全 文 ：Received 4 Nov. 2003 Accepted 1 Apr. 2004
Supported by the Hi-Tech Research and Development (863) Program of China (2001AA245021, 2003AA209020).
* Author for correspondence. E-mail: .
http://www.chineseplantscience.com
Acta Botanica Sinica
植 物 学 报 2004, 46 (7): 793-802
Modeling the Branching Patterns of Peach Tree Branches
(Prunus persica) After Being Pruned
XIA Ning1, 2, LI Bao-Guo1, DENG Xi-Min2, GUO Yan1*
(1. Key Laboratory of Plant-Soil Interactions, Ministry of Education, College of Resources and Environmental Sciences,
China Agricultural University, Beijing 100094, China;
2. Department of Fruit Sciences, College of Agronomy and Biotechnology, China Agricultural University, Beijing 100094, China)
Abstract: The shoot branching patterns of the two-year-old branches of peach trees (Prunus persica
(L.) Batsch cv. Elberta) were compared with different pruning measures. The branches were divided into a
basal non-branching zone, a proleptic branching zone, a sylleptic branching zone and the part removed. We
used the hidden semi-Markov model to capture the branching patterns. The final results showed that
theoretical probability distributions of diverse lateral shoots of the parent branches calculated on the basis
of the parameters of the hidden semi-Markov chain model were in good agreement with probabilities
extracted from the observed data. This paper described the quantitative effects of pruning on branching
architecture of a parent branch, taking into account of branch morphology. Results suggest that the
hidden semi-Markov model could be used as an effective tool to describe the branching patterns. In
addition, the application of hidden semi-Markov models to predict the effects of pruning on peach tree
branching pattern based on growth parameters was discussed.
Key words: peach tree (Prunus persica); pruning; stochastic process; Markov chain; plant architecture
Peach tree, originated from Central Asia, is now grow-
ing in many subtropical and temperate regions of the world.
Commercially cultivated peach trees (Prunus persica (L.)
Batsch) are trained onto given tree forms (central-leader,
columnar, open vase, etc.), by which tree branches are
pruned in various ways according to local and traditional
measures in order to optimize yield and fruit quality (Gradziel
et al., 2001; 2002; Wang and Huang, 2003). The currently
preferred tree form of peach tree in China is the open vase
in accordance with its growth and branching behaviors.
Peach tree productivity is determined by multiple factors,
including branching architecture. Judicious manipulation
of growth and production cycles in fruit trees, including
peach, requires the understanding of the tree developmen-
tal and architectural features. In addition, the introduction
of any new training and pruning systems in a given area
requires both pomological and ecophysiological evalua-
tions to determine their viability over time and how canopy
architecture interacts with the local climate. Unfortunately,
most of the comparisons among different training and prun-
ing systems performed under various environments have
been based on traditional growth yield-quality assessments
or the ratio of leaf area to canopy surface area (Cavallo
et al., 2001).
Since branching patterns are determined by the dynam-
ics of annual shoot growth (Grossman and DeJong, 1994;
Costes and Guédon, 1997; Seleznyova and Greer, 2001), it
is important to quantify effects of pruning on shoot branch-
ing patterns in modelling deciduous fruit trees.
Branching architecture and bearing habit are difficult to
characterize (Hiroaki et al., 1999; Laurens et al., 2000). Al-
though promising advances in modeling the shoot growth
have been reported for fruit trees such as apple (Takishita
et al., 1995; Costes and Guédon, 1997; Lauri et al., 1997;
Lindhagen and Marcelis, 1998), kiwifruit (Smith et al., 1994;
Seleznyova and Greer, 2001), apricot (Costes and Guédon,
1996), and pear (du Plooy et al., 2002), the extensive use of
winter and summer pruning for peach tree, however, limited
studies on modeling natural growth habits for this species
(Volz et al., 1991; Snelgar et al., 1998). Little information on
the morphology and architecture of peach tree influenced
by pruning has been published. Shoot extension and mor-
phology has been accounted for in computer programs de-
signed to model and simulate plant architecture and devel-
opment (Prusinkiewicz et al., 1994; de Reffye et al., 1995),
with potential uses in forestry, agriculture and ecology
(Reffye and Houllier, 1997). However, for many plant species,
including fruit trees, morphological and architectural infor-
mation necessary to achieve detailed modelling is far from
enough (Scorza, 1984; Genard et al., 1994; Pelt, 1997; Puntieri
et al., 1998; Stecconi et al., 2000; Passo et al., 2002).
