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(American Journal of Botany. 2002;89:1180-1187.)
© 2002 Botanical Society of America, Inc.


Tropical Biology

Synchronization of growth, branching and flowering processes in the South American tropical tree Cecropia obtusa (Cecropiaceae)1

Patrick Heuret3, Daniel Barthélémy, Yann Guédon, Xavier Coulmier2 and Juliette Tancre2

Unité mixte de recherche CIRAD-CNRS-EPHE-INRA-Université Montpellier 2 botanique et bioinformatique de l'architecture des plantes (AMAP), TA40/PS2, 34398 Montpellier cedex 5, France

Received for publication August 30, 2001. Accepted for publication January 29, 2002.


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Cecropia obtusa Trécul (Cecropiaceae) is a pioneer species associated with the initial phases of regeneration of tropical South American forests. A comparison of the succession of morphological events associated with each node (inflorescences or branches developed or aborted and underlying internode length) making up the axes of 30 trees helped to establish a link between their architecture and the regularity and synchronicity of their expression of growth, flowering, and branching processes over time on an individual and stand level. For a given individual, new nodes are emitted at the same rate on all the axes, irrespective of their branching order. Flowering and branching alternate, and these processes occur in all the axes of the tree synchronously. On a stand level, flowering and branching occur regularly every 35 nodes or so, which apparently corresponds to an annual rhythm. Under nonlimiting conditions, a single branch tier would be emitted each year, and it is thus possible to determine a posteriori the age of a crown accurately. The merits of the method, the possibility of estimating the age of natural Cecropia obtusa regrowth by observing tree architecture, and the possible applications in the field of ecology are discussed.

Key Words: branching • Cecropia obtusa • Cecropiaceae • flowering • growth • synchronicity • phenology


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
The genus Cecropia Loefl. includes around a hundred neotropical species (Berg, 1978 ), ranging from Mexico to northern Argentina and the West Indies (Wheeler, 1942 ). The species are pioneer trees that colonize cleared areas and open areas with high light levels (Whitmore, 1989 ; Alvarez-Buylla and Martinez-Ramos, 1992 ). As the trees are associated with the initial stages of forest succession, determining their age can help to pinpoint the date of the disturbance that prompted their establishment. To this end, it is necessary to understand the dynamics of their development and architecture over time.

In temperate tree species, meristem functioning is synchronized by an enforced rest period in the winter, and each year a shoot is emitted on all the axes of the tree. Observing morphological or macro-anatomical markers (cataphyll scars, reduction in internode length, growth rings, reduction in pith diameter, etc.; Hallé, Oldeman, and Tomlinson, 1978 ; Heuret et al., 2000 ) often serves to deduce annual growth halt retrospectively. This temporal reference can thus be used to estimate the age of an axis a posteriori and to compare the properties of the annual shoots established in a given year on the axes of a single tree or of several trees. In many tropical plants, the absence of temporal morphological markers makes the retrospective analysis of development difficult, but studies of the regularity of growth, branching, and flowering over time and the analysis of the synchronicity in time of these processes on distinct axes may help the observer to deduce past morphological events.

In Cecropia peltata L. and Cecropia insignis Liebm., flowering has been shown to be annual and to cover a period of several months (Frankie, Baker, and Opler, 1974 ; Fleming and Williams, 1990 ; Milton, 1991 ). In a study conducted on C. obtusifolia Bertol. and C. peltata in Costa Rica, Davis (1970) showed that internode length fluctuates according to an annual pattern that is correlated to rainfall amount.

