process
of the Hyomandibulare.
Morphometric characters
22. Maximal diameter of the anterior foramen in the
external surface of the Frontale.
251
23. Maximal diameter of the posterior foramen in the
external surface of the Frontale.
24. Minimal distance between the posterior edge of the
anterior foramen in the external surface and the
hollow in the posterior part of the Frontale.
25. Minimal distance between the hollow in the posterior part of the Frontale and the hollow in the
central part in the ventral surface of this bone.
26. Minimal distance between the appendix on the ventral edge and hollow in the posterior part of the inner
surface of the Maxillare.
27. Minimal distance between the appendix on the
upper edge on the anterior part and the hollow
on the anterior part of the inner surface of the
Maxillare.
28. Depth of the Quadraturn.
29. Minimal distance between the posteriormost point
and the hollow in the anterior part of the Quadratum.
30. Minimal distance between the posteriormost point
and the hollow in the inner surface of the posterior
part of the Quadratum.
31. Minimal distance between the edges of the transverse comb on the upper surface of the Supraoccipitale.
32. Minimal distance between the largest hole in the
body of the Orbitoshenoideum and its hollow in the
dorsal part of the bone's body.
33. Distance between the hollow in the ventral part and
the most anterior point of the Urochyale.
34. Minimal distance between the posterior edge and
the cavity in the external surface of the Ceratochyale.
35. Maximal diameter of the cavity in the external
surface of the Ceratochyale.
36. Distance between the most distant points of the
Ceratochyale.
37. Distance between the most anterior point of the
cavity on the inner surface and the most anterior
point of the Ceratochyale.
38. Distance between the hollow in the anterior part
and the nearest point of the hollow in the inner
anterior part of the Articulare.
39. Minimal distance between the hole in the lower part
of the Posttemporale and the hollow on the upper
edge of this bone.
40. Depth of the Supraoperculum.
41. Distance between the most distant points of the
Epichyale.
42. Minimal distance between the anteriormost
point and the hollow in the posterior part of the
Dentale.
252
11. L. LAJUS
1
3
2
7
10
14
11
12
4
15
&
19
18
Figure 6. Meristic characters used for analysis. Only holes which were used in the analysis are indicated.
VARIATION PATTERNS OF BILATERAL CHARACTERS
24
22
23
26
27
30
31
32
33
34
35
3E
37
38
39
40
41
29
Figure 6 (contd). Morphometric characters. Distance between crosses was measured
253