JXB Advance Access originally published online on August 25, 2006
Journal of Experimental Botany 2006 57(12):3131-3143; doi:10.1093/jxb/erl075
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RESEARCH PAPER |
Similarities and gradients in growth unit branching patterns during ontogeny in ‘Fuji’ apple trees: a stochastic approach
1UMR BEPC INRA/AgroM/CIRAD/IRD, Equipe Architecture et Fonctionnement des Espèces Fruitières, 2 Place P. Viala, F-34060 Montpellier Cedex 1, France
2UMR AMAP CIRAD/CNRS/INRA/IRD/Univ. Montp. II, Botanique et Bioinformatique de l'Architecture des Plantes, CIRAD TA40/PS2, F-34398 Montpellier Cedex 5, France
3INRIA, Virtual Plants Team, 2004 Route des Lucioles BP 93, F-06902, Sophia-Antipolis, France
*To whom correspondence should be addressed. E-mail: costes{at}ensam.inra.fr
Received 23 March 2006; Accepted 7 June 2006
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Abstract |
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This study aims to explore and model the changes in growth unit (GU) branching patterns during tree ontogeny. The question was addressed in apple trees cv. ‘Fuji’, by analysing the relative impact of GU length and within-tree position. The development of two 6-year-old trees was recorded over 6 years. The fate of axillary buds along each GU was represented as a sequence of symbols corresponding to five types of lateral growth: latent buds, short, medium, long, and floral lateral GUs. Based on an exploratory analysis of data and a priori hypotheses, a hidden semi-Markov chain was estimated from all of these GU sequences. This model was composed of six transient states representing successive branching zones along the GUs. The accuracy of this global model was a posteriori assessed by fitting the characteristic distributions computed from model parameters to the corresponding empirical characteristic distributions extracted from the observed sequences. The observed sequences were then grouped hierarchically according to the GU length, year of growth, and branching order. Comparing model parameters between these sub-groups revealed similarities between GUs. These similarities were based on particular branching zones whose composition and relative position within the GUs remained invariant across the subgroups: the latent zones, floral zone, and short-lateral zone. The probability of occurrence of the floral zone varied with the year, showing the alternate fruiting of ‘Fuji’. It is shown that, during tree ontogeny, as GU length decreases, branching patterns tend to progressively simplify due to the disappearance of the most central zones and a progressive reduction in the length of the floral zone.
Key words: Branching, flowering, hidden semi-Markov chain, tree architecture
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Introduction |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionReferences |
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Plant structures are often described as resulting from repetitive processes (White, 1979; Barlow, 1994). However, the repeated units are not totally similar due to morphogenetic gradients during tree ontogeny (Gatsuk et al., 1980; Barthélémy et al., 1997). One of the most evident signs of these gradients is the decrease in growth unit (GU) length with tree age and branching order. Branching patterns are likely to change with the GU length and, consequently, depend on tree age. Recently, the concept of similarity between branching systems has been revisited using different mathematical frameworks (Ferraro and Godin, 2000; Guédon et al., 2003; Prusinkiewicz, 2004), and new methods have been introduced to quantify the degree of self-similarity at the plant scale (Ferraro et al., 2005). However, changes in branching patterns during tree ontogeny, in particular, in relation to the parent GU length, have not been investigated so far.
In the present study, the question of similarities and gradients in GU branching patterns was addressed using a dedicated statistical model built from a database corresponding to entire trees described at the node scale. The apple tree was used because of its relatively small adult size (Costes et al., 2003), which makes it possible fully to describe the plant structure over several years. Moreover, in apple trees, tree structure, morphogenetic gradients, and GU branching patterns are closely connected to factors such as annual regularity (or alternance) of fruit production, the distribution of fruit within the tree structure, and fruit size (Laurens et al., 2000; Costes et al., 2006). Acrotonic gradients have been identified in apple (Crabbé, 1987) and the location of axillary buds along parent shoots determines their fate as short or long laterals (Kaini et al., 1984; Ouellette and Young, 1994). The mesotonic location of sylleptic shoots has also been demonstrated in this species (Crabbé, 1984; Costes and Guédon, 1997). Moreover, branching patterns along the first GU show a succession of homogeneous branching zones in different apple cultivars. These patterns have been modelled using a particular class of stochastic models referred to as hidden semi-Markov chains (Costes and Guédon, 2002).