Cecropia spp. have a very simple architecture and conform to Rauh's architectural model (Hallé, Oldeman, and Tomlinson, 1978 ). Their axes are made of a succession of nodes and internodes whose length and associated lateral productions remain visible and measurable over years. Our aim was to retrospectively study these morphological structures on an individual and stand level in Cecropia obtusa Trécul in order to analyze the regularity of growth, branching, and flowering processes over time with the objective of finding parameters that help reconstruct the developmental dynamic in this species. For this purpose we analyzed the morphological events associated with the successive nodes of an axis (inflorescence or inflorescence scar, branch, underlying internodal length) for all axes of an individual crown and several trees of a same regeneration after forest cutting along a roadside.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Study site
The Cecropia obtusa individuals studied belong to a naturally regenerated stand at the entrance to the Paracou site (5°18' N, 52°55' W) set up by CIRAD (Centre de Coopération Internationale en Recherche Agronomique pour le développement)-Forêt in French Guiana, some 40 km from Kourou. French Guiana is subject to seasonal variations characterized by a 3-mo dry season from mid-August to mid-November and a rainy season for the remaining 9 mo. In some years, there may also be an irregular short dry season in March (Fig. 1).



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Fig. 1. Mean rainfall over 10 yr (from 1981 to 1991) at the ECEREX (Ecologie-Erosion-Expérimentations station; after Sarrailh [1992 ])

 
Morphological features of Cecropia obtusa
Cecropia obtusa develop according to Rauh's architectural model (Hallé, Oldeman, and Tomlinson, 1978 ). The axes are orthotropic, with lateral flowering and rhythmic branching (Fig. 2). Phyllotaxy is alternate and spiral with a fraction of 3/7 (154.3° between two longitudinally adjacent leaves). The leaves are stipulate, entire in young trees, but subsequently become palmatilobate (six to eight lobes). It is a dioecious species with lateral inflorescences. There are three lateral buds in the axil of each leaf (Fig. 3a). The central bud is vegetative and may potentially give rise to a branch. The buds on each side correspond to two proximal axillary buds of the central bud and may give rise to inflorescences, which are thus arranged in pairs, each comprising a set of spikes. The immature spikes are protected by a bract that acts as a sheath, which opens on anthesis (Fig. 3b). Female inflorescences have 4 spikes (Fig. 3c) and male inflorescences have 12 to 15 spikes (Fig. 3d) (Trécul, 1847 ).



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Fig. 2. Habit of Cecropia obtusa Trécul

 


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Fig. 3. Types of axillary products in Cecropia obtusa Trécul. Three buds can be seen in the axil of young leaves (a). The buds on either side of the central bud may develop into inflorescences with several spikes (b). Immature inflorescences are protected by a bract that acts as a sheath. The species is dioecious: female inflorescences have 4 spikes (c), while male inflorescences have 12–15 smaller spikes (d). Figure Abbreviations: yl = young leaf, ls = leaf scar, c = calyptra (stipule), ss = stipule scar, vb = vegetative branching bud, ib = inflorescence bud, fs = female spike, ms = male spike, imi = immature male inflorescence (the protective bract has been removed), ip = peduncle of the inflorescence, abrs = aborted branch scar, ais = aborted inflorescence scar, dbr = developed branch, dis = developed inflorescence scar.

 
Reconstitution of plant growth
The enveloping stipule, or calyptra, found on each node leaves a characteristic ring-shaped scar that can be used to locate the limits of each internode right down to the foot of the tree. However, the frequent development of stilt roots makes locating the internodes nearest the cotyledons both difficult and uncertain. After abscission, the two inflorescence stalks leave characteristic scars that can be identified a posteriori on all the parts of the tree (Figs. 3 and 4). Some inflorescences may abort and fall before anthesis, in which case they leave smaller scars, which can thus be differentiated from those left by fully developed inflorescences. Branches may also abort early in their development, when the bud is beginning to swell, leaving small circular scars. Although branching and flowering zones generally alternate (Barthélémy, 1988 ), every possible combination of branch and inflorescence scars may be seen (aborted branch and aborted inflorescences, aborted branch and fully developed inflorescences, etc.; Fig. 4).



