Bud and growth-unit structure in seedlings and saplings of Nothofagus alpina (Nothofagaceae)

In temperate trees, axis length growth generally results from the differentiation of organs at the end of a growing season and the extension of such "preformed organs" in the next growing season. Neoformation, i.e., the simultaneous differentiation and extension of organs, has been studied for only a few species. Here we evaluated bud composition and growth unit (GU) size for seedlings and saplings of Nothofagus alpina, a valuable South American forest tree. Trunk GUs of seedlings and saplings included preformed and neoformed organs, whereas main-branch GUs of saplings were entirely preformed. The size of a GU was more closely related to the number of preformed green leaves than to the number of cataphylls of its preceding bud. Proximal buds of a trunk GU had more cataphylls and less green-leaf primordia than distal buds. Individual leaf area increased from proximal to distal positions on trunk GUs. For trunk and main-branch GUs, the length/width ratio was maximum for leaves in intermediate positions. The development of large neoformed leaves at the end of the growing season could increase the photosynthetic capacity of this species in late summer, when the activity of preformed organs is likely to be decreasing.     

Deciphering the ontogeny of a sympodial tree

This paper addresses the identification and characterization of developmental patterns in the whole structure of a sympodial species, the apple tree. Dedicated stochastic models (hidden variable-order Markov chains) were used to (i) categorise growth units (GUs) on the basis of their morphological characteristics (number of nodes and presence/absence of flowering) and position along axes, (ii) analyse dependencies between successive GUs and (iii) identify repeated patterns in GU sequences. Two successive phases, referred to as “adolescent” and “adult”, were identified in two apple tree cultivars. In the adolescent phase, “very” long monocyclic GUs were followed by long polycyclic GUs, whereas in the adult phase medium GUs were preferentially followed by short GUs. Flowering GUs constituted a preferential pathway between vegetative GUs of decreasing vigour (long, medium and short) and generated patterns that were interpreted with respect to fruiting regularity. The proposed modelling gave a global and quantitative picture of the two-scale structuring of apple tree ontogeny: a coarse scale corresponding to the succession of the previously mentioned phases and a fine scale corresponding to the alternation between flowering and vegetative GUs. This led us to propose a synthetic scheme of apple tree ontogeny that combines growth phases, polycyclism and flowering, and which could be transposed to other sympodial trees.     

Growth-unit structure in trees: effects of branch category and position on Nothofagus nervosa, N. obliqua and their hybrids (Nothofagaceae)

In plants with rhythmic growth, a branch segment extended in one event is known as growth unit (GU). GU structure, resulting from the resources allocated to stem length, volume and mass, and to leaf area and mass, is relevant for understanding branch functioning in the context of plant development. This study compares GU structure between main branches and short branches positioned at low and high positions on nursery-grown trees of three closely related genetic entities: Nothofagus nervosa, N. obliqua and natural hybrids between these species. GUs of short branches, compared to those of main branches, had lower length, diameter and number of leaves, and higher specific leaf area (SLA), stem density and proportional mass in leaves than in stems. GUs at high position on the trees had a higher proportion of their mass in stem than in leaves and a lower SLA than those at low position. Stem density was higher for N. nervosa and the hybrid trees than for N. obliqua. Most other GU traits did not differ statistically between the considered genetic entities. The three genetic entities exhibited distinct patterns of variation in leaf size with leaf position along main-branch GUs. The individual tree had a significant effect on most variables. GU structure would have a major ontogenetic component and would play a relevant role in the architecture of Nothofagus species and their adaptation to different environmental conditions.     

Modelling branching patterns on 1-year-old trunks of six apple cultivars

The structure resulting from branching on 1-year-old apple tree trunks was analysed in a set of apple cultivars with diverse branching and fruiting habits. Four different lateral types borne on successive nodes were observed when vegetative and flowering fates, as well as sylleptic and proleptic branching, were taken into account. The location and grouping of lateral types along the trunk were analysed for all cultivars, but are detailed for one cultivar only. This cultivar showed a succession of zones, each zone being characterized by its composition of lateral types. Statistical models-hidden semi-Markov chains-were built to take this structure into account and to characterize the cultivar's specific branching pattern. The models showed that most of the branching zones had a similar location in the different cultivars, even though zone composition and zone length differed among cultivars. On a more detailed scale, the nodes bearing a lateral, regardless of its type, were frequently followed by latent buds. The validity of the models and their biological interpretation are discussed with respect to parent shoot dynamics, hormonal gradients and competition between neighbouring buds.     