This paper used the idea of statistical modeling to study
Acta Botanica Sinica 植物学报 Vol.46 No.7 2004794
the branching patterns of the two-year-old branches of ma-
ture peach trees with various node ranks. The focus was
on the branching pattern led by different pruning measures
at the end of the growing period. The present study aimed
at providing information about the number and position of
lateral shoots initiated on parent branches in mature peach
trees to assess architectural variability with respect to prun-
ing practices.
1 Materials and Methods
1.1 Plant materials
Mature peach trees (Prunus persica (L.) Batsch cv.
Elberta) grown in Dongbeiwang Commercial Orchard,
Beijing, China (116°25 E, 39°50 N, 43.5 m above sea level)
were chosen for this study. The mean annual precipitation
in this area is about 600 mm and the soil derived from
meadow is classified as sandy clay loam (Aquic Cambisol).
Peach trees were planted at a spacing of 4 m×4 m with a
density of 625 trees/ha. Row orientation was from north to
south. Trees were managed according to local recommended
cultural standards. Twenty peach trees were randomly se-
lected and evaluated. The branches extended in the 2000-
2001 growing season were referred to as “parent branches”.
Parent branches were randomly selected within the sam-
pling area (1-2 m in height from the ground). Four main
types of current-year shoots could be identified according
to their length and development by the end of 2002: (1)
latent bud (i.e. undeveloped shoot), (2) short proleptic
shoot (<15 cm in length), (3) long proleptic shoot (>15 cm),
and (4) sylleptic shoot. Sylleptic shoot, also called immedi-
ate lateral shoot in other studies by Costes and Guédon
(1997), had secondary branching shoots.
1.2 Pruning
Peach trees were pruned by standard winter pruning
techniques with pruning targets of 300-600 fruiting
branches per tree. The parent branches were pruned to
leave three to twelve basal nodes. They were called 3-node-
left pruning (3nlp), 4-node-left pruning (4nlp), … , 12-node-
left pruning (12nlp). “3nlp” and less representing heavy
heading back, “4nlp” to “11nlp” representing moderate
heading back, and “12nlp” representing light heading back
in the pruning measures. Parent branches of each type,
ranging from 20 to 85, were selected from two trees. A total
of 20 trees and 600 branches were used for the study. We
investigated the number and layout of new shoots devel-
oping on these types of branches at the end of the growing
season.
The number, types, location, and length of the lateral
shoots developing from the retained buds of the parent
branches were recorded. In this study, the nodes of each
parent branch were numbered starting from the proximal
end.
1.3 Model
Each lateral shoot developing from the parent branches
was a discrete event in a given state. Thus branching pat-
tern could be modeled using the theory of Markov sto-
chastic process (Guédon, 1999; Seleznyova and Greer, 2001).
Markov chain, an intuitively appealing technique devised
by Markov, belongs to the class of discrete-time, discrete-
state-space stochastic processes and its state-transition
diagram can graphically illustrate the branching architec-
ture of the biological entities and sequences (Birney, 2001).
For biological sequences, the “time” dimension in the
Markov chain is replaced by the position in the sequence
(i.e. node rank).
A parent branch after being pruned was described as a
succession of nodes which produced discrete lateral shoots.
A given type of lateral shoots was represented by a symbol:
0 for a latent bud (i.e. an undeveloped shoot), 1 for a short
proleptic shoot, 2 for a long proleptic shoot, and 3 for a
sylleptic shoot. The parent branch consisted of a succes-
sion of differentiated zones. Each zone, representing a state
in Markov chain, was characterized by a single or mixture
lateral shoots: zone 1 was the non-branching zone, zone 2
was the proleptic branching zone (subfruiting zone, includ-
ing possible lateral shoot type 0, 1 and 2); zone 3 for the
sylleptic shoot zone (fruiting zone, including possible lat-
eral shoot type 0, 1, 2 and 3). The zone 2 and zone 3 could
be differentiated by the first occurrence of sylleptic shoots.
