Annals of Botany 81 : 545–555, 1998
A Model to Simulate the Final Number of Reproductive Nodes in Pea
(Pisum sativum L.)
R O M A I N R O C H E*, M A R IE-H E! L E' N E J E U F F R O Y† and B E R T R A N D N E Y
UniteU d’Agronomie INRA-INAPG, BP01, 78850 ThiŠerŠal-Grignon, France
Received : 13 June 1997
Returned for revision : 1 September 1997
Accepted : 5 January 1998
The final number of reproductive nodes (TRN) is highly variable in pea under field conditions and can limit yield.
However, the determinants of this variability are unknown. This is a problem for crop managers and for many crop
simulation models, in which the assimilate production and partitioning modules generally depend on a phenological
module including simulation of TRN. Previous studies in growth cabinets have linked the end of flowering to the
presence of growing pods near the apex. We investigated the effects of the position of reproductive organs on the stem
on the cessation of leaf emergence by analytical experiments involving pod removal. We then analysed whether
developmental characteristics, obtained in the field for various genotypes, locations, sowing dates, plant nitrogen
status, plant water status and plant densities, could account for the observed variation in the number of reproductive
nodes. On the basis of these results, we constructed a simple model simulating TRN from three developmental
parameters. The model was calibrated on cultivar ‘ Solara ’, evaluated for a wide range of situations and extrapolated
to many genotypes, and was found to have high predictive value.
# 1998 Annals of Botany Company
Key words : Pisum satiŠum L., pea, number of reproductive nodes, model, genotype, N nutrition, pod removal, plant
density, development, flowering, apical senescence.
INTRODUCTION
As development of the pea plant is indeterminate, flowering
at different nodes is not synchronous. Consequently, the
duration of the flowering period for the whole plant is
highly variable, depending on environmental conditions,
with the number of flowering nodes developed being the
main cause of variation. The total number of reproductive
nodes (TRN) reported per plant of cultivar ‘ Solara ’ ranges
from five (Jeuffroy and Devienne, 1995) to 12 (Crozat et al.,
1994). For the G2 genotype, Kelly and Davies (1986)
counted from nine to more than 40 flowering nodes,
according to the treatment applied. Moreover, variation
among plants within the same treatment may also be large
(Turc, 1988 ; Jeuffroy, 1991).
This high degree of variability is a major problem for
modelling yield in pea (Jeuffroy, 1991 ; Jeuffroy and
Devienne, 1995), because crop models generally have a
phenological module including the simulation of TRN, on
which the modules describing growth and assimilate
partitioning depend (Wilkerson et al., 1985 ; Jones and
Kiniry, 1986 ; Whisler et al., 1986 ; Brisson and Dele! colle,
1991). TRN is also an important breeding trait (Murfet,
1990) and may, in some cases, be limiting for yield (Pate,
1975 ; Murfet, 1982 ; Jeuffroy, 1991). Therefore, for indeterminate plants, it is essential to understand the
determinants of TRN, and particularly the mechanisms
explaining the end of flowering.
* Current address : Unite! de Bioclimatologie, BP01, 78850
Thiverval-Grignon, France.
† For correspondence. Fax 33 1 30 81 55 64 ; e-mail
jeuffroy!bcgn.grignon.inra.fr
0305-7364}98}040545­11 $25.00}0
Jeuffroy (1991) and Lecoeur (1994) have shown that there
are always several immature phytomers in the apex at the
cessation of leaf emergence (CLE). Thus, the end of
flowering is not due to a lack of initiated phytomers, but to
the end of their growth. This cessation of growth may result
from severe water stress (Lecoeur, 1994 ; Ney, Duthion and
Turc, 1994). In the absence of water stress, there are two
main hypotheses to explain the end of flowering : (1) a
trophic hypothesis, in which CLE is due to competition for
assimilates between the apex and the growing pods
(Hardwick, 1985) ; and (2) a hormonal hypothesis, in which
CLE is caused by hormonal signals from growing pods or
seeds (Lockhart and Gottschall, 1961 ; Gianfagna and
Davies, 1983).
There is no conclusive evidence for either hypothesis in
the literature, and no available model predicting TRN
based on one of them. However, in both hypotheses,
growing pods (Reid, 1980 ; Lecoeur, 1994), and particularly
pods with filling seeds (Ney and Duthion, 1992 ; Lecoeur,
1994), seem to play a determinant role.
Kelly and Davies (1988) showed, by "%C-labelling, that
the apex is supplied mainly with assimilates produced by the
leaf four nodes below the apical bud (position ®4), and
secondly by the leaf in position (®6). They then showed,
using the G2 photoperiodic line, that the end of flowering is
linked to the presence of growing pods near the top of the
stem. Under short photoperiod conditions, in which the
production of new nodes is unlimited for this genotype,
growing pods are always located four or five nodes beneath
the apex. Similarly, CLE in soybean seems to be linked to
the presence of pods longer than 5 mm over the last fully
developed node (Sinclair, 1984). This notion (local action) is
bo980592
# 1998 Annals of Botany Company
546
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
easy to express in a model, because in pea, as in soybean, the
progression of leaf emergence and flowering along the stem
can be fitted by linear models in cumulative degree-days
(Sinclair, 1984 ; Kelly and Davies, 1986 ; Ney and Turc,
1993 ; Munier-Jolain, Ney and Duthion, 1993). It is thus
possible at any given time to know the exact age of each pod
on the stem according to its relative position from the apex.
In this study, we investigated whether local action
accounted for TRN in field conditions by varying factors
known to affect TRN, such as plant nitrogen nutrition
(Jeuffroy, 1991 ; Sagan, Ney and Duc, 1993), water stress
(Ney et al., 1994 ; Lecoeur, 1994 ; Combaud, 1996), and
genotype (Kelly and Davies, 1986 ; Dumoulin, Ney and
Ete! ve! , 1994 ; Lecoeur, 1994 ; Combaud, 1996).
