3. Results
3
.
1
. Connectance and heritability Heritability h of each one of the six consid-
ered characters was calculated as the r-coefficient for the relationship between parental value and
offspring mean value for the eight lines consid- ered. The level of linkage between a character and
the five others was calculated separately for each line. The absolute value of these r-coefficients was
z-transformed according to Eq. 3, and exam- ined as a function of the population size accord-
ing to Eq. 5. For each character, these values were averaged according to Eq. 6, and consid-
ered as a global estimation of the connectance for the character. This global connectance was com-
pared to the heritability calculated for the same character. A negative significant correlation P B
0.01 is observed Fig. 1. This indicates that heritability of a character is inversely proportional
to its linkage to other developmental events. Two interpretations may be suggested:
1. Pre-existing information, as quantified by heri- tability, is the single source of control of the
development. Thus, the linkage of a character to the others generates a ‘developmental noise’
which disturbs expression of this pre-existing information.
2. The network of relationships is also a source of information for development, which com-
pletes, substitutes or even counteracts expres- sion of the pre-existing information.
These hypotheses are tested in the following.
3
.
2
. Connectance and 6ariability In a homogeneous population exposed to a
uniform environment, the noise in expression of a character may be estimated by the coefficient of
variation CV. The CV Eq. 1 and connectance Eq. 4 were calculated separately for each one
of the eight characters and each one of the six lines considered see Section 2. Large differences
in CV and connectance are observed between the lines and between the studied characters Tables 1
and 2. Corresponding connectance Table 2 and CV Table 1 values were plotted together. A
positive, significant P B 0.001 correlation is ob- served Fig. 2. Large between-characters differ-
ences in CV and connectance are observed Tables 1 and 2. In order to test whether the positive
correlation Fig. 2 is due to these initial differ- ences, all the values of Tables 1 and 2 were
standardized according to Eq. 2, see Section 2 before plotting. A positive, significant correlation
was also observed r = 0.336, P B 0.05, not shown. This result confirms the link between
connectance and phenotypic variation, and sug- gests that connectance generates a noise in expres-
sion of a pre-existing information. However, an accurate analysis of Fig. 2 reveals a complex
situation. A negative significant relationship may be observed between CV and connectance below a
critical value of 0.50 in connectance exponential regression,
17 df,
r = − 0.56, P B 0.02,
not shown.
3
.
3
. Relationship between connectance and de6elopment
Connectance varies according to the line con- sidered Table 2. These between-line variations
were compared as follows: for each line, the r-co- efficient was calculated for each possible couple of
the eight characters measured. The 28 r-coeffi- cients obtained were z-transformed according to
Eq. 3, see Section 2. For each possible couple of lines, the corresponding 28 z-coefficients calcu-
lated were plotted together. The r-coefficient for the relationship between the corresponding z-val-
ues provided an estimation of the similarity in connectance between the two lines. A high simi-
larity in connectance was observed between the lines 10, 15, 20 and 25 Table 3. The low relation-
ship between the lines 30 and 45 reveals that these two lines differed from the group of lines 10, 15,
20 and 25, but also one of the others Table 3.
Connectance is a mathematical transformation of the correlation coefficient, which has not direct
link with the real values measured for each parameter. For this reason, an indirect method is
required in order to estimate the influence of connectance on expression of a character. As for
connectance, the lines were compared for expres- sion of the eight characters considered. The level
G .N
. Amzallag
BioSystems
56 2000
1 –
11
5 Table 1
Within-line variability for the eight measured characters
a
Stem height Total seed wt.
