Formation of Pseudowhorls inPeperomia verticillata(L.) A. Dietr. Shoots Exhibiting Various Phyllotactic Patterns

Pseudowhorls are composed of leaves attached at almost equallevels and separated by single fully elongated internodes. InPeperomiaverticillata, pseudowhorls form regularly in shoots exhibitingboth spiral and truly whorled patterns of phyllotaxis. In spiralsystems, they are composed of successive leaves positioned onthe ontogenetic helix. In whorled phyllotaxis, leaves of twoadjacent whorls occur at almost the same level and this wayform a pseudowhorl. The number of leaves per pseudowhorl dependson the type of phyllotactic pattern and also the system of primordiapacking. In all the shoots, regardless of the type of phyllotaxis,the number of leaves per pseudowhorl equals the number of leafprimordia in physical contact with the apical dome. It is thesame as the higher number in contact parastichy pairs in spiralpatterns or the number of orthostichies in whorled phyllotaxis.The pseudowhorled pattern is already manifested in the arrangementof leaf primordia. In spiral and whorled phyllotaxis the plastochronratio calculated for primordia or whorls belonging to adjacentpseudowhorls is always higher than that calculated for membersof one pseudowhorl. Moreover, angular distances between primordiaof one pseudowhorl in spiral patterns are more uniform thanexpected in Fibonacci phyllotaxis. These observations were madeon plants both growing in pots and culturedin vitro. 6-Benzylaminopurine,a synthetic cytokinin, added to the medium increases the meannumber of leaves per pseudowhorl. It seems that this effectis indirect: phyllotaxis changes first rather than the destinyof a particular internode in a process of selective elongation.Copyright1999 Annals of Botany Company Peperomia verticillata, pseudowhorls, phyllotaxis, shoot apex.     

A contact pressure model for semi-decussate and related phyllotaxis

Semi-decussate phyllotaxis, in which leaves arise singly and the divergence angles between successive pairs of leaves alternate between approximately 90° and approximately 180°, is accounted for by a contact pressure model. It is assumed that leaf primordia are initiated at a divergence angle close to the Fibonacci angle of 137·5°, that the primordia move under contact pressure, and that when a primordium first experiences contact pressure all other primordia are fixed. Extensions of the model account for: psuedodecussate phyllotaxis, where the leaves appear to arise in pairs; semi-tricussate and pseudo-tricussate phyllotaxis, where the leaves are arranged in, respectively, dissolved or apparent trimerous whorls; and phyllotaxis of the 1,3 series, where the divergence angle is about 100°. The compatibility of the model with current theories of Fibonacci phyllotaxis is discussed.     

Application of Two Mathematical Models to the Araceae, a Family of Plants with Enigmatic Phyllotaxis

In this paper we show that two mathematical models can be ofgreat help in the analysis of observational data, in this casethe difficult and little studied phyllotactic phenomena thatoccur in the Araceae family. We apply the Fundamental Theoremof Phyllotaxis, together with an explanatory model of phyllotaxis,to plant specimens of this family, to obtain phyllotactic parametersand information that cannot be otherwise obtained. Most significantis the fact that the two models show evidence of regularitiesin the overwhelming diversity of the patterns observed in theAraceae (essentiallyDracontium and Anthurium) characterizedby discontinuous transitions. In particular, this work revealsthe regularity of the behaviour of the divergence angle in thespecimens analysed. Features of the inflorescences ofDracontium, especially the presence of whorls, are compared to those observedin inflorescences ofAnthurium (characterized by the absenceof whorls), and in the capitulae of Compositae (characterizedby continuous transition). We question the possible meaningat the genetic level of the diversity of patterns observed atthe macroscopic level. Copyright 2001 Annals of Botany Company Phyllotaxis, Araceae, mathematical models, inflorescence, development     

Properties of maximal spacing on a circle related to phyllotaxis and to the golden mean