We first examined the effect of pod position on CLE. We
then analysed how this mechanism generated various TRN
in different conditions. Finally, we constructed a simple
model simulating TRN, based on this mechanism, and
tested it in a large range of situations.
MATERIALS AND METHODS
1995) were used for ‘ Solara ’ and three (30 Jan., 25 Feb. and
10 Apr. 1995) for ‘ Frisson ’. Thrice daily irrigations with a
complete nutrient solution (NPK­oligo-elements) maintained the soil substrate near field capacity and prevented
any nutrient deficiency. For the second sowing date, three
levels of nitrogen fertilization (0±8, 3 and 14 mg N l−") were
applied per genotype, using pea symbiotic mutants [Nod-]
(P2 line ; see Duc and Messager, 1989 ; Sagan et al., 1993)
of the varieties ‘ Frisson ’ and ‘ Finale ’. Sterilized seeds of the
non-mutant ‘ Frisson ’ genotype were also grown at the two
extreme nitrogen levels, to check that the mutation had not
affected any other function of the plants. At the end of the
experiment, the plants for all these treatments were verified
to lack nodules.
Eight seeds per treatment were sown in 5 l pots filled with
# sterilized peat and " small expanded fireclay balls. Plants
$
$
were thinned to four per pot at the two- to three-leaf stage.
Lateral branches were removed throughout the growth
cycle. Daily minimum and maximum air temperatures
inside the glasshouse were recorded. A cooling system was
activated when the temperature exceeded 25 °C to avoid
high-temperature stress.
Plant material and growing conditions
We used several genotypes and various treatments per
genotype, to obtain a wide range of TRN values and allow
for diverse agronomic situations.
Field trials. The field trials took place in France at
Chartres, Dijon, Le Rheu, Bignan, Grignon and Estre! esMons, between 1989 and 1995. Various sowing dates,
sowing densities and varieties were used, particularly
‘ Finale ’ and ‘ Solara ’, which are known to produce few
reproductive nodes, and ‘ Alex ’ and ‘ Frisson ’, which
generally produce many reproductive nodes. Basic details of
these trials are summarized in Table 1. Daily climatic data
(mainly minimum and maximum air temperatures) were
measured at a local weather station located within 1 km of
the experimental plots.
Soil water content was monitored in all experiments and
was maintained by irrigation at a sufficiently high level to
avoid severe drought stress. Crops were fully protected
against weeds and pests, so that associated stresses were
negligible. Soil P and K contents were high enough to be
non-limiting for the crops, and the plants were verified to
have root nodules. Non- and partially-irrigated treatments
were also included at the Grignon site in 1995.
A pod removal experiment was conducted at Grignon in
1994 to assess the effect of pod position on CLE. The
cultivar ‘ Solara ’ was used, sown at densities of ten and 90
plants m−#. The treatments are described in Table 2.
Treatments differed in the number of pods removed, their
position relative to the apical bud and the date of excision
relative to the date of CLE for the control. We used three
successive replicates per treatment for the 90 plants m−#
density and two for the ten plants m−# density, differing by
2 d in the time of pod removal. At least 50 stems were used
per treatment and per replicate.
Glasshouse experiment. A glasshouse experiment was also
conducted at Grignon with natural light and daylength.
Four sowing dates (15 Jan., 15 Feb., 15 Mar. and 10 Apr.
Sampling and plant measurements
Field trials. Ten to 15 plants per plot, from three plots per
treatment, were randomly sampled twice per week between
the beginning and the end of flowering to estimate the
developmental parameters for each situation. The number
of the first flowering node (N1F) and the leaf number (LN)
on each stem (main and lateral) were recorded according to
the decimal scale of Maurer, Jaffray and Fletcher (1966).
The mean LN for each sampling date was calculated, and
the mean N1F for each treatment for all the samplings,
assuming that N1F on basal branches was equivalent to
(N1F®4) on main stem (data of preliminary experiments
not shown). The number of flowering nodes (NFN) was also
recorded for each stem at each date. A node was considered
to be flowering when the first (proximal) of its two flowers
had reached stage 0±5 on the scale of Maurer et al. (1966).
The mean NFN was calculated for all the stems at each
sampling date because there is no significant difference
between main stems and basal branches in terms of the date
of the first flower and the rate of progression of flowering
along the stem (Jeuffroy and Sebillotte, 1997). After
flowering ended, total leaf number (TLN) and N1F were
again counted on about 50 plants per treatment in the same
way as previously described. The last leaf recorded as
developed had to have a larger area than the stipule of the
previous leaf. The two values obtained for N1F were
compared to ensure that they were in good agreement : care
is required because flower or pod abortions may occur at the
first reproductive nodes. TRN was then calculated as :
TRN ¯ TLN®N1F­1.