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Fig. 4. Examples of scars resulting from axillary bud functioning. (a) Aborted branch and undeveloped inflorescence buds. (b) Aborted branch and aborted inflorescences. (c) Aborted branch and developed inflorescences. (d) Undeveloped branch and developed inflorescences. (e) Developed branch and developed inflorescences

 
Plant material and measurements made
Thirty trees (18 male and 12 female) were studied. They had 3–5 tiers of branches on the main axis, which was classed as an order 1 axis (A1), while the branches on it were classed as order 2 (A2) and so on, up to order 4. Trunk girth at a height of 1.30 m (GBH) was measured on the standing trees, and the diameter deduced assuming a circular cross section (DBH). The total height of the tree and of the first developed branch (still on the tree or pruned) was recorded on the felled tree.

The following data were recorded at each node: the type of axillary productions associated with the central bud, with the following coding of the three possible outcomes: (0) no branch, (1) aborted branch, and (2) developed branch (pruned branches were included in this category); the type of axillary productions associated with the lateral buds [(0) no inflorescence, (1) aborted inflorescences and (2) developed inflorescences]; and the length of the underlying internode.

The nodes of all the axes were described on ten trees, while only nodes on the main axis (A1) were measured on the other 20. Due to the frequent development of stilt roots, which made observation difficult towards the foot of the tree, the number of internodes separating the cotyledons of the first node measured is uncertain.

The topology, i.e., the relative positions of the different botanical units described (nodes and axes), was coded using the AMAPmod software (Godin et al., 1997 ; Godin, Costes, and Caraglio, 1997 ; Godin, Guédon, and Costes, 1999 ), enabling the precise location of each structure in space during analysis.

The axis are described node by node from the tip (hence, the ranks of the nodes are counted from the tip) (Fig. 5a). Assuming that the nodes of the axes compared were emitted at the same rate, we can consider that nodes with the same rank were emitted at the same time (rank 1 corresponded to the time of the study). If the nodes of the axes compared were emitted at different rates, this agreement between topology and chronology disappears more or less rapidly as the rank increases. In the case of the "internode length" variable, the A2 of a given tree were compared with A1 as per the following principle: the nodes of A1 were counted from the point of insertion of the first pruned or living branch (which determined the base of the crown) to the top of the tree. The rank on an A2 began at (rank of the bearing node on A1) +1 (Fig. 5b).



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Fig. 5. Node ranking methods according to their position on the axis. (a) To compare the values for the "axillary growth" variable, nodes are ranked according to their position in relation to the tip of the axis. (b) To compare the values for the "internodal length" variable, the nodes on A1 are ranked from the point of insertion of the first branch, and the A2 rank starts from that of the bearing node on A1 + 1. The nodes shown in black have the same rank according to this system

 
The regularity of expression and synchronicity of the flowering and branching phenomena on the different axes of a given individual were studied from the ten trees described in their entirety. The results we show on an individual level came from a characteristic tree. Those obtained on a stand level came from the analysis of the main axis of all 30 individuals.

The "branching" variable, with the possible outcome: bud (0), aborted branch (1), and developed branch (2), can be considered as an ordinal variable since the three possible values can be ordered in a meaningful way (corresponding to the code order). This reasoning transposes to the "flowering" variable with its possible (ordered) values: no inflorescence (0), aborted inflorescence (1), and developed inflorescence (2).

An important tool for exploring sequences built from quantitative variables is provided by a series of quantities called sample autocorrelation coefficients, which measure the correlation between observations at different distances apart. When the relevant variable is ordinal, the ordinary or Pearson correlation coefficients can be replaced by the rank correlation coefficients due to Spearman, i.e., the ordinary correlation coefficient between the ranked values. Hence, while the Pearson correlation coefficient looks for a linear relation between two variables, the Spearman rank correlation coefficient looks for a monotonic relation (for more details, see Guédon et al., 2001 ).