Analysis of the plant architecture via tree-structured statistical models: the hidden Markov tree models

Plant architecture is the result of repetitions that occur through growth and branching processes. During plant ontogeny, changes in the morphological characteristics of plant entities are interpreted as the indirect translation of different physiological states of the meristems. Thus connected entities can exhibit either similar or very contrasted characteristics. We propose a statistical model to reveal and characterize homogeneous zones and transitions between zones within tree-structured data: the hidden Markov tree (HMT) model. This model leads to a clustering of the entities into classes sharing the same 'hidden state'. The application of the HMT model to two plant sets (apple trees and bush willows), measured at annual shoot scale, highlights ordered states defined by different morphological characteristics. The model provides a synthetic overview of state locations, pointing out homogeneous zones or ruptures. It also illustrates where within branching structures, and when during plant ontogeny, morphological changes occur. However, the labelling exhibits some patterns that cannot be described by the model parameters. Some of these limitations are addressed by two alternative HMT families.     

Preformation and distribution of staminate and pistillate flowers in growth units of Nothofagus alpina and N. obliqua (Nothofagaceae)

Background and Aims

The distribution and differentiation times of flowers in monoecious wind-pollinated plants are fundamental for the understanding of their mating patterns and evolution. Two closely related South American Nothofagus species were compared with regard to the differentiation times and positions of staminate and pistillate flowers along their parent growth units (GUs) by quantitative means.

Methods

Two samples of GUs that had extended in the 2004–2005 growing season were taken in 2005 and 2006 from trees in the Lanín National Park, Patagonia, Argentina. For the first sample, axillary buds of the parent GUs were dissected and the leaf, bud and flower primordia of these buds were identified. The second sample included all branches derived from the parent GUs in the 2005–2006 growing season.

Key Results

Both species developed flowering GUs with staminate and/or pistillate flowers; GUs with both flower types were the most common. The position of staminate flowers along GUs was similar between species and close to the proximal end of the GUs. Pistillate flowers were developed more distally along the GUs in N. alpina than in N. obliqua. In N. alpina, the nodes bearing staminate and pistillate flowers were separated by one to several nodes with axillary buds, something not observed in N. obliqua. Markovian models supported this between-species difference. Flowering GUs, including all of their leaves and flowers were entirely preformed in the winter buds.

Conclusions

Staminate and pistillate flowers of N. alpina and N. obliqua are differentiated at precise locations on GUs in the growing season preceding that of their antheses. The differences between N. alpina and N. obliqua (and other South American Nothofagus species) regarding flower distribution might relate to the time of anthesis of each flower type and, in turn, to the probabilities of self-pollination at the GU level.Key words: Branch, bud, growth unit, Markovian models, Nothofagus alpina, N. obliqua, Patagonian forests, pistillate flower, preformation, staminate flower     

桃树修剪分枝模式的模拟

在不同修剪手法下,对栽培桃树(Prunuspersica(L.)Batsch)不同母枝上的分枝模式进行了比较研究.从分枝模式来看:修剪后的母枝基本由3个不同的区域组成,基部是不萌发的潜伏芽形成的未分枝区域;中部是延迟分枝和多次分枝组成的分枝区域(主要的枝条类型有短枝、长枝和多次枝);顶部是被剪除的部分.我们通过隐式半马尔可夫模型来模拟这一分枝模式,主要是定量描述1次枝和多次枝在母枝上的数量及其分布状况.在上述模型中,未分枝区、延迟分枝区和多次分枝区称为瞬时态,被剪除的部分称为吸收态.模拟的结果与观察的结果进行对比后发现,两者具有很好的一致性.这说明隐式半马尔可夫模型是模拟植物分枝过程的一种有效方法,尽管隐式半马尔可夫链模型只是一个描述性的模型,但仍能对其所描述的生物现象进行解释,在预测修剪手法对母枝分枝模式影响方面比传统的方法具有明显的优势.本研究结果是建立三维虚拟桃树树冠分枝结构的基础.     