A class of divergence angles φ_G of phyllotaxis is defined that distribute leaves about the stem of a plant in a more uniform manner than do nearby angles. A theorem of Swierczkowski concerning the intervals between adjacent points placed on a circle according to the divergence angle 137·5° is generalized to include the other angles encountered in phyllotaxis. These angles are characterized by having continued fraction expansions containing no intermediate fractions after a finite number of terms. This criterion is shown to be sufficient for uniform spacing of leaves.A morphogen concentration field established by the leaves acting as sources is determined principally by :he geometrical spacing of the leaves and hence by their divergence angle. It is shown that the mean square of such a concentration field, is a relative minimum if the leaves are positioned by means of one of the φ_G. Thornley's dynamic scheme for determining the phyllotaxis divergence angles by positioning a new leaf at the minimum of the concentration field of previously placed leaves is also shown to be related to the spacing properties of the φ_G.     

Geometrical relationships specifying the phyllotactic pattern of aquatic plants

The complete range of various phyllotaxes exemplified in aquatic plants provide an opportunity to characterize the fundamental geometrical relationships operating in leaf patterning. A new polar-coordinate model was used to characterize the correlation between the shapes of shoot meristems and the arrangements of young leaf primordia arising on those meristems. In aquatic plants, the primary geometrical relationship specifying spiral vs. whorled phyllotaxis is primordial position: primordia arising on the apical dome (as defined by displacement angles θ ≤ 90° during maximal phase) are often positioned in spiral patterns, whereas primordia arising on the subtending axis (as defined by displacement angles of θ ≥ 90° during maximal phase) are arranged in whorled patterns. A secondary geometrical relationship derived from the literature shows an inverse correlation between the primordial size?:?available space ratio and the magnitude of the Fibonacci numbers in spiral phyllotaxis or the number of leaves per whorl in whorled phyllotaxis. The data available for terrestrial plants suggest that their phyllotactic patterning may also be specified by these same geometrical relationships. Major exceptions to these correlations are attributable to persistent embryonic patterning, leaflike structures arising from stipules, congenital splitting of young primordia, and/or non-uniform elongating of internodes. The geometrical analysis described in this paper provides the morphological context for interpreting the phenotypes of phyllotaxis mutants and for constructing realistic models of the underlying mechanisms responsible for generating phyllotactic patterns.     

The Hierarchical Control of Phyllotaxis

Bolle's phyllotactic theory is enhanced here in the light ofrecent works which underline the importance of vascular organizationin the determination of phyllotactic patterns. It is emphasizedthat non-vascular plants, such as Fucus spiralis, can revealhow normal phyllotaxis originated. These two approaches to phyllotaxis,with others put forward here, present the problem of phyllotaxisas a matter of hierarchical control, which produces the integratedand simple behaviour of the primordia of growing plants. phyllotaxis, hierarchy, brown algae, evolution, vascularity, systems theory, control     

A Modification of Flowering and Phyllotaxis in Silene

Modified proliferous flowers arose spontaneously in a smallproportion of plants of Silene coeli-rosa growing in gardenplots. The modified flowers consisted of leaves, arranged spirallywith a mean divergence angle of 138.4° instead of the pentamerousarrangement of the normal flower, and sometimes also carpelswhich ranged from open structures with exposed ovules to follicle-likestructures, free or fused, to fully fused carpels with free-centralplacentation. In the modified flowers petals and stamens werenot formed. The primordia at initiation were intermediate insize (relative to the apical dome) between normal leaf and normalsepal primordia but were the same absolute size as the latter.The structure of these anomalous flowers is discussed in relationto the normal flowering process. Silene coeli-rosa, flowering, phyllotaxis     

A Model of Flowering in Chrysanthemum

A mathematical model of flowering in Chrysanthemum morifoliumRamat. is described which may be used to predict quantitiessuch as the number of primordia initiated by the apex, plastochronduration and apical dome mass before, during and after the transformationof the apical meristem from vegetative to reproductive development.The model assumes that primordial initiation is regulated byan inhibitor present in the apical dome. Within each plastochronthe apical dome grows exponentially, and the inhibitor concentrationdeclines through chemical decay and dilution. When the inhibitorconcentration falls to a critical level a new primordium isinitiated. There is instantaneous production of inhibitor, anda decrease in dome mass corresponding to the mass of the newprimordium. The process continues until the apical dome attainsa particular mass when the first bract primordium is produced.Subsequent primordia compete with the apical dome for substrates,and the specific growth rate of the dome declines with successiveplastochrons. Eventually, the net mass of the dome starts todecline until it is entirely consumed in the production of floralprimordia. Chrysanthemum morifoliumRamat, flowering, primordial initiation     