The correlation properties of multivariate sequences can be investigated by means of sample cross-correlation functions, which are a direct generalization of sample autocorrelation functions. The cross-correlation function measures the correlation between Xt and Xt+k as a function of the lag k, while the autocorrelation function measures the correlation between Xt and Xt+k as a function of the lag k. The sample autocorrelation function is an even function of the lag and hence needs to be plotted for k = 0, 1, 2, ..., while the sample cross-correlation function is not an even function of the lag and hence needs to be plotted for k = 0, ±1, ±2, ...


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Height, diameter, and position of the first branch and first inflorescence
The trees studied had a mean (±95% confidence limit) diameter of 18.1 ± 1.2 cm 1.30 m from the ground and a mean height of 13.9 ± 2.0 m. The main axis comprised 284 ± 15 nodes. The first branch, either living or pruned, occurred at a height of 6.9 ± 0.5 m on average, corresponding to 120 ± 10 nodes above the first visible node at stilt root level. For most individuals, the first inflorescences occurred just after the formation of the first or second tier of branches (Table 1). Male trees had slightly more developed inflorescences on the trunk than females on average (Table 2). There was no significant difference between males and females in the number of aborted inflorescences.


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Table 1. Location of the first inflorescence scars in relation to successive branch tiers

 

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Table 2. Mean frequency of nodes on A1 with, or having had, aborted, or developed inflorescences, for male and female trees. Nodes were taken from the first developed inflorescence to the tip of the axis. The means are associated with their 95% confidence limit, and the comparisons (Mann-Whitney-Wilcoxon test) of the corresponding distributions are represented by the letters a and b. For a given characteristic, if the letter changes, the corresponding distributions are significantly different at the 95% level

 
Synchronicity on an individual level
Irrespective of the order of the axis considered, the number of nodes per axis was positively correlated to the number of nodes of the bearing axis above its point of insertion (Fig. 6). The slopes of each regression line were very close to 1, suggesting that the establishment of new nodes occurs at the same rate on all the axes of a given tree.



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Fig. 6. Relationship between the number of nodes on the lateral axes (order n) and that of their bearing axis (order n – 1) above their point of insertion. This comparison was made for all the A2 (in relation to A1), A3 (in relation to bearing A2), and A4 (in relation to bearing A3) for ten trees studied

 
For the axes considered as a whole, branches and inflorescences were found in precise, distinct zones (Fig. 7). Flowering and branching zones alternated. For inflorescences, the maximum probabilities of observation were around the 4th, 31st, and 58th node below the apex, while for branches, they were around the 13th, 42nd, and 80th node below the apex. The branch tiers observed on the main axis were also found on all the other orders of branches, suggesting that the branching process affects every part of the tree synchronously. The same applied to the flowering process. Branches were much less represented than inflorescences, and there was a high proportion of aborted branches.



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Fig. 7. Frequency of observation of nodes bearing developed or aborted inflorescences and branches (based on direct observations of their structure or scars), according to the rank of the node from the tip of the axis for the A1, A2, A3, and A4 of a given representative individual. The numbers of nodes for each order, from which the frequencies of observation were computed, are shown below the probabilities of observation

 
The length of the successive internodes on A1 fluctuated, with an amplitude ranging from 2 to 8 cm (Fig. 8). The A2 began with long internodes (up to 14 cm), but their length subsequently decreased until they were shorter than internodes of the same rank on A1. On A2, we also observed fluctuations in internodal length similar to those seen on A1, but they were sometimes slightly staggered. For example, the increase in internodal length, which reached a maximum at rank 62 on A1, had an equivalent on A2 in the second tier of branches at rank 68 (Fig. 8a). The same phenomenon was seen at rank 117 of A1 and rank 124 of third-tier branches (Fig. 8b).



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Fig. 8. Length of successive internodes on A1 from the base of the crown (in grey), and on A2 (in black) of the second (a) and third tier of branches (b) on one characteristic tree

 
Synchronicity on a stand level
On the A1 of the 30 trees studied as a whole, branched zones alternated with zones with inflorescences (Fig. 9). This pattern was apparent on approximately 100 nodes.