Apple shoot architecture: evidence for strong variability of bud size and composition and hydraulics within a branching zone

* In the apple tree (Malus domestica), shoot architecture - the distribution of lateral bud types and growth along the parent shoot - has been extensively investigated. The distal zone of a shoot is characterized by a high proportion of vegetative or floral axillary branches mixed with latent buds and aborted laterals. The hypothesis tested here was that bud development was related to hydraulic conductance of the sap pathway to the bud, independently of an acrotonic (proximal vs distal) effect. * The distal zone of 1-yr-old shoots was studied on five cultivars for bud size and composition (number of appendages) and hydraulic conductance before bud burst. * Bud size, composition and hydraulic conductance were highly variable for all cultivars. A positive correlation was demonstrated between both the number of cataphylls and green-leaf primordia, and hydraulic conductance. Cultivar and bud size affected the intercept of these relationships more than the slope, suggesting similar scaling between these variables, but different hydraulic efficiencies. A great proportion of small buds were also characterized by null values of hydraulic conductance. * This study suggests that hydraulically mediated competition exists between adjacent buds within the same branching zone, prefiguring the variability of lateral types in the following growing season. It is hypothesized that this developmental patterning is driven by hydraulic characteristics of the whole metamer, including the subtending leaf, during bud development.     

Application of the Functional-Structural Tree Model LIGNUM to Sugar Maple Saplings (Acer saccharum Marsh) Growing in Forest Gaps

LIGNUM is a functional-structural model that represents a treeusing four modelling units which closely resemble the real structureof trees: tree segments, tree axes, branching points and buds.Metabolic processes are explicitly related to the structuralunits in which they take place. Here we adapt earlier versionsof LIGNUM designed to model growth of conifers for use withbroad-leaved trees. Two primary changes are involved. First,the tree segment for broad-leaved trees consists of enclosedcylinders of heartwood, sapwood and bark. Leaves consistingof petioles and blades are attached to the segments. Secondly,axillary buds and rules governing their dormancy are includedin the model. This modified version of LIGNUM is used to simulatethe growth and form of sugar maple saplings in forest gaps.The annual growth of the model tree is driven by net productionafter respiration losses are taken into account. The productionrate of each leaf depends on the amount of photosyntheticallyactive radiation it receives. The radiation regime is trackedexplicitly in different parts of the tree crown using a modelof mutual shading of the leaves. Forest gaps are representedby changing the radiation intensity in different parts of themodel sky. This version of LIGNUM modified for use with broad-leaf,deciduous trees and parameterized for sugar maple, yields goodsimulations of growth and form in saplings from different forestgap environments. Copyright 2001 Annals of Botany Company LIGNUM, functional-structural tree model, tree architecture, sugar maple, modelling growth and form     

Morphological and architectural features of young Nothofagus pumilio (Poepp. & Endl.) Krasser (Fagaceae)

The morphology and architecture of young Nothofagus pumilio plants growing as understorey and in a cleared area were assessed. Length, number of internodes, presence of branches and apex condition were registered for each growth unit (GU) in the sampled plant. GUs were grouped according to branching order and age of the bearing axis. Understorey plants were seven years old and had a short trunk bearing 2–3 orders of branches; all of their most recent GUs were horizontal and of comparable size. Plants growing in the cleared area were 10–16 years old and had a vigorous vertical and dominant trunk bearing 4–5 orders of less vigorous, horizontal branches. Plants from the cleared area showed signs of having had comparable-size GUs in all of their axes at a younger stage of growth. N. pumilio plants appear to start their growth with the production of short GUs in all of their axes irrespective of the light conditions. In contrast, the development of a vertical, vigorous trunk, seems to be restricted to plants growing in open environments.     