Experimental and Analytical Studies of Pteridophytes: XXIX. The Effect of Progressive Starvation on the Growth and Organization of the Shoot Apex of Dryopteris aristata Druce

Observations on shoot apices of Dryopteris aristata maintainedunder conditions of progressive starvation for periods of upto a year are recorded. Changes in the size of the shoot apexand leaf primordia, in the rates of inception and developmentof leaf primordia, and in phyllotaxis, are described and discussed.     

Branching Principles Governing the Architecture of Cornus kousa (Cornaceae)

The complex structure of the crown of Cornus kousa, generallyfive-forked in vegetative branching and two-forked in reproductivebranching, is analysed quantitatively and described by two basicbranching principles: decussate phyllotaxy and the resettingrule for planes of branching. Most Cornus species have opposite,decussate phyllotaxis. The leaf pair (with axillary buds) definesthe branching plane of a node. Because of regular phyllotaxis,the fundamental branching pattern is that every branching planealong an axis is perpendicular to the preceding one. However,the first node of a lateral horizontal shoot always has a horizontalbranching plane; we term this the resetting rule. We observedthat resetting occurs when the first nodes initiated in thevertical plane are repositioned by a twisting of their firstinternodes. All later nodes alternate directions, i.e. showusual decussate alternation. Foliage leaf nodes usually producethree-forked branchings. When vegetative winter buds are formed,a foliar node and adjacent scale leaf node produce a five-forkedbranching. When reproductive winter buds with a terminal inflorescenceare formed, the last foliar node and two adjacent scale leafnodes can produce a variety of branchings but usually producean equal two-forked branching. To understand better the architecturein C. kousa, we contrast it with C. capitata which does notproduce buds with scale leaves and whose vegetative nodes areclearly separated. Copyright 1999 Annals of Botany Company Branching pattern, Cornaceae, Cornus kousa, decussate branching, dogwood, Japanese strawberry tree, tree architecture, tree geometry.     

The diversity and ontogenetic changes of phyllotaxis in wild-types and two leaf form mutants of Antirrhinum majus L.

We have analysed the phyllotactic patterns of the main shoot in vegetative and generative phases of growth in wild type and mutant plants of Antirrhinum majus L. Wild types 'Sippe50' and 'W l08' were compared to mutants grminifolia and phanlastica . The normal vegetative phyllotaxis of the wild type plants is decussate, but the inflorescence phyllotaxis is spiral and of the Fibonacci type. The phyllotaxis patterns of the mutants differ strongly from that of the wild type. Besides decussate phyllotaxis, whorls of three or four elements as well as spiral patterns in vegetative phase were observed. The vegetative phyllotaxis in mutants is ontogenetically unstable with frequent transitions between patterns, including the reversion of chirality of spiral phyllotaxis. The number of transitions per plant was larger in graminifolia than in phantastica . The inflorescence phyllotaxis was more stable and occasional non-typical phyllotaxis patterns finally transformed to a Fibonacci pattern. The results suggest a possible role of genetic factors in determining the regularity of spatial arrangement of organs.     