Number of seeds Mean seed wt. Relative fertility
Mean CV per Shoot DW
Line Spike DW
Leaf DW line
10 30.3
20.2 12.6
22.4 23.6
25.3 40.8
5.4 31.6
30.8 24.7
56.4 34.6
45.8 36.3
15 3.9
47.1 31.7
46.1 27.2
35.8 12.6
28.8 28.5
32.4 38.4
6.3 20
6.2 44.8
36.0 15.1
25.1 29.5
25 33.8
34.1 40.6
32.7 16.2
34.0 27.6
35.6 31.2
4.9 37.2
30 28.9
32.8 19.0
26.6 11.9
34.8 22.5
23.5 27.1
4.7 45
39.4 27.6
32.0 15.5
33.6 29.7
38.6 5.2
Mean CV 3.28
4.37 11.11
6.23 6.43
S.D. 0.84
5.97 3.83
a
For each line, the variability is estimated as the coefficient of variation CV calculated from the 15 individuals sampled 13 individuals sampled in line 10. Relative fertility is the ratio between number of seeds and spike dry weight DW.
Table 2 Connectance of the eight studied characters, as calculated separately for each one of the six lines
a
Leaf DW Shoot DW
Line Spike DW
Stem height Total seed wt.
Number of seeds Mean seed wt. Relative fertility
Mean connectance per line
0.66 0.73
0.82 0.43
0.86 0.80
10 0.24
0.32 0.61
0.83 0.73
0.50 0.64
15 0.97
0.72 0.76
0.24 0.67
20 1.05
1.00 0.89
0.43 1.14
1.12 0.71
0.22 0.82
0.86 0.71
25 0.75
0.62 0.93
0.85 0.55
0.17 0.64
0.30 0.34
0.29 0.27
30 0.60
0.56 0.26
0.31 0.36
45 0.37
0.29 0.31
0.46 0.69
0.66 0.38
0.60 0.47
Mean 0.68
0.63 0.59
0.42 0.86
0.78 0.48
0.31 0.26
0.24 0.23
0.11 0.18
S.D. 0.17
0.20 0.14
a
Connectance is calculated as described in Section 2, for populations of 15 individuals except for line 10, 13 individuals.
Fig. 1. Relationship between connectance and heritability in S. bicolor grown in an optimal environment. Connectance and
heritability are calculated as described in Section 2. A negative significant P B 0.01 correlation is observed.
Fig. 3. Relationship between phenotypic and connectance comparison of lines. For each couple of lines, the connectance
and phenotypic comparisons Table 3 have been plotted together.
of ‘phenotypic similarity’ between two lines is generally estimated by comparing mean values of
the characters, but a more sensitive method was preferred here. Values of the eight characters
studied were standardized according to Eq. 2, see Section 2 for all the individuals of all the
lines. By this transformation, it was possible to compare individuals simultaneously for all their
characters independently of their real value. All the 15 samples from each line were ranked ac-
cording to their total weight. The 13 largest plants there was only 13 individuals in line 10 were
considered. For each couple of lines, the 104 standardized values for the 13 individuals ranked
according to their total weight were plotted to-
Fig. 2. Relationship between connectance and variability. Co- efficient of variations calculated for each parameter and each
line Table 1 have been plotted as a function of the corre- sponding connectance value Table 2. A significant, positive
correlation is observed r = 0.412, P B 0.001, 46 df. Data have been separated as a function of the connectance value of 0.5
circles for lower values and triangles for upper values in order to illustrate the negative relationship existing for connec-
tance values lower than 0.5. Fig. 4. Relationship between fluctuation in connectance and its
involvement in phenotypic stability. For each character, the fluctuation in connectance is estimated as the S.D. calculated
for the six lines considered Table 2. For each character, the linkage between connectance and phenotypic variability has
been estimated as the r-coefficient for the relationship between CV Table 1 and connectance Table 2.
Fig. 5. Coordination in connectance fluctuations. For each couple of parameters, the connectance calculated for each line
Table 2 has been plotted and the r-coefficient calculated. Continuous line: significant correlation at P B 0.05; dashed
line: significant correlation at P B 0.10. No line is represented if P \ 0.10.
inter-individual diversity in connectance. The mode of calculation used in this study prevents
any possibility to calculate connectance for each individual and to analyze its variation within a
line. However, lability in connectance of a charac- ter may be estimated by its between-line fluctua-
tions. For example, the low S.D. observed for connectance of stem height suggests that it is less
labile than that measured for leaf weight Table 2.