LIGNUM: A Tree Model Based on Simple Structural Units

The model LIGNUM treats a tree as a collection of a large numberof simple units which correspond to the organs of the tree.The model describes the three dimensional structure of the treecrown and defines the growth in terms of the metabolism takingplace in these units. The activities of physiological processescan be explicitly related to the tree structures in which theyare taking place. The time step is 1 year. The crown of the model tree consists of tree segments, branchingpoints and buds. Each pair of tree segments is separated bya branching point. The buds produce new tree segments, branchingpoints and buds. The tree segments contain wood, bark and foliage.A model tree consisting of simple elements translates convenientlyto a list structure: the computer program implementing LIGNUMtreats the tree as a collection of lists. The annual growth of the tree is driven by available photosyntheticproducts after respiration losses are accounted for. The photosyntheticrate of foliage depends on the amount of light. The amount ofphotosynthates allocated to the growth of new tree segmentsis controlled by the light conditions and the amount of foliageon the mother tree segment. In principle, the biomass relationshipsof the tree parts follow the pipe model hypothesis. The orientationof new tree segments results from the application of constantbranching angles. LIGNUM has been parametrized for young Scotspine (Pinus sylvestrisL.) trees. However, the model is generic;with a change of parameter values and minor modifications itcan be applied to other species as well. Growth model; object-oriented modelling; tree architecture; branching structure; Pinus sylvestrisL.; developmental morphology and physiology; photosynthesis; respiration     

Dynamics of non-structural carbohydrates in developing leaves, bracts and floral buds of cotton

Development of cotton (Gossypium hirsutum L.) squares (i.e. floral buds with bracts) is fundamental for yield formation. A 2-year field study was conducted to determine dry weight (DW) accumulations of cotton leaves, floral bracts and floral buds, and the changes in concentrations of non-structural carbohydrates (hexoses, sucrose and starch) in these tissues during square ontogeny as affected by fruiting positions within the plant canopy. During square development, DW accumulation of a subtending sympodial leaf and floral bracts followed a sigmoid growth curve with increasing square age, whereas the DW increase of a floral bud followed an exponential curve. Main-stem node (Node 8, 10 or 12) and branch position (proximal vs. distal) within a plant canopy significantly affected DW accumulations of the leaf, bracts and floral bud. Starch was the dominant non-structural carbohydrate in the three tissues, accounting for more than 65% of total non-structural carbohydrates (TNC). Subtending leaf TNC increased as square age increased. The bracts exhibited a smaller change in TNC than leaves. Non-structural carbohydrate concentration was the lowest in 10-day-old floral buds, and had little change during the first 15 days of square development. Within 5 days prior to anthesis, the floral-bud TNC increased dramatically, tripling at the time of floral anthesis compared with 15-day-old floral buds. Square age and fruiting position significantly affected non-structural carbohydrate concentrations of subtending leaves, bracts, and floral buds. The correlation did not exist between final boll retention and non-structural carbohydrate concentrations of floral buds at different fruiting positions under normal growth conditions. The pattern of floral-bud non-structural carbohydrates during square ontogeny suggests that major events in carbohydrate metabolism occur just prior to anthesis.     

Analysing branching pattern in plantations of young red oak trees (Quercus rubra L., Fagaceae)

Branching patterns of the growth units of monocyclic or bicyclic annual shoots on the main axis of 5-year-old red oaks were studied in a plantation in south-western France. For each growth unit, the production of axillary structures associated with each node was described in the form of a sequence. For a given category of growth units, homogeneous zones (i.e. zones in which composition in terms of type of axillary production does not change substantially) were identified on such sequences using a dedicated statistical model called a hidden semi-Markov chain. For instance, on the first growth unit of bicyclic annual shoots, a zone with 1-year-delayed branches was found systematically below a zone with buds and one-cycle-delayed branches. Branching patterns shown by the growth unit of monocyclic annual shoots and on the second growth unit of bicyclic annual shoots were very similar. Branches with a 1-year delay in development tended to be polycyclic at the top of the growth unit and monocyclic lower down. The number of nodes shown by the branched zone of the growth unit of monocyclic annual shoots was stable, irrespective of the total number of nodes of the growth unit. In contrast, the second growth unit of bicyclic annual shoots exhibited a correlation between the number of nodes in the branching zone and the total number of nodes. The contribution made by this method to understanding plant functioning is discussed.     