In addition, the progression of leaf development and
flowering along the stem was recorded in a non-destructive
way at Grignon. A coloured collar was put on 25 stems in
three plots per treatment each day to mark the last expanded
leaf and the last opened flower, determined as for the
destructive method. At the end of flowering, N1F and TLN
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
547
T     1. Basic features of the field trials
Location
Year
Variety
Chartres
48±0° N, 1±2° E
1989
‘ Solara ’
Bignan
Le Rheu
Grignon
47±9° N, 2±8° W
48±1° N, 1±8° W
48±9° N, 1±9° E
1994
1994
1994
‘ Solara ’
‘ Solara ’
‘ Solara ’
‘ Frisson ’
Grignon
1995
Grignon
1996
Dijon
47±2° N, 5±1° E
1994
Estre! es-Mons
49±7° N, 3±4° E
1995
‘ Solara ’
‘ Alex ’
‘ Finale ’
‘ Madria ’
‘ Solara ’
‘ Frisson ’
‘ Solara ’
‘ Frisson ’
‘ Alex ’
‘ Arthritic ’
‘ Baccara ’
‘ Ce! leste ’
‘ Magnus ’
‘ Messire ’
‘ Ritmo ’
‘ Scout ’
‘ Sentinel ’
‘ Solara ’
Sowing
date
Code
Densities
(plants m−#)
14
31
19
8
17
10
13
10
13
14
13
14
14
14
12
12
11
11
23
23
23
23
23
23
23
23
23
23
C89-S1
C89-S2
C89-S3
B94-S
LR94-S
G94-S1
G94-S2
G94-Fr1
G94-Fr2
G95-S1
G95-S2
G95-Al1
G95-Fi1
G95-Ma1
G96-S
G96-Fr
D94-S
D94-Fr
M95-Al
M95-Ar
M95-Ba
M95-Ce
M95-Ma
M95-Me
M95-Ri
M95-Sc
M95-Se
M95-S
40,
40,
40,
80
80
15,
45,
15,
45,
20,
45,
70
70
70
70
70
80
80
80
80
80
80
80
80
80
80
80
80
March
March
April
March
March
March
April
March
April
March
April
March
March
March
March
March
March
March
March
March
March
March
March
March
March
March
March
March
Observations
80, 160
80, 160
80, 160
45,
90,
45,
90,
45,
70,
90, 150
150
90, 150
150
70, 150
150
*
†
NIrr treatment
HIrr and NIrr treatments
NIrr, Additional non-irrigated treatment for the 70 density.
HIrr, Additional half-irrigated treatment for the 70 density.
*, Complete destruction caused by bird damage at emergence for the 90 and 150 densities.
†, Complete destruction caused by bird damage at emergence.
T     2. Basic features and results of the pod remoŠal experiment on ‘ Solara ’ in the field
Treatment
C90
High
Middle
Low
High-Middle
C10
Up
Down
Plant
density
(plants m−#)
Number of
days from
pod removal
to CLEC
Number
of nodes
with pod
removal
Mean node
numbers with
removed pods*
Mean distance
between removed
pods and apical bud
at CLEC†
Total
reproductive
node
number‡
90
90
90
90
90
10
10
10
—
10
10
10
3
—
3
3
0
2
2
2
3
0
4
4
—
6±3}7±3
4±3}5±3
2±3}3±3
5±3}®6±3}®7±3
—
7±2}8±2}9±2}10±2
2±2}3±2}4±2}5±2
—
®3±4}®2±4
®5±4}®4±4
®7±4}®6±4
®4±4}®3±4}®2±4
—
®5±1}®4±1}®3±1}®2±1
®10±1}®9±1}®8±1}®7±1
8±75a
8±60a
11±50b
8±81a
10±60b
11±25a
13±40c
12±34b
*, First reproductive node is counted 1.
†, Last developed leaf is counted ®1.
‡, Data followed by different lettering within densities are significantly different (P ! 0±05) according to the two methods of mean comparisons
(LSD and Tukey).
CLEC, Cessation of leaf emergence for control.
were also recorded on the same 25 stems and TRN
calculated.
Glasshouse experiment. Changes in LN and NFN were
recorded non-destructively twice each day for every stem
from six pots per treatment. N1F and TLN were recorded
and TRN calculated, as previously described. For the
nitrogen experiment, four pots per treatment were harvested
at the beginning of flowering. Total nitrogen concentration
in shoots was determined using the Dumas method (Dumas,
1831), as precisely described by Justes et al. (1994). This
method takes into account the total nitrogen content of the
plant, including nitrate.
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
Computational methods
Time was expressed in cumulative degree-days (CDD)
since sowing, using 0 °C as the base temperature (Ete! ve! and
Derieux, 1982). The number of CDD was calculated as the
sum of the mean daily temperature (average of the minimum
and maximum temperature for each day). The progression
of development was described by linear functions based on
CDD (Ney and Turc, 1993). The rate of leaf emergence
(RLE) was estimated as the slope of the linear regression
line between sampling date (in CDD) and LN. The rate of
progression of flowering (RF) was estimated as the slope of
the linear regression line between sampling date (in CDD)
and NFN. For the non-destructive method, final values of
LN or NFN when leaf emergence had ceased on half of the
recorded stems were not used for calculations, to avoid
sample bias.
Two pairwise methods were used to compare means.
The first is the most powerful existing method, the least
significant difference method (LSD). If no difference between
means is detected by LSD, one can be sure that no other
test would detect such a difference. This procedure is very
useful when there are only a few comparisons. It keeps the
comparisonwise error rate at α, but allows the experimentwise error rate to increase as the number of comparisons
increases. If there are P means, there are m ¯ P(P®1)}2
pairwise comparisons, so the number of comparisons grows
rapidly as the number of means increases (SAS Institute,
1987). To take into account the increase in experimentwise
error, we also used Tukey’s method which is based on the
studentized range statistic and controls the experimentwise
error rate. Although this test still is relatively powerful, it is
classified as conservative : any difference detected by this
method is likely to be significant at a lower error rate. These
two tests were preferred to the classical Student–Newman–
Keuls (SNK) method because this test does not keep the
error rate per experiment at α under a partial null hypothesis
(Einot and Gabriel, 1975).
Aberrant data were withdrawn from the calibration data
set for modelling of TRN when the absolute value of their
studentized residual exceeded two (SAS Institute, 1987), to
better estimate the parameters. No data were withdrawn
from the validation data set, to ensure conditions were as
realistic as possible. The model was evaluated using the
mean square error of prediction, MSEP (Wallach and
Goffinet, 1989).
RESULTS
Pod remoŠal experiments
The two methods used to compare means gave similar
results. For each planting density, all replicates gave
approximately the same values of TRN for each treatment
and the same significant differences between treatments
(data not shown). Therefore, only mean values are reported
in Table 2.