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Fig. 9. For all the A1 of the 30 trees studied, frequencies of observation of nodes with developed inflorescences (in grey) or branches (in black) according to node rank from the tip of the axis. The numbers of nodes for each rank, from which the frequencies of observation were calculated, are shown

 
The sample Spearman rank autocorrelation functions for the two variables (Fig. 10a) showed a sinusoidal pattern of period approximately 35 nodes, gradually damping out with the lag. Since the length of branching zones was shorter than the length of flowering zones, the positive "wave" was narrower for the "branching" variable than for the "flowering" variable, while the complementary negative "wave" was larger.



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Fig. 10. Sample Spearman rank autocorrelation function (a) and sample Spearman rank cross-correlation function (b) for the type of axillary production (branching in black and flowering in grey) for all the A1 of the 30 trees studied. The confidence limits are computed under the null condition of no correlation (purely random sequences)

 
The sample Spearman rank cross-correlation functions for the "branching" and "flowering" variables clearly show the alternation between branching and flowering zones with a periodicity of approximately 35 nodes for the basic pattern, corresponding to the succession of a branched zone and a flowering zone (Fig. 10b).

As regards the internodal lengths of the 30 trunks measured, autocorrelation coefficients failed to reveal any significant regularity. Moreover, we did not detect any relation between variations in internodal length and branching or flowering events.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
The significant correlation between the number of nodes on an axis and the number of nodes on its bearing axis above its point of insertion, associated with a slope of the regression lines close to one, suggests that the establishment of new nodes occurs at the same rate on all the axes of the Cecropia obtusa individuals studied. Even in the absence of data on the rate of emission of nodes and on its possible variability over the year, it is thus possible to establish a link between topology and growth patterns over time: two nodes from two different axes on a given tree were established roughly at the same time if they are of the same rank counting from the tip of the axis. This property was also checked on a set of data gathered by D. Barthélémy and C. Edelin in 1983 (unpublished data) concerning Cecropia obtusa trees at different stages of their development (from one to six tiers of branches). On an individual level, the flowering and branching processes alternate at quite specific periods. These two processes affect all the axes and lead to the establishment of developed or aborted structures.

On a stand level, the rate of emission of new nodes (apparent plastochron) and flowering periods of Cecropia obtusa have never been studied for more than a year or at short, regular intervals, as far as we know. On the basis of an analysis, over 5 wk, on 20 axes of trees whose stage of development was not stated, Lauri (1988) estimated the plastochron at between 7 and 12 d. Belin-Depoux et al. (1997) , based on records of the number of nodes established over a 9-mo period, estimated the figure at around 10 d. If one assumes that growth is continuous in this species, the emission of a new node every 10 d or so corresponds to the establishment of around 36 nodes in the course of a year, which coincides with the period observed in the pattern of expression of branching and flowering (Figs. 10a–b). Twice-weekly measurements taken for 2 yr in Costa Rica on Cecropia peltata (Frankie, Baker, and Opler, 1974 ; Fleming and Williams, 1990 ) showed that flowering was annual and spread from April to August during the dry season. The annual nature of flowering was also demonstrated on Cecropia insignis by 2 yr of growth monitoring on Barro Colorado Island, Panama (Milton, 1991 ). As far as we know, no other work refers to flowering patterns with periodicities of more than or less than a year in species of the genus Cecropia. The annual periodicity therefore seems to be appropriate for describing the flowering and branching pattern observed in Cecropia obtusa. The stability of the number of nodes between two zones with branches or flowers, underlined by the significant autocorrelation coefficients over 100 nodes or so (expression of three periods), suggests that the plastochron is highly stable not only for the different axes of a given tree, but also for the different trees in a stand.