Hidden semi-Markov chains are particularly useful for identifying homogeneous zones within sequences and detecting transitions between zones. They have been applied in various biological contexts, such as gene finding (Burge and Karlin, 1997; Lukashin and Borodovsky, 1998), protein secondary structure prediction (Schmidler et al., 2000), and the analysis of branching and flowering patterns in plants (Guédon et al., 2001). Hidden semi-Markov chains generalize hidden Markov chains (for a tutorial about hidden Markovian models, see Ephraim and Merhav, 2002) with the distinctive property of explicitly modelling the length of each zone. A hidden semi-Markov chain is constructed from a semi-Markov chain which represents both the succession of zones and the length of each zone, while observation distributions attached to each state of the semi-Markov chain represent the observed composition within each zone. For gene finding, the possible zones include the exons and introns which are characterized by different compositions in terms of the nucleotides. In plants, the branching zones are characterized by different compositions in terms of branching types. For instance, a zone characterized by a mixture of latent buds and shorts shoots may be followed by a zone characterized by a mixture of latent buds, short shoots, and floral shoots. The fact that latent buds and short shoots can be observed in different branching zones entails that the branching zones are not directly observable (hence the ‘hidden’ qualifier of the model).
In this paper, the similarities and gradients in GU branching patterns during tree ontogeny are explored. The possibility of capturing all branching patterns observed within the trees in a single global model was tested. This global model was then used to evaluate the degree of similarity in the branching patterns by using the invariance of subsets of parameters as indicators of common patterns. In addition, the impact of morphogenetic gradients during tree ontogeny on the stability of model parameters was investigated. The gradients were characterized by (i) GU length in the number of nodes which represents the potential growth of the corresponding axis when it developed and (ii) the position of the GU within the tree, represented by its year of growth and its branching order.
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Materials and methods |
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Extracting sequences from the encoded database of measured tree structures
The database consists of recorded measurements for two 6-year-old Fuji apple trees (Costes et al., 2003). The trees observed were grafted on ‘M9 Pajam 1’ rootstock in the nursery and were planted when they were 1 year old at 2 mx5 m at the INRA experimental station near Montpellier, France. Development over the 6 years was deduced using morphological markers such as leaf scars, according to a method fully described by Costes et al. (2003). Within this database, four types of GUs were considered: short (<5 cm), medium (5–20 cm), long (>20 cm), and floral GUs. A sequence of symbols representing the fate of the axillary buds along the GU, from the base to the top, was then extracted for every GU in the database, resulting in a new database of GU sequences. Five types of lateral growth were considered: latent buds, short lateral GUs, medium lateral GUs, long lateral GUs, and floral GUs.
Representing branching patterns with a hidden semi-Markov chain
The statistical modelling of the branching patterns relies on the following assumptions which have to be validated a posteriori, i.e. after model estimation:
- Well-defined zones with stable branching types can be identified in all the GUs (i.e. branching types do not change substantially within each zone but change markedly between zones). In particular, the branching types within the different zones are assumed to be independent of GU length, year of growth, and branching order.
- Each branching zone may be present or absent depending on GU length, year of growth, and branching order.
- Some branching zones may be longer or shorter, depending on GU length.
- Each branching zone may be present or absent depending on GU length, year of growth, and branching order.