In this study, we used hidden semi-Markov model with
four states to model the branching patterns of peach trees
(P. persica) after being pruned.
In our context, the succession of branching zones along
the parent branches was modeled by a first-order Markov
chain. Then, an occupancy distribution, which describes
the length of the corresponding branching zone in terms of
number of internodes, was attached to each of the first-
order Markov chain. Both of them (first-order Markov chain
and occupancy distribution) constituted a semi-Markov
chain. For each parent branch, the branching zones (states)
of this semi-Markov chain could not be directly observed
but related to the observation probabilities of types of lat-
eral shoot in the corresponding zone. The observation prob-
abilities constituted a nonparametric distribution defined
on the set of possible symbols. The complete model, com-
posed of underlying semi-Markov chain and observation
probabilities, was a hidden semi-Markov chain (for detailed
definition of hidden semi-Markov chain model and discussion
XIA Ning et al.: Modeling the Branching Patterns of Peach Tree Branches (Prunus persica) After Being Pruned 795
of its computation methods, see Guédon, 1999).
A j-state hidden semi-Markov chain was defined by the
following parameters:
The initial probability (pj) is the probability of the proxi-
mal bud of the parent branch to be in a given state j:
pj=P(S1 =j) , with j = 1,...,J (1)
where pj=1
The transition probability (pij ) is the probability of state
transfer from i to j:
pij=P(Sn=j/Sn-1=i), with i=1,… ,J-1 and j=1,… ,J
where i e {1, ..., J-1}, with pij=1 (2)
The occupancy distribution (dj(u)) is the distribution of
each state on the parent branch measured in number of
nodes:
dj(u) = P(Sn+u+1≠j, Sn+u-v= j, v = 1, ...,
u-1/Sn+1= j, Sn≠j), u = 1, 2, ... (3)
The first occurrence distribution (ak, y (n)) is the first
occurrence of a given lateral shoot type y measured in num-
ber of nodes in state k:
ak, y (n)=P(Sn+1≠k, Sn = k, Xn-v≠y, v = 1, ..., n) (4)
The recurrence distribution (bk,y(v)) is the interval be-
tween occurring and reoccurring of a given lateral shoot
type y measured in number of nodes in state k:
bk,y(v) = P (Sn+u = k, Sn+u-w ≠ k, Xn+v-w ≠ y, w =
1, ..., v-1/Sn = k, Xn = y), v = 1, 2, ... (5)
The sojourn distribution (gk,y(v)) is the successive oc-
currences of a given lateral shoot type y in a given state
measured in number of nodes in state k:
gk,y(v) = P (Sn+u+1 ≠ k, Sn+u-v = k, Xn+v-w = y, v = 1, ...,
u-1, w = 1, ..., v-1/Sn+1 = k, Sn ≠ k, Xn+1 = y,
Xn ≠ y), u = 1, 2, ... (6)
The parameters of the model were estimated by an itera-
tive algorithm (i.e. Expectation-Maximization (EM)
algorithm), which maximizes the likelihood of the observed
data (Costes and Guédon, 1997; Guédon, 1999). The theo-
retical characteristic distributions were computed from the
estimated parameters of the underlying semi-Markov chain
(initial probabilities, transition probabilities and occupancy
distribution), using the STAT module of Matlab® software.
The effects of the different pruning measures on branching
pattern were analyzed and compared by examining model
parameters and observation probabilities of diverse lateral
shoots.
2 Results
2.1 Quantitative analysis of branching patterns of the
parent branches
The quantitative analysis was based on the study of
the morphological features, i.e. the number, types, and lo-
cation of the lateral shoots developing from the retained
buds of the parent branches being pruned. In this study,
the nodes of each parent branches were numbered starting
from the proximal nodes. Furthermore, we have character-
ized four categories of the lateral shoots among the branch-
ing zone and the observed data were summarized in a syn-
thetic table (Table 1).
The total node number of the parent branches varied
from 3 to 12 nodes, depending on the pruning measures
(Table 1). The proportion of proleptic and sylleptic shoots
was consistent with the classification of pruning measures,
that is to say, light heading back tended to have,
proportionally, fewer lateral shoots than heavy heading
back and medium heading back, whereas the mean number
of latent buds in non-branching zone for parent branches
was relatively constant and varied slightly from 1.1 to 1.5
over pruning measures, except for “3nlp” (Fig.1a).