It is thus possible to determine the age of tree crowns precisely, simply by counting the number of tiers of branches. In view of these results, it seems to us that the number of nodes and the number of branch tiers should be taken into account to the same extent as branch length or total number of branches when studying Cecropia obtusa growth. On certain individuals (five out of 30 in this study), a branch may be missing from the main axis, or only the scars of aborted buds may be visible. Observing these scars and counting the number of nodes between two successive tiers (from 57 to 63 nodes for the five individuals in question, i.e., more or less double the identified period of 35 nodes between two normally branches developed tiers) proved that a tier was missing, corresponding to a year. This phenomenon was also often observed on branches of the first tier.

Davis (1970) described variations in internodal length in Cecropia peltata and Cecropia obtusifolia in Costa Rica, which depended on the variations in annual rainfall. The internodes established during the dry season were shorter than those established during the rainy season. Under these conditions, observing the alternation of short and long internodes on the main axis would be a way of estimating the age of individuals. Although we observed variations in internodal length, we did not observe any such marked patterns in our study. This can be attributed to the less marked difference between the dry and rainy seasons at our site than in Costa Rica and to the occasional occurrence of a short, more or less severe dry season in March. If we assume that the variations in internodal length observed on the various axes of a given tree are directly linked to the climatic conditions, the slight lag observed between the variations in internodal length on A1 and A2 suggests that the A2 produce slightly more nodes in the early stages of their growth. Internodal length, which is directly affected by environmental factors such as rainfall (Davis, 1970 ), seems to be less stable than the rhythm of new node emission.

In the genus Cecropia, the height of the first branch is always highly stable for a given species (Oldeman, 1974 ; Alvarez-Buylla and Martinez-Ramos, 1992 ; Sposito and Santos, 2001a , b ). In our study, the first branch was at a height of around 7 m, which corresponds to around 120 nodes (with a degree of uncertainty due to the difficulty of observing the lowest nodes). In view of the stability of the number of nodes produced each year (around 35 nodes) and of the number of nodes below the first branches in the crown, the age at which the tree begins to branch would apparently be between 4 and 5 yr. It is highly likely that the plastochron changes during the establishment phase, in line with a "establishment effect" found in most plants obtained from seed (Barthélémy, Caraglio, and Costes, 1997 ). Moreover, tree development may be modified by environmental conditions. Barthélémy (1988) observed Cecropia obtusa growing on bare soils that were both eroded and deprived of humus, which remained single-stemmed all their life and did not exceed a height of a few meters. For trees growing in nonoptimum conditions, the point at which the tree produces its first tier of branches may be linked more to a stage of development than to a chronological age. Knowledge of the stage at which Cecropia obtusa individuals produce branches and of the variability of that age would enable an easy assessment of the age of a regenerated stand, based simply on counting the number of branch tiers on the individuals in the stand. As Cecropia spp. are associated with the initial phases of vegetation sequences (Whitmore, 1989 ; Alvarez-Buylla and Martinez-Ramos, 1992 ), this would enable an estimation of the age of gaps and a better understanding of the development over time of other pioneer species associated with recolonization.

The annual pattern seen for growth, branching, and flowering would also be worth studying on other species of the genus Cecropia, particularly those that live longer, so as to see how less favorable environmental conditions (physical interference, competition for light, etc.) affect tree architecture. It is likely that the plastochron diminishes with trees age as a result of a drift phenomenon (Barthélémy, Caraglio, and Costes, 1997 ).

This study, which was solely based on a posteriori observations, revealed that growth, flowering, and branching were both temporally and topologically organized. Combining this method with growth monitoring could help to detect markers in other species that would provide a clearer understanding of the phenology of those species and of their growth dynamics over time.