Therefore a single hidden semi-Markov chain was built for the branching patterns of all the GUs observed in the tree (based on the first assumption). Then the stability of model parameters across different groups of GUs was investigated. The GUs were classified into groups by considering different potential growth (represented by GU length in number of nodes) and positions (represented by the year of growth and the branching order). ‘Contextual’ model parameters inferred from these sub-groups of sequences were then compared in order to investigate the similarities and gradients in GU branching patterns.
In the estimated hidden semi-Markov chain, ‘time’ refers to the index parameter of the sequence which is, in the present application, the node rank, and each zone is represented by a mathematical object called a state. The possible successions of zones and the length of each zone (in number of nodes) are both represented by the semi-Markov chain, while the proportion of branching types observed within a zone is represented by observation distributions attached to each state of the semi-Markov chain (Guédon et al., 2001). A hidden semi-Markov chain is thus defined by four subsets of parameters:
- Initial probabilities to model which is the first zone occurring in a GU.
- Transition probabilities to model the succession of zones along the GUs.
- Occupancy distributions attached to non-absorbing states to represent the zone length in number of nodes (a state is said to be absorbing if, after entering this state, it is impossible to leave it).
- Observation distributions to model the composition properties within the zones (proportions of different branching types).
- Transition probabilities to model the succession of zones along the GUs.
It is generally assumed, while using hidden semi-Markov chains, that the sequence length is independent of the process that is supposed to have generated the sequence (Guédon, 2003). This assumption entails that the time spent in the last visited state is ‘censored’ or truncated, i.e. the most distal branching zone was randomly truncated by growth cessation. In this study, it was chosen to assume instead that the end of an observed sequence systematically coincides with the transition from the current state to an extra absorbing ‘end’ state. To fulfil this requirement, each observed sequence was completed with an extra symbol. Hence, at the end of an observed sequence, the process systematically jumps to the absorbing ‘end’ state. In this way, the sequence length distribution is implicitly modelled by a combination of the state occupancy distributions (Guédon, 2005; for further discussions of this modelling in the case of hidden Markov chains, also see Durbin et al., 1998, chapter 3).
The model specification relies in a crucial way on the choice of the number of states (i.e. zones). On the basis of both an exploratory analysis and previous studies (Costes and Guédon, 2002), a range of possible values was a priori selected for the number of states and a hidden semi-Markov chain estimated for each possible number of states (from 5 to 7). For each estimated hidden semi-Markov chain, the accuracy was a posteriori assessed by fitting the characteristic distributions computed from model parameters to the corresponding empirical characteristic distributions extracted from the observed sequences. The main characteristic distributions used were the intensity characteristics, i.e. the probabilities of the different branching types as a function of the node rank [see Guédon (2003) where this point is illustrated with another apple tree data set]. Finally, a hidden semi-Markov chain composed of six successive transient states and an absorbing ‘end’ state was selected. The semi-Markov chain was ‘left–right’, i.e. transitions from a given state to following states were possible, while transitions to states already visited were not possible. The assumption was also made that only latent buds can be observed in the first state (state 0), which corresponds to the basal unbranched zone of the GUs, which, in turn, corresponds partly to the preformed part of the GUs (Costes, 2003).
The maximum likelihood estimation of the parameters of a hidden semi-Markov chain requires an iterative optimization technique, which is an application of the expectation–maximization (EM) algorithm (Guédon, 2003, 2005). The hidden semi-Markov chain was estimated on the basis of 699 sequences of cumulated length 48 930. The 44 independent parameters consisted of two independent initial probabilities, 12 independent transition probabilities, 12 parameters for the occupancy distributions attached to the six non-absorbing states (all these occupancy distributions were negative binomial distributions defined by two parameters), and 18 independent observation probabilities.