Genetic determinism of the vegetative and reproductive traits in an F1 olive tree progeny

The agronomic performance of fruit trees is significantly influenced by tree internal organization. Introducing architectural traits in breeding programs could thus lead to select new varieties with a regular bearing and lower input demand in order to reduce training and environmental costs. However, an interaction between tree ontogeny and genetic factors is expected. In this study, we investigated the genetic determinism of architectural traits in the olive tree, accounting for tree development over 5 years until first flowering occurrence. We studied an F1 progeny issued from a cross between two contrasted genotypes, ‘Olivière’ and ‘Arbequina’. Tree architecture was decomposed in quantitative traits, related to (1) growth and branching, (2) first flowering and fruiting. Models, including the year of growth, branching order and genotype effects, were built with variance function and covariance structure when necessary. After a model selection, broad sense heritabilities were calculated. During the first 3 years, both the mean values of vegetative traits and genetic factor significance depended on the shoot within-tree position. Dependencies between consecutive years were revealed for traits related to whole tree form. Whole tree form variables showed medium to high broad sense heritability values, whereas reproductive traits were highly heritable. This study demonstrates the existence of ontogenic trends in the olive tree, which result in traits heritable only at the tree periphery. A phenotyping strategy adapted to its architectural characteristics and a list of relevant traits, such as maximal internode length, is proposed. Transgressive effects suggest that genetic progress could be performed in future selection programs.     

疏花对富士苹果光合同化物分配的外部调节和生理表现

在盛花期,利用对树冠不同部位疏除花序的试验。对富士苹果树体内同化物的调配及其生理表现进行了研究。结果表明,苹果平均单果重和平均单果叶面积之间关系呈线性正相关。该相关关系在不同处理之间无差异（r=0.91),充分说明在苹果树体内存在一个可自由流动的碳水化合物库或者说树体对结果具有光合调节作用,疏花可以从外部调节光合同化物分配的方向。对每株苹果树未结果部位和结果部位短枝及延长枝叶片净光合速率测定表明。结果和未结果部位光合速率没有显著差异。虽然疏花没有显著影响苹果单株枝条生长量和叶面积,但是,苹果树树冠全部疏除花序的一侧 或主枝的平均枝条生长量和叶面积去比该树其它结果部位分别平均高出153.5cm和8900cm^2,差异极为显著。苹果树疏除花序1/2或3/4的数量使苹果平均单果重比不疏花分别显著增加了33g或79g。而果实钙浓度每百克鲜重分别降低了1.62mg或2.66mg,充分说明当疏花显著地影响果实大小时,果实内钙浓度也会明显地发生相应的变化,虽然在疏花处理之间不同部位疏除花序没有影响单株花芽总数量,但是,每株树前一年春季疏花的部位比未疏花,结果的部位极显著地增加了花芽数量（SED=11.6)。     

Terminal and intermediate segment lenghts in neuronal trees with finite length

A basic but neglected property of neuronal trees is their finite length. This finite length restricts the length of a segment to a certain maximum. The implications of the finite length of the tree with respect to the segment length distributions of terminal and intermediate segments are shown by means of a stochastic model. In the model it is assumed that branching is governed by a Poisson process. The model shows that terminal segments are expected to be longer than intermediate segments. Terminal and intermediate segments are expected to decrease in length with incrasing centrifugal order. The results are compared with data fromin vivo pyramidal cells from rat brain and tissue cultured ganglion cells from chicken. A good agreement between data and model was found.     

Apple dwarfing rootstocks and interstocks affect the type of growth units produced during the annual growth cycle: precocious transition to flowering affects the composition and vigour of annual shoots