    FOOTNOTES
 
1 The authors thank Helen Burford for translating the article and the ENGREF (Kourou) for enabling us to carry out this work. Back

2 Current address: Ecole Nationale du Génie Rural, des Eaux et Forêts, 14 Rue Girardet, 54000 Nancy, France Back

3 Author for reprint requests (patrick.heuret{at}cirad.fr ) Back


    LITERATURE CITED
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 LITERATURE CITED
 
Alvarez-Buylla E. R. M. Martinez-Ramos 1992 Demography and allometry of Cecropia obtusifolia, a neotropical pioneer tree—an evaluation of the climax–pioneer paradigm for tropical rain forest. Journal of Ecology 80: 275-290[CrossRef]

Barthélémy D. 1988 Architecture et sexualité chez quelques plantes tropicales: le concept de floraison automatique. Ph.D dissertation, Université Sciences et Techniques du Languedoc Montpellier II, France

Barthélémy D. Y. Caraglio E. Costes 1997 Architecture, gradients morphogénétiques et âge physiologique des végétaux. In J. Bouchon, P. de Reffye and D. Barthélémy [eds.], Modélisation et simulation de l'architecture des végétaux. Institut national de la recherche agronomique, 89–234. Science Update, Paris, France

Belin-Depoux M. P.-J. Solano C. Lubrano J.-R. Robin P. Chouteau M.-C. Touzet 1997 La fonction myrmécophile de Cecropia obtusa Trecul (Cecropiaceae) en Guyane française. Acta Botanica Gallica 144: 289-313[ISI]

Berg C. C. 1978 Espécies de Cécropia da Amazônia Brasileira. Acta Amazônica 8: 149-182

Davis R. B. 1970 Seasonal differences in internodal lengths in Cecropia trees: a suggested method for measurement of past growth in height. Turrialba 20: 100-104[ISI]

Fleming T. H. C. F. Williams 1990 Phenology, seed dispersal, and recruitment in Cecropia peltata (Moraceae) in Costa Rican tropical dry forest. Journal of Tropical Ecology 6: 163-178

Frankie G. W. H. G. Baker P. A. Opler 1974 Comparative phenological studies of trees in tropical wet and dry forest in the lowlands of Costa Rica. Journal of Ecology 62: 881-919[CrossRef]

Godin C. E. Costes Y. Caraglio 1997 Exploring plant topological structure with the AMAPmod software: an outline. Silva Fennica 31: 355-366

Godin C. Y. Guédon E. Costes 1999 Exploration of plant architecture databases with the AMAPmod software illustrated on an apple-tree hybrid family. Agronomie 19: 163-184[CrossRef][ISI]

Godin C. Y. Guédon E. Costes Y. Caraglio 1997 Measuring and analyzing plants with AMAP-mod software. In M. T. Michalewicz [ed.], Advances in computational life sciences I: plants to ecosystems, 63–94. CSIRO, Melbourne, Australia

Guédon Y. D. Barthélémy Y. Caraglio E. Costes 2001 Pattern analysis in branching and axillary flowering sequences. Journal of Theoritical Biology 212: 481-520

Hallé F. R. A. A. Oldeman P. B. Tomlinson 1978 Tropical trees and forests. Springer Verlag, Berlin, Germany

Heuret P. D. Barthélémy E. Nicolini C. Atger 2000 Analyse des composantes de la croissance en hauteur et de la formation du tronc chez le chêne sessile (Quercus petraea (Matt.) Liebl., Fagaceae) en sylviculture dynamique. Canadian Journal of Botany 78: 361-373[CrossRef]

Lauri P.-E. 1988 Le mouvement morphogénétique, approche morphométrique et restitution graphique. L'exemple de quelques plantes tropicales. Ph.D dissertation, Université Sciences et Techniques du Languedoc Montpellier II, France

Milton K. 1991 Leaf change and fruit production in six neotropical Moraceae species. Journal of Ecology 79: 1-26[CrossRef][ISI]

Oldeman R. A. A. 1974 L'architecture de la forêt guyanaise. Mémoire no. 73, O.R.S.T.O.M, Paris, France

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