Grouping sequences according to morphogenetic gradients
In order to explore the changes in GU branching patterns during tree ontogeny, GU sequences were grouped hierarchically according to their length, year of growth, and branching order (Fig. 1). Each group thus represents the GUs with a certain growth that can be observed at the different positions within the trees. In the original dataset there was a fundamental distinction between medium and long GUs, considered as two different developmental stages (short GUs, which correspond to a third stage, were not considered since they are usually not branched). Therefore the procedure was started by grouping sequences into medium and long categories, with a threshold of 15 nodes which corresponds approximately to the mean number of preformed organs within winter axillary buds (Costes, 2003). Each subgroup of sequences was then further divided according to their year of growth, from year 1 to year 5, with years 1 and 2 grouped together. The sixth-year GUs had been recorded to provide the information for the fifth-year GU sequences, but these sixth-year GUs were not yet branched. The distinction between GUs was again refined by considering their branching order (0 for trunks, 1 for branches borne along the trunks, and so on). This procedure resulted in a set of ‘GU sequence groups’. In most cases, the number of sequences in a group was >10 and the sequence group was therefore included in the analysis for comparison of the model parameters with other groups (Table 1). Even though the group of long GUs in year 2 comprised only 10 members, it was included in the analysis because it contained all the information regarding the oldest and most central GUs in the trees.
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Comparing contextual model parameters
‘Contextual’ models were inferred from each GU group so that their parameters could be compared across the groups. This was done in the following way. First, the most probable state sequence was computed for each observed sequence on the basis of the estimated global model. Here, the most probable state sequence can be interpreted as the optimal segmentation of the corresponding observed sequence into successive branching zones. Secondly, bivariate sequences were built by associating each observed sequence with the corresponding most probable state sequence. For each subgroup of bivariate sequences, counts for the transition between states, the ‘time’ spent in each state, and the branching types observed in each state were extracted. Thirdly, the contextual parameters estimated from these counts were compared with the global parameters and with contextual parameters of other groups in order to assess which parameters are conserved or modified according to the context. It is important to notice that contextual parameters are estimated conditionally to the global estimated model, since the most probable state sequences from which the counts are extracted were computed on the basis of this global model. Three sets of contextual parameters regarding the GU structure in terms of zones were compared between subgroups of GUs: (i) the probability of occurrence of each zone; (ii) the zone length distributions (i.e. contextual occupancy distributions); and (iii) the transition probabilities between zones. In addition, the branching-type distributions (i.e. contextual observation distributions) were compared for each zone that was present in the groups of GUs considered.
Zone length distributions, which were often asymmetric and thus not normally distributed, were compared using the Wilcoxon–Mann–Whitney test (with P <0.05). Branching-type distributions were compared using chi-squared tests for contingency tables (with P <0.05) since the observed variable is qualitative (the types of axillary production cannot be ordered in a meaningful way because of the floral shoots). All the statistical analyses were carried out using the Stat module of the AMAPmod software (Godin et al., 1997).
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Results |
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Global model
The global hidden semi-Markov chain estimated using all sequences grouped together had seven states, corresponding to six homogeneous zones along the GUs and an absorbing ‘end’ state (Fig. 2). The states were defined on the basis of their respective observation distributions:
- State 0 corresponds to the initial zone that contains only latent buds and is always present at the base of the GUs (in the following, this state will be referred to as the basal latent zone).
- State 1 corresponds to a mixture of short lateral and latent buds (referred to as the short-lateral branching zone).
- State 2 is a poorly branched zone with a mixture of all four possible lateral GUs (the long diffuse zone).
- State 3 corresponds to a second short/latent zone which differs from state 1 by the possible presence of lateral medium GUs (the short-medium-lateral zone).
- State 4 corresponds to the floral zone, with lateral floral GUs mixed with latent buds and short GUs (the floral zone).
- State 5 contains a large majority of latent buds mixed with a few short laterals (the top latent zone).
- State 6 is the absorbing ‘end’ state that corresponds to the extra symbol added at the end of the sequences; this state, which does not correspond to a zone in the GU, will be considered only if necessary in the following.
- State 1 corresponds to a mixture of short lateral and latent buds (referred to as the short-lateral branching zone).