Four treatments resulted in significantly more flowering
nodes than their respective control : treatments Up, Down,
Middle and High-Middle. Thus it was possible to make the
stems produce more flowering nodes by removing various
Number of reproductive nodes
548
15
13
11
9
7
5
INI
3
1
0
50
RLE
RF
100 150 200 250 300 350 400 450 500
Cumulative degree-days
F. 1. Progression of leaf emergence (E) and flowering opening (D)
along the stem (mean for main stems and basal branches), for treatment
G95-S3* in the glasshouse. The three developmental parameters INI
(initial node interval), RLE (rate of leaf emergence) and RF (rate of
flowering) are also shown.
numbers of pods. However, this effect was not systematic
because the treatments High and Low did not produce more
flowering nodes than their control. Furthermore, the number
of extra flowering nodes produced did not depend on the
number of nodes with removed pods. Removing the pods at
two nodes produced about three more nodes than the
control (Middle), but TRN did not increase further if pods
were removed from four nodes (Up).
We removed pods from two nodes in each case when
comparing the High, Middle and Low treatments. However,
only the Middle treatment produced significantly more
flowering nodes than the control. In this case, the two
removed organs were at a relative mean position of (®4±4)
and (®5±4) from the apical bud at CLE, in the range of
nodes (®4, ®6) shown to supply photosynthates to the
apical bud by Kelly and Davies (1988). The High-Middle
treatment had the pods of one more node than the High
treatment removed, at position (®4±4). This produced
significantly more flowering nodes. Thus, the role played by
the pods at mean node (®4±4) is critical. According to Kelly
and Davies (1988), node (®4) is the most committed to
supplying the apical bud.
The treatments Up and Down produced significantly
more flowering nodes than the control, although pods were
only removed from position (®4) for Up. However, the
effect was weak and pods were removed from four nodes.
This is consistent with the results of Jeuffroy (1991) who
showed that removal of the lower pods could significantly
delay CLE only when a large number of pods were involved.
Thus, pod removal had some effect on TRN if the node at
position (®4) was involved or if a large number of pods
were removed. However, the effect of removing a large
number of pods is weak.
Modelling the progression in deŠelopment during the
flowering period
For all treatments, the progression of leaf emergence and
flower opening along the stem were linearly correlated to
CDD, as shown by treatment G95-S3* (third sowing date of
‘ Solara ’ in the glasshouse experiment) in Fig. 1. All
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
549
T     3. Values of the deŠelopmental parameters : number of the first flowering node, initial node interŠal (see Fig. 1), rate
of leaf emergence and rate of flowering, and of total reproductiŠe node number for main treatments in all situations
Treatment
(codes : see
Table 1)
First
flowering
node
(N1F)
C89-S1
C89-S2
C89-S3
G94-S1
G94-S2
G94-Fr
G95-S1
G95-S2
G95-Al
G95-Fi
G95-Ma
G95-S1*
G95-S2*
G95-S3*
G95-S4*
G95-Fr1*
G95-Fr2*
G95-Fr3*
D94-Fr
D94-S
M95-Al
M95-Ar
M95-Ba
M95-Ce
M95-Ma
M95-Me
M95-Ri
M95-Sc
M95-Se
M95-S
B94-S
LR94-S
14±6
14±6
14±3
15±1
14±9
15±6
14±8
14±5
15±1
14±8
16±2
17±6
15±8
16±5
16±2
16±7
13±8
15±0
14±2
14±7
15±7
16±8
14±1
15±7
20±2
14±4
10±7
11±0
14±6
14±6
15±2
14±8
Initial
node
interval
(INI)
®0±234
0±188
0±747
0±886
0±869
0±919
0±963
0±739
1±341
0±476
0±598
1±656
1±526
1±663
1±388
1±996
1±382
1±362
1±402
0±714
1±134
0±664
0±693
0±768
0±309
0±593
2±150
2±219
1±066
0±531
0±592
0±772
Rate
of leaf
emergence
(RLE)
(node dd−")
Correlation
coefficient
for RLE
(r#)
Flowering
rate
(RF)
(node dd−")
Correlation
coefficient
for RF
(r#)
Total
reproductive
node number
(TRN)
0±0195
0±0221
0±0183
0±0208
0±0254
0±0244
0±0229
0±0247
0±0235
0±0201
0±0207
0±0226
0±0257
0±0264
0±0272
0±0273
0±0308
0±0307
0±0234
0±0218
0±0207
0±0208
0±0204
0±0258
0±0229
0±0238
0±0165
0±0182
0±0253
0±0225
0±0224
0±0196
0±992
0±996
—
0±996
0±998
0±998
0±989
0±993
0±994
0±997
0±987
0±999
0±997
0±998
0±999
0±997
0±997
0±998
0±986
0±977
0±986
0±971
0±992
0±983
0±934
0±981
0±984
0±955
0±961
0±998
0±983
0±973
0±0202
0±0269
0±0309
0±0256
0±0296
0±0301
0±0274
0±0300
0±0278
0±0260
0±0262
0±0289
0±0312
0±0332
0±0317
0±0355
0±0367
0±0366
0±0284
0±0244
0±0233
0±0207
0±0233
0±0276
0±0245
0±0261
0±0237
0±0260
0±0276
0±0239
0.0265
0±0243
0±982
0±997
—
0±996
0±997
0±997
0±985
0±985
0±987
0±980
0±988
0±999
0±994
0±999
0±998
0±995
0±997
0±999
0±992
0±996
0±995
0±981
0±988
0±996
0±993
0±980
0±996
0±993
0±961
0±989
0±988
0±987
4±50
5±50
5±60
8±69
10±2
11±7
8±96
7±72
12±4
6±36
7±09
12±2
13±8
13±5
12±7
14±0
13±5
13±5
10±6
7±00
8±92
6±56
6±23
7±44
5±01
7±23
8±97
9±36
8±67
6±46
8±16
7±60
*, Glasshouse experiment.