Background and Aims: Precocious flowering in apple trees is often associated witha smaller tree size. The hypothesis was tested that floral evocationin axillary buds, induced by dwarfing rootstocks, reduces thevigour of annual shoots developing from these buds comparedwith shoots developing from vegetative buds. Methods: The experimental system provided a wide range of possible treevigour using ‘Royal Gala’ scions and M.9 (dwarfing)and MM.106 (non-dwarfing) as rootstocks and interstocks. Second-yearannual shoots were divided into growth units corresponding toperiods (flushes) of growth namely, vegetative spur, extensiongrowth unit, uninterrupted growth unit, floral growth unit (bourse)and extended bourse. The differences between the floral andvegetative shoots were quantified by the constituent growthunits produced. Key Results: The dwarfing influence was expressed, firstly, in reduced proportionsof shoots that contained at least one extension growth unitand secondly, in reduced proportions of bicyclic shoots (containingtwo extension growth units) and shoots with an uninterruptedgrowth unit. In treatments where floral shoots were present,they were markedly less vigorous than vegetative shoots withrespect to both measures. In treatments with M.9 rootstock,vegetative and floral shoots produced on average 0·52and 0·17 extension growth units, compared with 0·77extension growth units per shoot in the MM.106 rootstock treatment.Remarkably, the number of nodes per extension growth unit wasnot affected by the rootstock/interstock treatments. Conclusions: These results showed that rootstocks/interstocks affect thetype of growth units produced during the annual growth cycle,reducing the number of extension growth units, thus affectingthe composition and vigour of annual shoots. This effect isparticularly amplified by the transition to flowering inducedby dwarfing rootstocks. The division of annual shoot into growthunits will also be useful for measuring and modelling effectsof age on apple tree architecture.     

桃树修剪分枝模式的模拟

在不同修剪手法下,对栽培桃树(Prunuspersica(L.)Batsch)不同母枝上的分枝模式进行了比较研究。从分枝模式来看修剪后的母枝基本由3个不同的区域组成,基部是不萌发的潜伏芽形成的未分枝区域;中部是延迟分枝和多次分枝组成的分枝区域(主要的枝条类型有短枝、长枝和多次枝);顶部是被剪除的部分。我们通过隐式半马尔可夫模型来模拟这一分枝模式,主要是定量描述1次枝和多次枝在母枝上的数量及其分布状况。在上述模型中,未分枝区、延迟分枝区和多次分枝区称为瞬时态,被剪除的部分称为吸收态。模拟的结果与观察的结果进行对比后发现,两者具有很好的一致性。这说明隐式半马尔可夫模型是模拟植物分枝过程的一种有效方法,尽管隐式半马尔可夫链模型只是一个描述性的模型,但仍能对其所描述的生物现象进行解释,在预测修剪手法对母枝分枝模式影响方面比传统的方法具有明显的优势。本研究结果是建立三维虚拟桃树树冠分枝结构的基础。     

Vertex analysis of Purkinje cell dendritic trees in the cerebellum of the rat

All networks are made up of vertices (points interconnected by segments), which include terminals interconnected by terminal segments, nodes interconnected by link segments and the root point connected to the tree by the root segment. All nodes may be classified into unique types according to the number of terminal and link segments they drain. For example, there are three distinct dichotomous nodes, a 'primary' node draining two terminal segments, a 'secondary' node draining one terminal segment and a link segment, and a 'tertiary' node draining two link segments. The numbers of primary and tertiary nodes approximate to equality in large networks and thus the ratio of primary to secondary nodes defines topology. All higher order nodes ( trichotomous and beyond) may be resolved into dichotomous forms and incorporated into the analysis. Different forms of growth may thus be analysed by comparing the frequency distributions of nodes with those generated by computer simulated growth models. Moreover, all vertices can be ordered so that metrical parameters are easily incorporated and the hierarchical arrangements of vertices of different order discerned. The dendritic trees of 48 Purkinje cells, taken from folia along the primary fissure, were analysed using vertex analysis. The mean number of segments in Purkinje cell trees was 881 +/- 23 (s.e.) and mean total dendritic length 7959 +/- 233 (s.e.) micrometers. Segment lengths were longest over proximal segments but over most of the tree segment lengths were constant at 10 +/- 0.2 (s.e.) micrometers. Vertex, segment and terminal frequency distributions of equivalent orders were all normal with a slight positive skew. Peak frequencies were recorded at the 12th equivalent order. The mean primary/secondary nodal vertex ratio was 0.93 and the proportion of trichotomous branch points in the tree was 5%. Comparison of the frequency distribution of all vertices with computer generated models showed that growth of the Purkinje cell was most closely simulated by a random terminal growth model, incorporating 5% trichotomy , in which the branching of high order terminals was more likely than low order terminals. It was concluded that growth of the Purkinje cell tree could proceed by random terminal branching with growth occurring preferentially over a front composed of terminals that are ascending through a corridor in the molecular layer whose margins are defined by neighbouring trees.