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Each zone, modelled by a state, covered three to five successive nodes on average, except the long diffuse branching zone whose length was about 20 nodes on average. A high degree of variability regarding the transition probabilities between zones was observed in the sequences. Some zones were skipped more often than others (Table 2). The analysis of this variability is described below in relation to the contextual models obtained from the GU groups.
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The accuracy of the estimated global model was then assessed by examining the fit of characteristic distributions computed from model parameters to the corresponding empirical characteristic distributions extracted from the observed sequences (Guédon et al., 2001). In the present case, the most useful characteristic distributions were the distributions of the number of successive occurrences of a branching type and the distributions of the total number of occurrences of a branching type per sequence (Fig. 3). Because the distributions for long and medium lateral GUs were similar, only those for long lateral GUs are presented. The number of latent buds per GU was 10 on average. The distribution was slightly asymmetric with up to 40 latent buds observed per GU. The number of long and medium laterals varied from one to seven per GU. The distributions for the number of short and floral lateral GUs were similar to each other, ranging from one to 15 per GU. For each of the different types of lateral GU, the number of successive occurrences was approximately geometrically distributed, with a high frequency of value 1 corresponding to isolated laterals. All these empirical distributions extracted from the observed sequences were adequately fitted by the corresponding theoretical distributions computed from the estimated model (Fig. 3).
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Comparing branching patterns of GU
In order to test the original assumptions made in building the global model and to examine the impact of GU length, year, and order on branching pattern, the ‘contextual’ parameters obtained from the different sub-groups of GUs were compared (Fig. 1). Refining the strategy of grouping led to smaller numbers of GUs with similar length and position within the tree to be considered (Table 1). Since years and orders are closely linked in the first years of growth, subgroups of GUs classified by length, years, and orders were compared only from year 3 to year 5 and from order 0–1 to order 4. In each case, the three characteristics dealing with the GU branching structure in terms of zones (i.e. the probability of occurrence of each zone, the length distributions, and the transition probabilities between zones) and the branching type distributions for each zone were compared between the subgroups of GUs.
Occurrence of the different zones
Except for the two latent zones, the probability of occurrence of a zone varied with the length category, the year, and the branching order (Table 2; Fig. 4). The short-lateral and floral zones occurred less frequently in the medium GUs than in the long GUs. In addition, the long diffuse branching zone and the short-medium zone sometimes occurred in the long GUs, while these zones were almost entirely absent in the medium GUs. This led to different branching patterns between long and medium GUs (Fig. 4a). In the medium GUs, 43% of the sequences were unbranched (direct transitions from basal latent zone to the latent zone at the top) and about half of the sequences contained only a median branched zone between the two latent zones. This median zone was either floral (11% of the sequences) or vegetative (37% of the sequences) with almost only short laterals. Few sequences exhibited both short-lateral and floral zones in succession. In long GUs (Fig. 4a), no sequences were unbranched. About half the long GUs contained a single median zone, either floral or vegetative (24% and 28% of the sequences, respectively). In all other long GUs, several zones in succession were observed between the two latent zones. In 20% of these sequences, the short-lateral zone was followed by the floral zone, while in another 20% it was followed by the short-medium zone. In this later case, since the observation distributions for these short-lateral and short-medium-lateral zones are quite similar, they may have been difficult to separate clearly. Only 8% of the sequences contained a long diffuse branching zone (zone 2). The observation of three zones in succession was particularly rare but still possible.
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Regarding changes by year, the main differences were observed for the long diffuse branching zone and the floral zone (Table 2; Fig. 4b, c). For long GUs, the diffuse branching zone was observed with a high probability (P=0.9) in the first 2 years of growth, while it was rarely observed in the third year (P=0.13) and not observed at all in subsequent years. It was never observed in medium GUs. Thus, the long diffuse branching zone is characteristic of the long GUs that developed in the first 2 years of growth and is rare in the global sample. The probability of occurrence of the floral zone was alternatively high and low over successive years (Table 2). These fluctuations highlight the alternate fruiting of ‘Fuji’ trees. All the GUs of the trees, whether long or medium, had a similar alternate behaviour over successive years. In addition, the probability of occurrence of the short-lateral and short-medium-lateral lateral zones tended to decrease over successive years, in particular in medium GUs (Table 2; Fig. 4b, c).