—, Not available (there are only 2 points).
dd, Degree-day.
regression lines for RLE and RF had correlation coefficients
greater than 0±95 (Table 3), most of them being greater than
0±99.
In most situations, RF was higher than RLE (Table 3).
Moreover, flower opening and leaf emergence did not occur
at the same time at N1F (Fig. 1). We defined ITI (initial time
interval) as the time interval in degree-days between leaf
emergence and the flowering of N1F, and INI (initial node
interval) as the number of developed nodes above N1F at
flowering of N1F (Fig. 1). Negative values of INI mean that
flowering of N1F occurred before the complete emergence
of the subtending leaf, and positive values that flowering
occurred after the subtending leaf had fully emerged. These
intervals differed greatly between treatments, but in most
cases flowering of N1F occurred after emergence of its
subtending leaf (Table 3). Therefore, when N1F flowered,
there were already expanded leaves above it.
Thus three parameters are required to describe the course
of development during flowering : RLE, RF and either ITI
or INI (Fig. 1) ; ITI being equal to INI}RLE according to
Pythagoras’ theorem. INI was easier to measure than ITI
(simple count of nodes), so was used instead of ITI in the
analysis.
Variability of deŠelopmental parameters and TRN in
Šarious conditions
Variation with genotype. Some cultivars generally produce many reproductive nodes (e.g. ‘ Alex ’ and ‘ Frisson ’),
whereas others produce few (‘ Finale ’ and, to a lesser extent,
‘ Solara ’). Under similar growing conditions in the glasshouse or in field experiments, our results were consistent
with this observation (Table 3). At Grignon in 1995, ‘ Alex ’
produced more than six reproductive nodes more than
‘ Finale ’. Therefore, changing the genotype is a good way to
change TRN.
The three developmental parameters also differed greatly
according to genotype. Thus at Estre! es-Mons in 1995, RLE
varied between 0±0165 and 0±0258, RF between 0±0207 and
0±0276, and INI between 0±309 and 2±219 among the ten
genotypes (Table 3).
Variation with location, year and sowing date. These
550
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
T     4. Effect of plant nitrogen nutrition on the deŠelopmental parameters : initial node interŠal, rate of leaf emergence and
rate of flowering, and on total reproductiŠe node number, in the glasshouse experiment at Grignon in 1995
Cultivars
‘ Frisson ’
‘ Finale ’
Type
N content of
the nutritive
solution
(mg l−")
Plant N content
at the beginning
of flowering
(% d. wt)
M
C
M
M
C
M
M
M
0±8
0±8
3±0
14
14
0±8
3±0
14
2±04
2±17
2±62
4±00
3±97
1±23
2±99
4±71
Developmental parameters
INI
0±690a
0±749a
1±077b
1±503c
1±382c
®1±139a
0±019b
0±271b
RLE
(node dd−")
RF
(node dd−")
0±0230a(a)
0±0238a(a)
0±0278b(b)
0±0304bc(b)
0±0308c(b)
0±0183a
0±0183a
0±0227b
0±0329a(")
0±0339ab
0±0331ab
0±0368b
0±0367b
0±0176"
0±0234
0±0254
TRN
5±13a
5±38a
10±8b
14±1c
13±5c
2±33a
5±54b
9±21c
M, Symbiotic mutant [Nod-] (Duc and Messager, 1989).
C, Control (wild type initial line).
dd, Degree-day.
Data followed by different superscripts within varieties are significantly different (P ! 0±05) according to the two methods of comparing means
(LSD and Tukey) ; when there is some disagreement between the two methods, Tukey’s results are given in parentheses.
"No significant difference. (")No significant difference with Tukey’s method.
variations were often very large. For example, at Grignon in
1995 cultivars produced up to 50 % more reproductive
nodes in the glasshouse than in the field (Table 3). However,
variation associated with these factors was not systematic.
At Grignon, the second sowing date produced higher TRN
in 1994 and lower TRN in 1995 than the first sowing date.
In the glasshouse, there were no significant differences
between sowing dates for ‘ Frisson ’ (Table 3, mean
comparisons not shown) whereas for ‘ Solara ’, the first
sowing date produced significantly fewer reproductive nodes
than the other three. So the effect of sowing date is unclear,
or at least linked to undetermined variation in environmental
factors. The effects of such variation are difficult to analyse
in real conditions because all the factors interact. Therefore,
we also carried out particular treatments to assess the effects
of the main agronomic factors, plant nitrogen nutrition,
water status and plant density.
Effect of plant nitrogen nutrition. Applied N treatments
greatly affected plant growth. Shoot dry weight at the
beginning of flowering was ten times higher with the highest
level of nitrogen than with the lowest for ‘ Frisson ’, and four
times higher for ‘ Finale ’ (data not shown). Shoot N content
at this stage was twice as high with the highest level of N
than with the lowest for ‘ Frisson ’ and four times higher for
‘ Finale ’ (Table 4). Consistent with Jeuffroy (1991), Jeuffroy
and Sebillotte (1997) and Sagan et al. (1993), N deficiency
resulted in much lower TRN, in both ‘ Finale ’ and ‘ Frisson ’.
Of the three developmental parameters, INI was the most
affected by N deficiency (Table 4). For ‘ Finale ’, we even
obtained some negative values. These results are consistent
with those of Truong and Duthion (1993) who observed a
strong linear correlation between ITI (error E1 in their
paper) and plant N concentration at the beginning of
flowering. RLE was the second most responsive parameter
to N deficiency (Table 4). This effect has not previously been
reported in pea, but Longnecker, Kirby and Robson (1993)
found that N deficiency decreases RLE in spring wheat. RF
was only significantly affected by N nutrition for ‘ Frisson ’,
and this was only detected by the LSD method. In field
experiments using ‘ Frisson ’ and three mutants, Sagan et al.