To give an intuitive interpretation of branching pattern,
a faithful and particular description for “7nlp” was given as
a reference frame for the quantitative analysis of other
branching patterns of the parent branches after being
pruned.
Table 1 Main characteristic on the branching zone of parent branches after being pruned
Pruning Mean No. laterals as sum of mean No. of Mean first Mean first Mean first
measures lateral shoot occurrences: occurrence of short occurrence of long occurrence of
T=y1 (0)+y2 (1)+y3 (2)+y4 (3) proleptic shoot (1) proleptic shoot (2) sylleptic shoot (3)
3nlp 2.7=0.1 (0)+1.0 (1)+1.0 (2)+0.6 (3) 0.9 1.1 0.9
4nlp 2.9=0.2 (0)+1.1 (1)+1.0 (2)+0.6 (3) 1.7 1.6 1.4
5nlp 3.7=0.4 (0)+1.6 (1)+1.2 (2)+0.5 (3) 1.7 2.2 2.8
6nlp 4.5=0.5 (0)+1.5 (1)+2.0 (2)+0.5 (3) 1.7 2.9 3.6
7nlp 5.7=0.9 (0)+1.6 (1)+2.2 (2)+1.0 (3) 1.7 3.1 3.5
8nlp 6.7=1.3 (0)+2.1 (1)+2.2 (2)+1.1 (3) 1.9 2.9 5.0
9nlp 7.6=1.6 (0)+2.7 (1)+2.3 (2)+1.0 (3) 1.8 3.7 5.4
10nlp 8.8=1.8 (0)+2.8 (1)+3.1 (2)+1.1 (3) 2.0 3.1 5.3
11nlp 9.5=2.1 (0)+3.0 (1)+3.0 (2)+1.4 (3) 2.1 3.8 6.0
12nlp 10.5=2.7 (0)+3.5 (1)+2.6 (2)+1.7 (3) 2.7 4.6 7.9
Σ
J
j =1
Σ
J
j =1
Acta Botanica Sinica 植物学报 Vol.46 No.7 2004796
The parent branches in “7nlp” were divided into four
succession zones. The first basal zone was non-branching
zone located on the first 1.3 nodes with latent buds. The
following second zone was occupied mainly by short and
long proleptic shoots with a few latent buds. The third
zone had sylleptic shoots located on the last 3.5 nodes
with a few latent buds plus short and long proleptic shoots.
The fourth zone was the part being removed from the par-
ent branch.
We used a hidden semi-Markov chain model with four
states to represent this branching pattern (Fig.1b). The
model was composed of three successive transient states
representing the successive zones (zone 1, zone 2, and zone
3), and a final absorbing state, representing the removed
parts (zone 4). Therefore, the parameter of this final absorb-
ing state was unnecessary to be considered in this study.
The three transient states corresponded to three well-dif-
ferentiated successive zones, the first zone exclusively com-
prised latent buds and located just at the base of the hid-
den semi-Markov chain. This zone encompassed approxi-
mately 19% of the nodes on the parent branches. The two
middle zones, differentiated by the presence of the sylleptic
shoot, contained mixtures of latent buds, proleptic and/or
sylleptic shoots as indicated above and manifested in the
observation probabilities (Fig.1b). The length of each zone
was reflected in the corresponding state occupancy
distribution, which was binomial distribution. Figure 1a
shows the mean of the state occupancy distribution.
The balance between zone 2 and zone 3 showed that the
number of short proleptic shoots were different in the two
branching zones. The density of the short proleptic shoots
within a given zone was evaluated by their frequency in
this zone and their isolation was examined by the charac-
teristic distributions (sojourn distribution and recurrence
Fig.1. Hidden semi-Markov models corresponding to different pruning measures. (a) Mean state occupancy distribution of branching
zones. (b) Schematic representations of transition probabilities and observed probabilities of the branching zones. The branching zones
are represented by different boxes from zone 1 to zone 4. The observed probabilities of the lateral shoots are given within the zone boxes
(except for the base and top zones), while the possible state transitions are represented by arrows (the associated transition probabilities
are noted nearby).