Branching order impacted on the probability of occurrence of the long diffuse branching zone and the short-medium-lateral zone (Table 2). The long diffuse zone was observed only in long GUs and only until year 3. Moreover, it only occurred in year 3 at order 0 or 1 and was absent at order 2. Similarly, the occurrence of the short-medium-lateral zone in long GUs in year 4 decreased as the order increased from 0–1 to 3. In year 5, this zone was observed only in the GUs at order 0 or 1. This means that both these zones were observed only in the GUs that were the continuation of the trunk or the main branches. The occurrence of the short-lateral zone in the long GUs also tended to decrease with branching order, but in year 5 only. The occurrence of the latent and floral zones showed no obvious variation with order.
Variation in zone length
The lengths of the six zones were significantly different for long and medium GUs (Table 3). The mean zone lengths were higher in long GUs than in medium GUs. In particular, the floral zone was twice as long in long GUs as in medium GUs. Thus an investigation, at the level of individual sequences, was undertaken to find out if the zone lengths were correlated with the total GU length. A high positive correlation coefficient (0.79) was found between the length of the diffuse branching zone and the total GU length (Fig. 5). The length of the floral zone also tended to increase with the total GU length, but only for sequences with <25 nodes (Fig. 5). However, the correlation coefficient was quite low (0.60). No correlation existed for latent and vegetative zones (states 0, 1, 3, and 5; data not shown). Thus, zone length increases, at least to some extent, with the total GU length in the two zones that contained lateral floral GUs. In all the other zones, the zone length could be considered as being independent of the total GU length.
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The zone length distributions did not show large differences between subsamples of sequences classified per year or branching orders (Table 3). In fact, the differences between length categories were far more pronounced than those related to the year or order. Even though significant differences between length distributions were found in the latent zones and the short-lateral zones (states 0, 5, and 1) in long GUs according to the year, these differences did not involve more than three internodes on average and did not correspond to a systematic variation with years or orders. In medium GUs, the zone length distributions did not show any significant difference in any year. In particular, the floral zone had similar length distributions regardless of the year within each length category.
Zone composition
The branching-type distribution for the three zones that were present in all of the different GU subgroups (corresponding to short-lateral, short-medium-lateral, and floral zones, respectively) were compared. In both long and medium GU subgroups, the distributions for the short-lateral zone were almost the same, with a large number of short laterals mixed with latent buds and very few floral laterals (Fig. 6). However, a significant difference between the medium and long GUs was highlighted by a non-parametric Kruskal–Wallis test. This was interpreted as resulting mainly from the very high numbers of observed sequences (>1000). In the two other zones (short-medium-lateral and floral), the branching-type distributions were similar and no significant difference was detected by the statistical test (illustrated only for floral zone in Fig. 6).
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Similarly, the branching-type distributions for the short-lateral, short-medium-lateral, and floral zones were found to be essentially not significantly different across different years (years 3, 4, and 5) within length categories (Fig. 6b, c). As mentioned previously, the short-lateral zone contained a slightly higher proportion of latent buds in long GUs than in medium GUs, but this was only true for years 4 and 5 (data not shown). The only significant difference was in the composition of the floral zone in long GUs since the ‘off year’ (year 3) contained a lower proportion of lateral floral GU. However, this difference concerned only 12% of the lateral GUs within the zone.
When GUs were grouped by order, the zones had similar branching-type distributions (data not shown). In particular, the floral zone which occurred with greater or lower probability depending on the year, always had the same composition.