Implications of opposite phyllotaxis for light interception efficiency of Mediterranean woody plants

Opposite leaves lead to a greater leaf overlapping than leaves spirally arranged along a shoot, decreasing light interception efficiency (Ea, fraction of the light reaching the plant actually intercepted by the leaves) of the crown. However, Ea results from a whole suite of morphological traits. The interplay between phyllotaxis, crown architecture, leaf morphology and Ea was explored in 12 woody species from Mediterranean-type ecosystems, where the abundance of woody species with opposite phyllotaxis is unusually high. The three-dimensional model Y-plant was used to estimate Ea in unbranched, vertical shoots of each species encompassing the natural morphological variation found from moderate shade to open light environments. Ea exhibited significant interspecific differences, ranging from 0.25 in Daphne gnidium to 0.75 in Cistus ladanifer, Olea europaea and Salvia officinalis, decreasing with leaf inclination angle and leaf area ratio (LAR), and increasing with internode-to-leaf-length ratio and supporting biomass. Species with spiral vs. opposite phyllotaxis did not differ in their mean Ea. However, the former had higher Ea than the latter at short internode lengths. The natural range of variation in internode length had a larger effect on Ea than the natural range of leaf elevation angle. Principal component analysis segregated species with opposite phyllotaxis from those with spiral leaves because of their greater self-shading for high sun elevation angles (>45°); they were in turn distributed in two groups, one with high Ea, large investment in supporting biomass and long internodes, and another with low Ea and large LAR. Species with spiral phyllotaxis all had intermediate or low Ea and steep leaf elevation angles. Species with opposite phyllotaxis can compensate their less efficient leaf arrangement by decreasing leaf elevation angle and increasing internode length, but they may experience a real phylogenetic constraint for light interception when biomass allocation to supporting tissues (internodes and petioles) becomes very costly. This constraint could be involved in the shade intolerance of woody Mediterranean species exhibiting opposite phyllotaxis.     

Flower Development in Silene: Morphology and Sequence of Initiation of Primordia

The initiation and development of the flower of Silene coeli-rosawas followed by examining apices by scanning electron microscopy.The sepals, stamens and carpets are initiated in a spiral sequence,the direction of the spiral king the opposite of the acropetalhelix of unequal axillary buds at the nodes below the flower.The petals are initiated almost simultaneously and at the sametime as the first few stamens. The change in phyllotaxis fromopposite and decussate in the vegetative shoot to spiral inthe flower occurs with the displacement of the first two sepalsaway from the mid-line of the apex and towards the axillarybud at the node below the flower. The sizes of the sepals andstamens are a function of their age since initiation but thepetals grow more slowly. The Silene flower can be interpretedas a shoot bearing primordia with associated axillary primordia,some of the latter being precocious in their development. Silent weli-rosa, flower initiation, flower development, phyllotaxis, primordia     

Leaf phyllotaxis: Does it really affect light capture?

The intriguing mathematical properties of leaf phyllotaxis still attract scientific attention after centuries of research. Phyllotaxis, and in particular the divergence angle between successive leaves, have been frequently interpreted in terms of maximization of light capture, although certain model simulations of light capture by vertical shoots revealed minor effects of phyllotaxis in comparison with the effect of other morphological features of the plant. However, these simulations assumed a number of simplifications, did not take into account diffuse light, and were not based on real plants with their natural range of morphological variation. This study was aimed at filling these gaps by examining the influence on light harvesting of shoot architecture and divergence angle in four species with spiral phyllotaxis (Quercus ilex, Arbutus unedo, Heteromeles arbutifolia and Daphne gnidium) with a realistic 3-D model (Y-plant). A wide range of divergence angles (from 100° to 154°) was observed within each species, with 144° being the most frequent one. These different divergence angles rendered very different vertical projections of the shoot due to contrasting patterns of leaf overlap as seen from above, but they rendered indistinguishable light interception efficiencies (Ea). Setting the leaves with an opposite-decussate phyllotaxis led, however, to a 40–50% decrease of Ea. The interplay of internode length, leaf size and shape, and leaf elevation angle led to significant species differences in Ea. Thus, only particular phyllotaxis (e.g., decussate) might be functionally inefficient under certain combinations of the various morphological variables that influence light capture of a shoot. This revised version was published online in June 2006 with corrections to the Cover Date.     