(1993) also found that N deficiency did not affect RF.
Despite symbiotic fixation, N starvation can occur in pea
crops in real agronomic situations (Bouniols et al., 1985 ;
Deschamps and Wery, 1987 ; Crozat et al., 1994) and it has
been reported to be one of the main factors limiting yield
(Dore! , Meynard and Sebillotte, 1998).
Effect of plant water status. TRN was significantly lower
for non-irrigated treatments at Grignon in 1995, for both
sowing dates (Table 5). The effect was larger for the second
sowing date, probably because the stress was earlier and
more pronounced (Table 5). These results are consistent
with those of Lecoeur (1994) who showed that drought
stresses affect TRN to various extents, according to their
position in the cycle and their intensity.
Lecoeur (1994) also showed that RLE and RF are greatly
affected by water stress before the start of flowering. In our
field experiment at Grignon in 1995, we observed a slightly
lower RLE (about 15 %) and a markedly lower INI (about
25 %) for the non-irrigated treatment for the second sowing
date than for the control treatment (Table 5). There was no
corresponding change in RF. Irrigation had no significant
effect on any of the three parameters for the first sowing
date because there was abundant rainfall before flowering
(the stress occurred only at the end of the flowering period).
Effect of plant density. Plant density had a small but
significant effect on TRN (Table 6). TRN was slightly lower
at higher density, as were INI and RLE in most cases. The
other parameter, RF, was not largely affected (Table 6).
Jeuffroy (1991), using plant shading, found that carbon
nutrition had very little, if any, effect on TRN and the
developmental parameters.
Modelling total reproductiŠe node number
We investigated how much variation in TRN could be
explained by variation in the three developmental
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
551
T     5. Effect of plant water status on the deŠelopmental parameters : initial node interŠal, rate of leaf emergence and
rate of flowering, and on total reproductiŠe node number
Developmental parameters
Treatment
(codes : see
Table 1)
Time in days from the
beginning of flowering
to ψ ! ®0±06 MPa
INI
RLE
(node dd−")
RF
(node dd−")
—
­1
0±963a
1±039a
0±0229a
0±0222a
0±0274a
0±0281a
8±96a
7±08b
—
­2
®5
0±739a
0±680ab
0±501b
0±0247a
0±0244a
0±0221a
0±0300a
0±0321a
0±0314a
7±72a(a)
5±62b(a)
4±76c(b)
G95-S1
FIrr
NIrr
G95-S2
FIrr
HIrr
NIrr
TRN
Data followed by different superscripts within sowing dates are significantly different (P ! 0±05) according to the two methods of comparing
means (LSD and Tukey) ; when there is some disagreement between the two methods, Tukey’s results are given in parentheses.
dd, Degree-day.
T     6. Effect of plant density on the deŠelopmental parameters : initial node interŠal, rate of leaf emergence and rate of
flowering, and on total reproductiŠe node number
Experiment
(codes : see
Table 1)
C89-S1
C89-S2
C89-S3
G94-S1
G94-Fr
G95-S1
G95-S2
Plant
density
(m−#)
40
80
160
40
80
160
40
80
160
15
45
90
150
15
45
90
150
20
45
70
150
45
70
150
Developmental parameters
INI
0±026a
®0±234b
®0±396b
0±822a
0±188b
0±104b
1±330a
0±747b
0±657b
1±172a(a)
1±060a(ab)
0±886b(bc)
0±681c(c)
1±240a
1±210ab
0±919b
0±931ab
1±076
1±035
0±963
0±957
0±794"
0±739
0±567
RLE
RF
TRN
0±0195"
0±0195
0±0195
0±0233"
0±0221
0±0192
0±0225"
0±0183
0±0206
0±0226a
0±0223a
0±0208b
0±0207b
0±0273a
0±0266a
0±0244b
0±0243b
0±0240a(a)
0±0230a(ab)
0±0229ab(ab)
0±0215b(b)
0±0259"
0±0247
0±0243
0±0207"
0±0202
0±0190
0±0278"
0±0269
0±0222
0±0337"
0±0309
0±0299
0±0269a(a)
0±0280b(ab)
0±0256c(bc)
0±0247c(c)
0±0319a(")
0±0317a
0±0301ab
0±0292b
0±0282"
0±0273
0±0274
0±0277
0±0311"
0±0300
0±0295
5±71a
4±50b
4±00b
7±85a
5±50b
5±20b
7±10a
5±60b
5±60b
11±3a(a)
9±65b(b)
8±69c(bc)
8±40c(c)
14±8a(a)
13±1b(ab)
11±7c(bc)
11±1c(c)
10±1a(a)
9±07b(ab)
8±96b(ab)
8±52b(b)
7±91"
7±72
7±04
"No significant difference. (")No significant difference with Tukey’s method.
Data followed by different superscripts within sowing dates and varieties are significantly different (P ! 0±05) according to the two methods
of comparing means (LSD and Tukey) ; when there is some disagreement between the two methods, Tukey’s results are given in parentheses.
parameters. In the absence of a particular hypothesis, we
first used a multilinear form for the model, with simple and
additive effects. However, this was found to be inappropriate
because plausible negative values for INI could give negative
values for TRN, which does not make biological sense. INI
had by far the strongest effect (accounting for more than
80 % of the variation in TRN) and a simple plot of the data
showed there was an exponential relationship between these
two variables (data not shown). This is consistent with the
data of Murfet and Cayzer (1989) obtained using several
lines from a genetic segregation. Thus, we used a model with
an exponential term for INI and linear terms for the other
two parameters. Regression r# can be used to assess the
linear relationship between the two variables (Snedecor and
Cochran, 1984) and the MSEP can be used to assess the
accuracy of the model for predicting TRN for independent
data.