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Discussion |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionReferences |
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GU branching patterns were represented by six successive zones defined by substantially different branching types. This zonal structure results from the impact of the node position (distance from the basis and the apex) on the axillary bud fate during shoot ontogeny (Sachs, 1999) and possibly from a hormonal equilibrium involving auxin and cytokinin fluxes (Cline, 2000; Wilson, 2000; Cook et al., 2001). Four zones constitute a common theme within the trees: the basal and subapical latent zones, the short lateral zone, and the floral zone. These zones were also present along the 1-year-old trunks of ‘Fuji’ (Costes and Guédon, 2002). However, two of the zones previously observed along trunks were not identified here: the median zone with sylleptic lateral GUs and the subapical zone with long lateral GUS, which corresponds to the acrotonic distribution of branching (Crabbé, 1987), were not observed. The absence of sylleptic laterals may result from a difference in growing conditions of the plant material. Indeed, the rootstock used, ‘Pajam 1’, is known to be dwarfing (Ferree, 1988) and may have reduced the expression of syllepsis. Moreover, in an earlier study, plants were cut back after 1 year of growth (Costes and Guédon, 1997), which may have enhanced sylleptic branching. In other locations within the trees besides the trunk, the absence of syllepsis in the data set may be interpreted as a consequence of the decrease in annual shoot growth with increasing tree age, which suppresses syllepsis in the case of apple trees, as shown by Crabbé (1987).
The vegetative long or medium lateral GUs were located in a median position along the parent GUs (in states 1, 2, and 3), which may appear to contradict the acrotonic branching pattern usually described in apple trees. However, this median position of vegetative lateral GUs probably results from the orientation of the GUs in space, since most of the GUs analysed were subjected to bending (except trunks, which are rare in the present set of sequences). This orientation may impact on the branching pattern by decreasing apical growth and promoting vegetative re-growth on the curved portions of the stem (Wareing and Nasr, 1961). Even though the branch response to bending depends on both time and genotype (Lauri and Lespinasse, 2001), the present results suggest that, in the case of ‘Fuji’, bending promoted vegetative regrowth in zones located below the floral zone, i.e. in the short-medium zone (which is the only zone with medium lateral GUs). Interestingly, the position of the floral zone remained unchanged since it was still located in the upper third of the GUs.
The within-tree changes in GU branching patterns were explored by analysing the relative impact of the length of the parent GU and of different positions in the trees (year of growth and branching orders). These three factors were not independent, since GU length decreases with both year and order (Costes et al., 2003). However, each grouping provided its own insight: parent GU length had the strongest impact on branching patterns, followed by year and then by branching order. GU length clearly impacted on both the number of branching zones and the length of branching zones. As GU length decreased with tree age, the zones located in median positions, which contained vegetative long and medium lateral GUs tended to disappear. By contrast, the zones located at the upper and basal ends of the GUs remained unchanged in both length and composition. A similar dependency of the branching structure upon GU length, with median zones disappearing progressively, has been observed previously in the peach tree (Fournier et al., 1998). This suggests that the shoot structure and succession of zones are closely related to the shoot growth periods during the growth season. This assumption is supported by previous studies that have analysed axillary meristem fates in relation to shoot growth rate, in particular for syllepsis (Powell and Vescio, 1986; Génard et al., 1994) and axillary flowering (Costes and Lauri, 1995). A second dependency concerns parent GU length and zone length. This type of dependency has been shown previously in oak trees (Heuret et al., 2003). In ‘Fuji’ apple trees, this relationship was only evident for the long diffuse branching zone and, to a lesser extent, for the floral zone, the only two zones containing lateral floral GUs. This suggests that changes in GU length mainly impact on the flowering zone, while the latent and vegetative zones are less dependent upon GU length.