XIA Ning et al.: Modeling the Branching Patterns of Peach Tree Branches (Prunus persica) After Being Pruned 797
distribution shown in Figs. 2 and 3, respectively). These
data highlighted the isolation of short proleptic shoots
along the parent branches because the most frequent so-
journ-node or the recurrence-node was one. When the other
types of lateral shoot in “7nlp” were considered (Table 1),
69% of lateral buds developed along the shoots. Of the
developing buds, approximately 33%, 46%, and 21% differ-
entiated into short proleptic shoots, long proleptic shoots,
and sylleptic shoots, respectively. The total mean number
of latent buds and sylleptic shoots were approximately 0.9
and 1.0, respectively. The long proleptic shoots and
sylleptic shoots were isolated in the same manner as the
short proleptic shoots (Figs.2, 3).
The accuracy of the entire model was evaluated by com-
paring the theoretical distributions with the observed dis-
tributions extracted from data (Fig.4). From the result, we
could conclude that a hidden semi-Markov chain is a valid
model of the branching pattern of the peach parent branches
after being pruned.
2.2 Comparison of branching patterns among different
pruning measures
Figure 1 shows schematic representations of the mod-
els corresponding to each pruning measure. The results
indicated that all of the branching zones were located in the
same order as previously described for “7nlp”, which ex-
hibited high transition probabilities from zone 1 to zone 2.
However, the initiation probability of each zone with differ-
ent pruning measure was very inconsistent: the initiation
probability of three zones (zones 1-3) for “3nlp”
(representing heavy heading back) was 0.35, 0.53, and 0.12,
while that of three zones for “7nlp” (representing moderate
heading back) was 0.70, 0.29, and 0.01, respectively. The
little initial probabilities of sylleptic branching zones were
observed on “7nlp” and “12nlp” (representing light head-
ing back), whereas the initial probabilities of proleptic
branching zones were similar (Table 2). Therefore, for these
pruning measures, the beginning of the parent branches
was either non-branching zone or proleptic branching zone,
and it was hardly sylleptic branching zone. This represented
the effect of different pruning measures on lateral shoot
Fig.2. Sojourn-nodes distribution of lateral shoots on the parent
branches after being pruned. This is the example of “7nlp” prun-
ing measure. a. Short proleptic shoot. b. Long proleptic shoot. c.
Sylleptic shoot. The observed data are represented by the blank
histogram and the theoretical distributions by the shaded
histogram.
Fig.3. Recurrence-nodes distribution of lateral shoots on the
parent branches after being pruned. This is the example of “7nlp”
pruning measure. a. Short proleptic shoot. b. Long proleptic shoot.
c. Sylleptic shoot. The observed data are represented by the blank
histogram and the theoretical distributions by the shaded
histogram.
Acta Botanica Sinica 植物学报 Vol.46 No.7 2004798
distribution, “3nlp” (heavy heading back) triggered the pro-
leptic and/or sylleptic branching.
The two types of pruning measures, “4nlp to 11nlp”
representing the medium heading back and “12nlp” repre-
senting the light heading back, differed in first occurrence
node of the short proleptic shoot, which was mainly lo-
cated at the second node and the third node, respectively.
“3nlp” was characterized by the absence of a non-branch-
ing zone in more than 65% of the parent branches. The
number of the latent buds in non-branching zones were
more than overall (proleptic and sylleptic) branching zones
for “3nlp to 7nlp”, as much as in branching zones for “8nlp”,
while it was less for “9nlp to 12nlp” (Table 1). “5nlp” and
“6nlp” exhibited a similar number of short proleptic shoots
to that of “7nlp” and differed only by less frequency of the
long proleptic and sylleptic shoots. Of the “5nlp to 7nlp”
pruning measures, the proleptic branching zones were
shorter than the sylleptic branching zones. “8nlp” and
“9nlp” were characterized by the same length of proleptic
and sylleptic branching zones. “10nlp” and “11nlp” were
similar to “5nlp to 7nlp”, whereas “12nlp” showed shorter
sylleptic branching zones.