Calibration of the model on ‘ Solara ’. The model was
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
16
16
14
14
12
12
Observed node number
Observed node number
552
10
8
6
4
10
8
6
4
2
2
2
4
6
8
10
12
Simulated node number
14
16
F. 2. Observed Šs. simulated values of total reproductive node
number (TRN) for ‘ Solara ’ (
, calibration data (Grignon 95) ; D,
Grignon 94 ; E, Mons 95 ; *, Le Rheu 94 ; +, Bignan 94 ; ^, Chartres
89 ; _, Dijon 94 ; V, Grignon 96). The line is y ¯ x.
calibrated using data from field and glasshouse experiments
at Grignon in 1995 because this was the most complete trial
(14 treatments for ‘ Solara ’). There were three replicates per
treatment, giving 42 data points in total. Five points were
withdrawn as aberrant. In the final sample TRN was
between four and 15. Data were adjusted using the following
equation :
TRN ¯®9±76­10±47exp(0±38INI)
­502±40RLE®291±80RF
r# ¯ 0±959
Therefore, up to 96 % of the variance in TRN was
accounted for by variation in the three developmental
parameters used in this trial. This strong correlation shows
that the assumptions made about the form of the model are
not unrealistic. This is supported by the absence of positive
and negative auto-correlation (Durbin Watson’s statistic
close to 2±07, expected value about 2±08).
EŠaluation of the model using ‘ Solara ’. Simulated and
observed TRN were compared for all other available
‘ Solara ’ data (Fig. 2). The calibration sample is plotted in
Fig. 2 as an illustration, but was not used for the calculations.
All points are close to the first bisecting line for the whole
range of INI, including the low values, with a high
correlation coefficient (r# ¯ 0±892), indicating that the two
variables are closely correlated. Thus, the model fits the data
for all the trials at six locations and in 4 years. The
square root of MSEP was 1±01 nodes, which is close to the
experimental error.
Simulated and observed TRN were also compared for
individual stems for the highest and lowest densities (15 and
150 plants m−#) at the first sowing date and for the only
density (45 plants m−#) at the second sowing date at Grignon
in 1994 (Fig. 3). The observed TRN was between six and 15
0
2
4
6
8
12
10
Simulated node number
14
16
F. 3. Observed Šs. simulated values of total reproductive node
number (TRN) for individual stems (main stems and basal branches) of
‘ Solara ’ (Grignon 94). The line is y ¯ x.
25
20
Observed node number
0
15
10
5
0
5
10
15
Simulated node number
20
25
F. 4. Observed Šs. simulated values of total reproductive node
number (TRN) for all genotypes (
, Solara ; D, Frisson at Grignon
94 ; E, Frisson in glasshouse 95 ; *, Frisson at Dijon 94 ; +, Frisson
at Grignon 96 ; ^, all genotypes at Mons 95 ; _, ‘ Alex ’, ‘ Finale ’ and
‘ Madria ’ at Grignon 95 ; V, ‘ Finale ’ in glasshouse 95 ; U, I3G2, L60,
G2 from Kelly and Davies, 1986). The line is y ¯ x.
nodes. The correlation between the two variables was still
strong (r# ¯ 0±791) but the points were more dispersed
around the first bisecting line than for treatment mean
values. However, as there was a systematic bias of about
1±07 nodes, the points tend to be above the first bisecting
line. This is probably due to some effect of the year : this
effect can also be seen in Fig. 2, where the points from
Grignon 1994 tend to be above those from Grignon 1995
(shown by the first bisecting line). For individual stems, the
square root of MSEP was 1±87 nodes.
Extrapolation to other genotypes. Simulated and observed
TRN were compared for all genotypes (13 in all ; Fig. 4),
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
DISCUSSION
Previous studies have emphasized the role of pods in CLE.
The results of our excision experiment support this idea
because pod removal led to the growth of more nodes.
However, not all pods play the same role, because pod
removal had no effect on CLE in two excision treatments.
Ripening seeds are thought to affect CLE (Ney and Duthion,
1992 ; Lecoeur, 1994). In our experiment, there were six
nodes above the highest removed pods in treatment Down
at CLE for the control treatment C10. The mean phyllochron
is about 50 degree-days for ‘ Solara ’ (Turc, 1988 ; Dumoulin
et al., 1994 ; Combaud, 1996), so the excised pods of the
Down treatment would have been at least 300 CDD old.
This is approximately the age at which seed filling begins
(Ney, Duthion and Fontaine, 1993). So, according to this
hypothesis, removing pods with ripening seeds leads to an
increase in TRN. However, in the Up and High-Middle
treatments, about two more flowering nodes were produced
although no pod with ripening seeds was removed : the
oldest removed pods in each treatment were about 200 and
170 CDD old, respectively. Thus, the effect of ripening seeds
cannot account for CLE. The sink strength of the developing
pods is also used to explain CLE (Ney and Duthion, 1992 ;
Lecoeur, 1994), but we showed that the relative vertical
position of the pods along the stem is at least as important
as their number or their sink strength. Thus, the proximity
of actively growing pods from the apical bud may result in
the pods inhibiting the apical bud more strongly. Our results
are in good agreement with those of Kelly and Davies
(1988). Pods at position (®4) relative to the apical bud have
been shown to play a key role in near-optimal growth
conditions and thus the approaches used by Kelly and
Davies (1988) and in this study are complementary.
"%C-labelling using photoperiodic mutants made it possible
to assess the physiological mechanisms involved, and pod
removal allowed us to test the hypothesis proposed from
this method. CLE appeared to be caused by the combination
of two conditions : the presence of enough pods to compete
with the apical bud, either in a trophic or hormonal way,
and the regulation of their action according to their relative
vertical position.