Growth year mostly impacted on the probability of occurrence of the floral zone, while its length and composition remained almost unchanged. This is consistent with the alternate fruiting of ‘Fuji’ (Ferree and Smid, 2000). Climatic conditions and within-tree competition (between developing organs and with floral initiations for the next year) are likely to be involved in biennial bearing (Jonkers, 1979). The present study provides new insight into where and how it occurs within entire trees: the variation had the same intensity (same probability of occurrence of the floral zone) and was synchronous in all of the GUs of the tree, whatever their branching order and length category. However, focusing on branching patterns, the present study accounted only for axillary flowering on 1-year-old GUs which is usually considered as having a relatively low impact on total fruit production (Wünsche et al., 1996). Despite this limitation, the general conclusion regarding the correlation between flowering and year on all the GUs remains consistent with previous results obtained on the same trees that included both terminal and axillary flowering (Costes et al., 2003).
The impact of branching order was relatively low compared with the two previous factors. It was quite similar to that of GU length, since it mainly concerned the progressive disappearance of the long diffuse and short-medium branching zones. However, this disappearance was less rapid in the GUs that continued the trunk and the main branches than in GUs at higher branching orders. This is consistent with a slower decrease in growth on the trunk and main branches than in higher orders, as previously shown in both ‘Fuji’ and ‘Braeburn’ cultivars (Costes et al., 2003).
Despite the relative variability of its occurrence probability and length, the floral zone had a remarkable stable position along its parent GU. It was always located in the upper third of the GU. A similar location has also been observed in peach trees (Fournier, 1998) and on a set of apple cultivars (Costes and Guédon, 2002) whose fruiting types ranged from Type I to Type IV according to Lespinasse's classification (Lespinasse, 1977). Thus, the location of the axillary flowering zone appears stable with both the genotype and within-tree GU position. This stability provides new insights into the timing of floral differentiation in apple trees. Some authors have estimated this event could occur between 3 and 6 weeks after full bloom (Foster et al., 2003), while others have estimated it to occur much later (Fulford, 1966a, b). However, considering that floral differentiation is a continuous process in axillary buds under formation, the present results suggest that axillary floral differentiation may be more related to the parent GU growth than to a particular period of time. Indeed, medium and long GUs cease growing at different times (unpublished personal observation) and therefore the period of floral differentiation in their axillary buds is likely to occur earlier in medium than in long GUs. More precisely, floral differentiation in axillary buds could occur when the plastochronic index (defined as the time spent between the emergence of two successive leaf primordia) is slowing down, after a fast growing period during which syllepsis occurs and before growth ceases (Fulford, 1965; Crabbé and Escobedo-Alvarez, 1991). This interpretation remains consistent with the dependency upon node position and GU hormonal equilibrium mentioned previously. The present results suggest that the concept of ‘node counting’, proposed by Sachs (1999) to account for the transition between the juvenile and adult stages on annual plants, could be extended to the different GUs of a tree. Finally, axillary flowering appears to be a two-step process: (i) a global flowering potential, which determines the occurrence of the flowering zone, seems to be defined each year at the whole-tree level, while (ii) a local induction of axillary buds determines the length of the flowering zone at the level of each GU, depending on its within-tree location.
To summarize, GU branching patterns exhibited both similarities and gradients during tree ontogeny. It has been shown that the degree of similarity of GUs over the years depends on them sharing certain zones, in particular the latent bud zones, the floral, and the short-lateral zones. A progressive simplification of the branching patterns was observed when moving from the centre of the trees towards their periphery. Complex branching structures with more than one median branched zone (either vegetative or floral) tended to decrease in number towards the periphery, while the percentage of unbranched medium GUs progressively increased. Two phenomena contributed to this simplification: (i) the two median states disappeared with increasing tree age and branching order; and (ii) the floral zone length decreased with the parent GU length.
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M Renton's postdoctoral degree was granted by the INRA Department of Genetics and Plant Breeding. We gratefully thank JC Salles, G Garcia, and S Ploquin for their contribution in field observations.
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