For each character, the CV and the correspond- ing connectance calculated for each line were plot-
ted together. The r-coefficient of this correlation was considered as an estimation of the link be-
tween connectance and variability in expression of the character. This r-coefficient was plotted as a
Table 3 Phenotypic and connectance comparisons between the six lines
considered
a
Connectance Couple
Phenotypic of lines
comparisons comparisons
0.312 15
0.802 10
0.473 20
0.860 10
0.768 0.212
10 25
10 30
0.187 0.501
0.446 10
0.283 45
20 0.334
15 0.947
15 0.812
0.336 25
0.318 0.538
30 15
45 15
0.060 0.594
25 20
0.369 0.768
20 0.515
30 0.174
20 0.538
0.127 45
0.058 0.531
30 25
25 45
0.288 0.450
0.574 45
0.088 30
26 df
102
a
For each line, 28 r-coefficients are calculated by correlat- ing values for all the possible couples of the eight parameters
studied. The z-transformation of the absolute value of these r-coefficients see Section 2 has been calculated. The similarity
between two lines is estimated by plotting the corresponding z-values and calculating the r-coefficient 26 df for the linear
regression. The phenotypic comparisons have been calculated by plotting together the standardized values of all the eight
characters measured for 13 individuals of each line, ranked according to their shoot DW. The r-coefficient calculated
between two corresponding sets of data 102 df provides an estimation of the phenotypic similarity between the lines.
gether. The r-coefficient for the linear regression between these two sets of standardized values was
considered as an estimation of the phenotypic similarity between the two compared lines. This
analysis was performed for all the possible cou- ples of the six lines studied. Different levels of
phenotypic similarity are observed Table 3.
The between-line levels of similarities in connec- tance and in phenotype were compared. A posi-
tive correlation was observed Fig. 3. This suggests that connectance is not only a noise in
expression of pre-existing information, but that it also influences the development in an oriented
way.
3
.
4
. Connectance and indi6iduality At first sight, the above results seem contradic-
tory: connectance enhances the noise in expres- sion of a character Fig. 2 but it is also related to
expression of the phenotype as a whole Fig. 3. This contradiction may be resolved when suppos-
ing that connectance is involved in expression of the phenotype but that it is not a constant value,
even within a line. In this latter case, the increase in variability observed is a consequence of an
function of the S.D. of connectance for the same character Table 2. A positive relationship is
observed below a certain level of lability in con- nectance about 0.18, see Fig. 4. This suggests
that, below a critical value of lability, expression of a character is controlled by its connectance.
The link between connectance and variability pro- gressively decreases beyond this critical value
Fig. 4. This suggests that an increased lability in connectance reduced its involvement in character
expression, which became probably mainly deter- mined by a pre-existing information.
3
.
5
. Control of lability in connectance The determining influence of connectance in
expression of a character seems conditioned by its lability Fig. 4. Thus, it may be asked whether
connectance itself is the expression of a pre-exist- ing information which is also perturbed by noise
or is an ‘autonomous factor’ involved in pheno- type expression. This point was investigated by
comparing between-line variations in connec- tance. For each couple of characters, the connec-
tances calculated for each one of the six lines considered Table 2 were plotted together and the
r-coefficient was calculated. This measurement provides an estimation of the interdependency in
connectance variations. Connectance varies inde- pendently for some characters especially stem
height and fertility but is strongly related for other such as spike weight, seed weight or num-
ber of seeds Fig. 5. When compared with Table 2, it appears that lability of a connectance is
related to its level of interdependency, suggesting that it is controlled by the structure of the
network.
4. Discussion
Kategori