Other distribution characteristics for the “7nlp” to
“12nlp”, such as the Sojourn-nodes and the recurrence-
nodes (Figs.2, 3, 5, 6), highlighted an interesting occupancy
Fig.4. Observed and theoretical probabilities of the peach lateral
shoots according to the node rank on “7bp”. Dotted lines repre-
sent probabilities extracted from the observed data, and solid
lines represent theoretical probabilities calculated by the hidden
semi-Markov chain model.
Fig.5. Sojourn-nodes distribution of lateral shoots on the parent
branch after being pruned. This is the example of “12nlp” pruning
measure. a. Short proleptic shoot. b. Long proleptic shoot. c.
Sylleptic shoot. The observed data are represented by the blank
histogram and the theoretical distributions by the shaded
histogram.
Fig.6. Recurrence-nodes distribution of lateral shoots on the
parent branch after being pruned. This is the example of “12nlp”
pruning measure. a. Short proleptic shoot. b. Long proleptic shoot.
c. Sylleptic shoot. The observed data are represented by the blank
histogram and the theoretical distributions by the shaded
histogram.
XIA Ning et al.: Modeling the Branching Patterns of Peach Tree Branches (Prunus persica) After Being Pruned 799
distribution of sylleptic branching zones for bearing. The
sojourn nodes of the sylleptic branching zones for the
“7nlp” to “12nlp” were more than those for “3nlp” to “6nlp”,
suggesting that the fruiting zones were greater in these
pruning measures. More details were provided by distribu-
tion characteristics on the branching zone of parent
branches being pruned in Table 1.
3 Discussion
As previously described, the underlying first-order
Markov chain of the parent branch is generally composed
of three transient states and a final absorbing state.
However, such architecture was probably not found on all
parent branches. For example, “3nlp” was obviously char-
acterized by the shortest non-branching zone and high
branching probability; the branching zones were present
on 90% of the nodes of each parent branches with average
length of 2.7 nodes. Therefore, in the case of this pruning
measure, one to two states were probably absent in the
parent branches. Among the pruning measures, “3nlp” rep-
resenting heavy heading back had a strong basal branch-
ing pattern, which appeared in the parameters of the mod-
els and in other variables, such as the first occurrence-
nodes of long proleptic and sylleptic shoots. This architec-
ture confirmed that the fate of buds on parent branches
being pruned depended on the number of the retained buds
and that heavy heading back could stimulate sprouting.
It was noteworthy that most of the fruits were located
within the sylleptic branching zone in peach tree. The mean
numbers of fruits located in sylleptic branching zones were
twice as many as in proleptic branching zones (data not
presented). In comparison with light heading back, medium
heading back had a higher proportion of fruiting zones. As
the latter pruning measures are usually considered balanc-
ing vegetative and reproductive growth in comparison with
the former, this classification is coherent with the conven-
tional pruning measures. The proportion of proleptic branch-
ing zones and sylleptic branching zones increased from
“3nlp” to “12nlp”. This suggests that, therefore, the bal-
ance between proleptic branching zones and sylleptic
branching zones on the parent branches appears to predict
the later fruiting behavior of the different pruning measures
(Lauri et al., 1997; Nunez-Elisea and Crane, 2000).
The results of modelling the branching patterns empha-
sized the proximity and difference of pruning measures. In
the case of light heading back, more branching shoots oc-
curred along the central and distal portion of the parent
branches. Sylleptic shoots had their highest probability at
most distal nodes on parent branch, while the most proxi-
mal nodes remained unbranched. The increase in the prob-
ability of sylleptic branching towards the proximal end was
more notable in parent branches being heavy heading back
than in those being light and medium heading back. The
degree of pruning on two-year-old parent branch was thus
probably important in orientating the development of the
lateral shoots and branching patterns. Most of the crop
was produced on the canopy periphery on sylleptic shoots
and proleptic shoots arising from parent branches. The most
distal node of each parent branch being pruned was the
one with the highest probability of producing the sylleptic
shoot. A better knowledge of these effects of pruning should
lead to an improvement in the pruning program of mature
trees (Lauri et al., 1997; Nunez-Elisea and Crane, 2000).