Experimental and Analytical Studies of Pteridophytes: XXXVIII. Some Observations on Spiral and Bijugate Phyllotaxis in Dryopteris aristata Druce

In an attempt to assess some of the factors which determineleaf arrangement at the shoot apex, a study has been made ofphyllotaxis in the fern Dryopteris aristata. It is shown thatclockwise and counter-clockwise spirals occur with equal frequencyboth in field collections and in adventitious and experimentallyinduced buds which arise on the rhizomes and apices of plantsgrown in the laboratory. In addition to the two common spiralarrangements, a form with bijugate phyllotaxis has been noted.It is concluded that the three types of leaf arrangement arenot under direct genetic control, but rather are dependent oncircumstances of growth at the apex.     

Induced Abscission Sites in Internodal Explants of Impatiens sultani: A New System for Studying Positional Control: with an Appendix: A Mathematical Model for Abscission Sites

Intemodes from Impatiens sultani shoots, explanted into sterileculture, often developed a transverse separation layer afterone to two weeks and the top then abscised from the bottom ofthe explant. Such abscission occurred more rapidly and in agreater proportion of explants when 00001 per cent auxin (IAA)was provided basally and when younger intemodes and shorterexplants were used. The distance of the separation layer fromthe base of the explant varied little with explant length, butincreased with the concentration of auxin applied basally. It seems that in this adventitious abscission the processesof positional definition and differentiation proceed withoutpause, whereas in normal abscission the position is definedearly in development but the final stage of differentiationof the separation layer is delayed until much later when theorgan senesces. To account for the results from the internodal explants andfrom surgical operations on shoots as well as for the characteristicposition of abscission sites of leaves and fruits, we suggestthat the position of abscission is controlled primarily by auxinacting as a morphogen: abscission sites occur at Y-junctionsjust above the base of the arm with the lower activity and auxinstatus, or in single axes above a region of higher auxin status.In both sites, the auxin concentration decreases in the apicaldirection. This hypothesis is supported by a mathematical model (see Appendix)of the interaction of diffusive and polar transport in controllingthe concentration gradient along intemodes with specified auxinconcentrations maintained basally. The model allows predictionsconcerning the site and timing of abscission which accord withobservations on intemodal explants. Impatiens sultani Hook., abscission, auxin, differentiation, diffusion coefficient, IAA, morphogen, polar transport coefficient, positional control, separation layer     

Spatiotemporal mechanisms of morphogen gradient interpretation

Few mechanistic ideas from the pre-molecular era of biology have had as enduring an impact as the morphogen concept. In the classical view, cells in developing embryos obtain positional information by measuring morphogen concentrations and comparing them with fixed concentration thresholds; as a result, graded morphogen distributions map into discrete spatial arrangements of gene expression. Recent studies on Hedgehog and other morphogens suggest that establishing patterns of gene expression may be less a function of absolute morphogen concentrations, than of the dynamics of signal transduction, gene expression, and gradient formation. The data point away from any universal model of morphogen interpretation and suggest that organisms use multiple mechanisms for reading out developmental signals in order to accomplish specific patterning goals.     

Phyllotaxis and the Initiation of Primordia During Flower Development in Silene

The measured divergence angles between successive primordiain the developing flower were compared with angles expectedon several hypotheses concerning primordial initiation. Theresults lead to the conclusion that the position and sequenceof initiation of the younger sepals is determined by the olderones but that the influence of an older primordium lasts foronly two plastochrons. The petals and carpels are apparentlypositioned by the sepals. The positions of the stamens are consistentwith their king determined by the sepals (antesepalous stamens)or petals (antepctalous stamens), but their sequence of initiationis consistent with its being determined, like the sepals, bythe two youngest primordia. The data indicate that there aretwo sets of factors governing the initiation of the primordiasubsequent to the sepals: one governing the positioning of theprimordia and resembling the factors governing the positionsof axillary buds, and the other governing the sequence of primordiaand resembling the factors which determine the initiation ofleaves. Measurements of the plastochron ratios were used tocalculate the sizes of the sepal, petal and stamen primordiaat initiation. At the moment of initiation the sepal primordiawere about one third, and the petal and stamen primordia aboutone sixth, of the size of the leaf primordia. In its early developmentthe Silene flower therefore resembles a condensed leafy shootwith precocious axillary buds but with primordia which are smallcompared to leaf primordia. Silene coeli-rosa, flower development, primordia, phyllotaxis