By modelling development in various situations, we
found that flowering on N1F generally occurred after leaf
emergence, and that flowering tends to progress faster along
the stem than leaf emergence. Consequently, the first pod to
A
INI (1) < INI (2)
Number of reproductive nodes
using the equation obtained for ‘ Solara ’ at Grignon in
1995. Data from the nitrogen nutrition experiments were
included, and data from ‘ Solara ’ were added as a reference.
The observed TRN was between two and 25. All genotypes
except ‘ Ritmo ’ and ‘ Scout ’ from the Estre! es-Mons experiment gave points that lay along or close to the first
bisecting line. The high correlation coefficient (r# ¯ 0±847)
confirmed the good fit. If the data for ‘ Ritmo ’ and ‘ Scout ’
at Estre! es-Mons in 1995 are excluded, the correlation
coefficient is higher (r# ¯ 0±915) and the square root of
MSEP falls to 1±78 nodes, which is still high, probably due
to the very diverse conditions.
553
B
RLE (1) < RLE (2)
C
RF (1) < RF (2)
Cumulative degree-days
F. 5. Effects of variation in the three developmental parameters, INI
(initial node interval, A), RLE (rate of leaf emergence, B) and RF
(rate of flowering, C) on total reproductive node number (TRN).
grow is generally well below the apical bud, allowing more
flowering nodes to form with little competition. As more
reproductive nodes form, flowers open nearer to the apical
bud, and developing pods and seeds compete more strongly.
Thus, in almost all treatments, with TRN between two and
25, CLE occurred after flower opening had overtaken leaf
emergence. We found that development during the flowering
phase can be completely defined by three parameters : INI,
RLE and RF. The importance of INI has already been
assessed by Murfet (1982) and Murfet and Cayzer (1989),
who found strong correlations between TRN and flower}
leaf relativity (FLR) at N1F, this variable being the same as
INI, but with the opposite sign. Murfet (1989) also reported
that FLR increases in a near linear manner throughout the
reproductive phase of an early photoperiodic line. According
to Thales’ theorem among parallel straight lines, and given
the linear nature of the RLE and RF plots, our data showed
that this result could be extended to late photoperiodic
genotypes.
Thus, the time taken for flowering to catch up with leaf
emergence, and hence TRN, will be high when INI (Fig.
5 A) or RLE (Fig. 5 B) is high, or when RF is low (Fig. 5 C),
554
Roche et al.—Modelling Final Number of ReproductiŠe Nodes in Pea
the other two parameters being constant in each case.
Figure 5 explains and classifies the effects of the growing
factors. Thus, genotype acts on the three development
parameters, whereas nitrogen and water stresses act mainly
by reducing INI, with RLE, plant density and shading
having only a small effect on the developmental parameters
and TRN.
All our data are consistent with the suggested mechanism
for CLE, and in most cases variation in TRN was accounted
for by variation in the three developmental parameters
INI, RLE and RF. Setting parameters for a simple
multilinear, additive model, with an exponential term for
the INI effect, gave a good fit to the data. As expected, the
regression coefficients were positive for INI and RLE, and
negative for RF, consistent with previous analysis. It is
noteworthy that this model, so simply parameterized, fitted
the data so well. It probably means that the mechanism
involved is very robust. Indeed, the model fitted the data
well not only for mean values but also for individual stems,
and for highly variable situations including data from field
and glasshouse conditions, treatments with N deficiency,
various genotypes, and so on.
However, this model has limitations. The year effect for
‘ Solara ’ at Grignon is not completely integrated : if the
parameters are set using 1995 data, the model tends to
underpredict TRN in 1994. Furthermore, although the fit is
good for various genotypes, TRN was systematically
overpredicted at Mons in 1995. Any change in the growing
conditions after flowering reduced performance of the model
because such changes do not generally affect one of the three
developmental parameters but may have a direct effect on
CLE, e.g., increasing water stress after flowering has begun
(Ney et al., 1994 ; Lecoeur, 1994). However, this weakness in
the model can be turned to advantage for diagnosing stress
during the reproductive phase. This model could also be
used in plant breeding. Thus, Murfet (1982, 1985) and
Murfet and Cayzer (1989) showed that INI clearly distinguishes photoperiodic segregants when N1F cannot be
used to distinguish the genotypes, and the model explains
why some cultivars produce more nodes than others. It also
allows us to classify cultivars according to their behaviour
with regard to the model : for example, cultivars for which
TRN is underestimated by the model presumably have an
apical bud that is strong relative to their reproductive
organs. The TRN of ‘ Scout ’ and ‘ Ritmo ’ at Estre! es-Mons
in 1995 were strongly overestimated by the model. However,
both these cultivars differ greatly from the others : their N1F
is much lower than the N1F of the other lines and their
leaves are much smaller. So, these two genotypes may be
considered to be a separate type, characterized by weak
vegetative development. Finally, this model will be of value
for simulating TRN within crop models (Jeuffroy and
Devienne, 1995).
A C K N O W L E D G E M E N TS
We thank colleagues from the Institut National de la
Recherche Agronomique (I.N.R.A.) Pathologie ve! ge! tale
(Rennes) and from Groupement des Se! lectionneurs de Pois
(G.S.P., Estre! es-Mons) for providing us with data. We
thank Florence Lafouge for nitrogen analysis. We acknowledge our colleagues from I.N.R.A. Dijon (Ge! ne! tique
et ame! lioration des plantes) for providing us with non fixing
pea mutants. The experiments were conducted at several
experimental stations of I.N.R.A. (Dijon, Grignon, Le
Rheu, Estre! es-Mons). We are grateful to the Union National
Interprofessionnelle des plantes riches en Prote! ines
(U.N.I.P.) for financial support.
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