As typical sun-adapted plant, both leaves and fruits of
the peach tree need exposure to light for high fruit quality
(Biasi et al., 1993). The conventional pruning (“5nlp” to
“10nlp”) measure of the parent branches might lead to less
latent buds, medium fruiting shoots, and more open
canopies, so that fruit yield and soluble solids concentra-
tion could be improved (Smith et al., 1994). In the meantime,
a large proportion of the one-year-old shoot was located
away from each other, leaving this space open to light
penetration, and air movement within the canopy, thus en-
vironmental conditions suitable for fungal diseases were
minimized (Miller et al., 2001). Manipulating the vegetative
and reproductive growth relationships may be considered
as the ultimate goal of fruit tree management systems. Se-
lecting the most appropriate pruning measures could be
possible, provided that the branching and fruiting habits
of the trees are known (Lauri et al., 1997; Nunez-Elisea and
Crane, 2000).
The present study provided the evidence of the varia-
tion in shoot growth within a population of mature peach
trees and enabled us to recognize discrete shoot types.
Table 2 Initial probability of the hidden semi-Markov models corresponding to different pruning measures

State
Initial probability
3nlp 4nlp 5nlp 6nlp 7nlp 8nlp 9nlp 10nlp 11nlp 12nlp
0 0.35 0.80 0.74 0.73 0.70 0.67 0.74 0.71 0.80 0.74
1 0.53 0.20 0.26 0.27 0.29 0.32 0.26 0.28 0.20 0.26
2 0.12 0.00 0.00 0.00 0.01 0.01 0.00 0.01 0.00 0.00
Acta Botanica Sinica 植物学报 Vol.46 No.7 2004800
The presented stochastic model was able to take into ac-
count all lateral shoot types even if the causalities were
numerous and complex. Unlike the usual methods for sim-
ply estimating branching densities, the methodology of the
statistical modelling led us to capture the embedded archi-
tecture and contributed to a more precise analysis of the
branching pattern for parent branches. The model was there-
fore a useful tool for characterizing shoot distribution in-
side a branching zone according to function of the diverse
lateral shoot, for example, vegetative and/or reproductive
branching shoots. The determination of the branching and
fruiting rules of the parent branches being pruned could
help to develop more effective pruning measures to main-
tain fruit yield and to attain high quality.
The whole structural forms of some tree species have
been described through hidden semi-Markov models and
computer simulations with a wide range of applications,
including plant breeding programs and landscape design
(Costes and Guédon, 1997; Reffye and Houllier, 1997; Godin
et al., 1999; Godin, 2000). For many other tree species,
however, the lack of information concerning basic archi-
tectural and developmental pattern prevents the applica-
tion of the models.
Our present study could serve as a reference frame
against which quantitative differences in branching pat-
terns of different pruning measures can be compared. We
presented more detailed observation data and give general
principles for branching pattern on the parent branches
being pruned. These results would be used for a computer
simulation of architecture in the whole tree canopy (Honda
et al., 1997; Hiroaki et al., 1999). The distribution of the
lateral shoots can be visualized in 3-D by using the
AMAPsim growth generator (de Reffye and Houllier, 1997).
Branching patterns of the parent branches being pruned
are indeed likely to vary with cultivars and rootstocks, thus,
the effects of the conditions remain to be studied and fur-
ther work is needed.
The simulation of the branching architecture, which is
based on stochastic models, opens the field to numerous
agronomic applications. Combined with a mechanistic model
of photosynthesis, for example, it would substitute for the
large-scale field experiments which test the alternative man-
agement strategies (planting density, fruit load, thinning,
etc.).
4 Conclusion
The Markov chain stochastic process is thus more gen-
eral approach than a simple branching probability for
modeling the branching process of the parent branch
being pruned. Though hidden semi-Markov chain model is
only a descriptive model, it can still interpret some of the
biological phenomena it describes. This study is the first
step in the elaboration of a stochastic model of the archi-
tecture of the whole peach tree canopy. It is clear that the
stochastic modeling of the branching process will improve
predictions on the effects of different pruning measures.
Our work would suggest that light heading back was
not recommended to alleviate shoot crowding, to improve
fruit size and quality and to maintain an optimum light ex-
posure on all tree parts, whereas moderate heading back
was a sustainable management strategy that growers can
adopt to improve profitability of the orchard. From a practi-
cal point of view, our result suggested that the effective-
ness of heavy heading back, usually recommended on weak
ageing trees, could be improved if it was carried out on the
parent branches.
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(Managing editor: WANG Wei)