ity. As emphasized by Lewontin 1974, this mode of interpretation involving a cumulative effect of
specific alleles ‘‘comes from a general Cartesian world view that things can be broken down into
parts without losing any essential information…’’ Lewontin, 1974.
Development is extremely extended in plants, as compared with animals. This may be the reason
why, in plants, most of the morphological, behav- ioral and physiological differences among individ-
ual do not ‘mendelize’ Sultan, 1992, and why the plasticity observed during development is so
adaptive Bradshaw, 1965; Moran et al., 1981; Sultan, 1987. Accordingly, there must be another
central factor, generated by the de6elopment itself, which enables harmonized achievement of the de-
velopment in spite of genetic, developmental or environmental perturbations. Such a property has
been termed canalization Waddington, 1942, equifinality von Bertalanffy, 1950, correcti6e
pleiotropy Warburton, 1955, or adapti6e deter- minism Seligmann and Amzallag, 1995. Its in-
volvement
does not
imply any
vitalistic explanation, but only to consider living organisms
in development as open systems with a sponta- neous tendency to reach the minimal free-energy
status Prigogine and Wiame, 1946. More re- cently, Conrad 1990 suggested the existence of
thermodynamic
basins of
attraction sponta-
neously emerging in the phenotypic landscape, which are involved in a structural increase in
complexity and adaptive responses during devel- opment. These considerations point to the emer-
gence of a self-organized dimension during development Conrad, 1983; Ito and Gunji, 1997;
Hiett, 1999. Recently, experimental measure- ments have confirmed the self-organizing nature
of specific transition phases in plant development Amzallag, 1999a,b.
Theoretical considerations suggest that emer- gence of the self-organization dimension in devel-
opment results from changes in the level of self-association Chauvet, 1993. On the other
hand, it was observed that, in Sorghum bicolor, the level of linkage between different organs is not
constant during development, and that sudden modifications occurred specifically during the
transition phases Amzallag, 1999a. More gener- ally, Trewavas and Malho 1997 have suggested
that the phenotypic dimension is generated by the network of cell-to-cell, and organ-to-organ rela-
tionships. All these considerations indicate that the level of linkage during development may be
both the result and the condition for emergence of self-organizing processes. The aim of the present
study is to investigate whether connectance, a quantification of the network of relationships
within the developing organism, is an expression of the self-organized dimension of development.
This hypothesis is tested here through analysis of connectance and its relationship with expression
and transmissibility of reproductive characters in S. bicolor.
2. Materials and methods
2
.
1
. Plant material and growth conditions Seeds of S. bicolor inbred line, parent male of
the commercial cultivar 610 were a gift of the Hazera Seed Company, Israel. The first genera-
tion of plants was grown in optimal conditions in a greenhouse, as previously described Amzallag,
1998. Seeds from eight plants were harvested separately and defined eight lines of progenies. A
year later, 15 seeds from each plant were ran- domly taken and grown in a field three separated
blocks of five plants as previously described by Amzallag et al. 1998. These eight lines were used
for calculation of the link between heritability and connectance. There was less than 10 individuals in
two of these lines. They were considered for calcu- lation of the connectance of each organ and its
comparison with heritability after examination of the calculated connectances see below, and Fig.
1. However, these two lines were not considered for further analyses Figs. 2 – 5, Tables 1 – 3 in
order to prevent any bias in comparison of connectances.
2
.
2
. Measurements All the plants were harvested at the end of their
life-cycle, after complete senescence of the shoot. The measurements were performed only on the
main tiller. Stem height was defined as the length between the first adventitious roots and the top of
the spike. Total seed weight was measured and the average seed weight was determined after weigh-
ing three groups of 10 seeds randomly taken. The number of seeds was estimated as the ratio be-
tween total and average seed weight. After remov- ing the seeds, the shoot was dried at 60°C for 2
weeks. Because some old leaves were frequently missing, shoot dry weight DW was measured
after removing all the blades. The blades from the four last leaves were weighed and considered as
an estimation of the weight of functional leaves during seed maturation.
Connectance was calculated on the basis of six characters for analysis of its relationship with
heritability Fig. 1. These six characters are stem height, shoot DW, total seed weight, harvest in-
dex total seed weightshoot DW ratio, average seed weight, and relative fertility number of
seedstotal stem weight ratio. The link between connectance and character expression Figs. 2 – 5,
Tables 1 – 3 was analysed after a recalculation of connectance based on a new set of eight charac-
ters which are: stem height, number of seeds, total seed weight, average seed height, leaf weight DW
of the four last leaves, stem DW, spike DW without seeds, and fertility estimated as the
ratio between spike DW and the number of seeds.
2
.
3
. Calculations Heredity was estimated for each character as
the r-coefficient between parental and mean progeny value. The coefficient of variation CV
of a parameter P was calculated as follows:
CVP = 100 × avgPS.D.P 1
where avgP and S.D.P are respectively the between-line mean and S.D. calculated for the
parameter P. Standardisation of the p-value of a parameter P abbreviated as sp was performed as
follows:
sp = [p-avgP]S.D.P 2
Connectance, a term defined by Gardner and Ashby 1970, is the expression, within an ensem-
ble P
1
,…,P
m
of measured characters, of the level of linkage between a character P
k
and the m − 1 others. The r-coefficients for linear regression be-
tween the character P
k
and each one of the other characters was calculated. Before using them as
parametric variables, the r-coefficients non-nor- mally distributed were transformed into z-values
normally-distributed, according to Sokal and Rohlf 1981:
z = 0.5 × ln[1 + r1 − r] 3
Within a
population, connectance
of a
character P
k
abbreviated as CP
k
is defined as the mean of the absolute value of z for all
the m − 1 correlations including the character P
k
. CP
k
= [1m − 1] ×
m − 1 i = 1
zP
k
, P
i
4 The z-transformation values are influenced
by the size of the population considered for calculation of the r-coefficients. The calculation of
the mean connectance of a character between populations with different sizes as performed in
Fig. 1 was realized after examination of the z-values. The characters P
1
,…P
k
,…,P
m
were measured on each population f including n
f
sam- ples.
For a character P
k
one of the m characters previously considered, the linkage with the m − 1
other characters
in the
population f
was quantified by the ensemble of z-coefficients
[z
f
P
k
, P
1
,…,z
f
P
k
, P
m − 1
] The z
f
-coefficients were weighted wz
f
accord- ing to Sokal and Rohlf 1981:
wz
f
P
k
, P
i
= n
f
− 3 × z
f
P
k
, P
i
5 Thus, the connectance C of a character P
k
was calculated, on the basis of a number of
s popula- tions, as follows:
CP
k
= 1
m − 1 ×
s f = 1
n
f
− 3
n
×
s f = 1
m − 1 i = 1
wz
f
P
k
, P
i
6
3. Results
