Leaf phyllotaxis: Does it really affect light capture?

Fernando Valladares* and Daniela BritesCentro de Ciencias Medioambientales C.S.I.C. Serrano 115 dpdo, Madrid E-28006. Spain; *Author forcorrespondence (tel.: 34 917452500 ext 1 287; fax: 34 915640800; e-mail: valladares@ccma.csic.es)

Received 14 March 2003; accepted in revised form 8 July 2003

Key words: Light harvesting, Mediterranean plants, Phyllotaxis, Self-shading

Abstract

The intriguing mathematical properties of leaf phyllotaxis still attract scientific attention after centuries of re-search. Phyllotaxis, and in particular the divergence angle between successive leaves, have been frequently in-terpreted in terms of maximization of light capture, although certain model simulations of light capture by verticalshoots revealed minor effects of phyllotaxis in comparison with the effect of other morphological features of theplant. 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 atfilling these gaps by examining the influence on light harvesting of shoot architecture and divergence angle infour 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 withineach species, with 144° being the most frequent one. These different divergence angles rendered very differentvertical projections of the shoot due to contrasting patterns of leaf overlap as seen from above, but they renderedindistinguishable light interception efficiencies �Ea�. Setting the leaves with an opposite-decussate phyllotaxisled, however, to a 40–50% decrease of Ea. The interplay of internode length, leaf size and shape, and leaf el-evation angle led to significant species differences in Ea. Thus, only particular phyllotaxis �e.g., decussate� mightbe functionally inefficient under certain combinations of the various morphological variables that influence lightcapture of a shoot.

Introduction

The fact that the spiral arrangement of leaves on astem represent successive numbers in the famous se-ries discovered by the Italian mathematician Fi-bonacci in the thirteenth century has attractedscientific attention for centuries �Adler, Barabé andJean 1997�. Many scientists have been captivated bythe intriguing mathematical properties of plant geom-etry, which still attract intensive research �Prusink-iewicz and Lindenmayer 1996; Jean and Barabé1998�. The divergence angle between successiveleaves has been traditionally described by means offractions having as numerator the number of turnsaround a stem found preceding a leaf repeated posi-

tion, and as denominator the number of leaves foundin between; this fraction multiplied by 360° providesthe divergence angle. The numerators and denomina-tors of the fractions of these spirals are generally twosuccessive terms of the main Fibonacci series, inwhich each term is the sum of the two previous ones�Adler et al. 1997�. The ratio of successive numbersof Fibonacci series as they get bigger approximatesan irrational number that results, when multiplied by360°, in the famous ‘golden angle’ of 137,50776...°.The frequent occurrence of the golden angle in bo-tanical patterns is the central theme of the old disci-pline of phyllotaxis, which can be traced back to thefourteenth century �Guerreiro and Rothen 1995; Adleret al. 1997�. The mathematical description of phyllo-

Plant Ecology 174: 11–17, 2004.© 2004 Kluwer Academic Publishers. Printed in the Netherlands.

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taxis was followed by an interest on the morphoge-netic and physiological processes that determine theactual pattern formation in the plant �Jean 1994;Douady and Couder 1996�, which are still far fromelucidated �Klar 2002�. Another line of research fo-cused on the adaptive significance of plant architec-ture and phyllotaxis �Honda and Fisher 1978; Givnish1986� and on computer explorations of plant evolu-tion by simulated adaptive walks through fitnesslandscapes �Niklas 1986�. Since the spatial arrange-ment of leaves determines the interception of solarradiation, plant architecture in general and leaf phyl-lotaxis in particular has been often studied from thepoint of view of optimisation of light capture �Niklas1988; Sekimura 1995; Valladares and Pearcy 1999�.One remarkable property of the golden angle is thatan infinite number of leaves can be placed around astem with a divergence angle of 137.5° without acomplete overlap among any two of them �Figure 1�.Thus, and because the most common phyllotacticpattern minimizes leaf-overlap, phyllotaxis has beeninterpreted in terms of maximization of light capturesince the earlier studies �e.g., Wright 1873� to thepresent �Sekimura 1995�. However, the computersimulations of Niklas �1988, 1998� showed that phyl-lotaxy per se has little effect on the ability of shootsto harvest sunlight because other morphological var-iables such as petiole length or leaf shape can obviateself-shading of leaves. Nevertheless, these elegantsimulations of light capture by virtual shoots forwhich morphological variables were independentlyvaried, required certain simplifications to reduce thenumber of all conceivable phenotypes to a manage-able size. These simplifications included: 1� all phyl-lotactic patterns were described by the Fibonacciseries; 2� all the leaves on the stem had an ellipticaloutline: and 3� every shoot bears the same number ofleaves. Besides, only direct radiation was consideredin these studies despite the fact that diffuse light re-presents ca. 10% of the total sun radiation in cleardays and that this percentage increases rapidly withcloudiness �Ross and Sulev 2000�. Diffuse light canbe very important in the cases of steep foliages, sincethis light can be harvested not only from above butalso from the sides �Valladares and Pearcy 1998; Val-ladares 1999�.

The objective of this study was to explore the ef-fect on light interception efficiency of natural inter-and intraspecific variation in the phyllotactic angle infour evergreen species from Mediterranean-type eco-systems, taking into account their real leaf shape and

their characteristic values for other architectural fea-tures that influence light interception, such as theirsteep leaf elevation angles, the short to very shortlength of their petioles, and their relatively shortinternodes. The ultimate goal was to study the effectof phyllotaxis on light harvesting under realistic con-ditions for a given group of plants with a 3-D model�Y-plant�, �Pearcy and Yang 1996� capable of calcu-lating the interception of both direct and diffuse lightby complex canopies with proven accuracy �Valla-dares and Pearcy 1998�.

Materials and methods

The shoot architecture and phyllotaxis of four plantspecies �Quercus ilex L., Arbutus unedo L., Heter-omeles arbutifolia M. Roem. and Daphne gnidium L.�characteristic of Mediterranean-type ecosystems werestudied. The species were evergreen shrubs or treeswith spiral phyllotactic pattern and exhibited a widerange of variation in structural features such as sizeand shape of the leaves, length of the internodes, andleaf elevation angles �Table 1�. Morphological andgeometrical measurements of leaves and shoots weremade either in natural populations in the field or inplanted semi-natural formations in botanical gardens�Table 1�. Mean values were used to reconstruct un-branched, vertical shoots of each species with thethree-dimensional computer model Y-plant �Figure 1��Pearcy and Yang 1996�. Vertical stems are character-istic in plant populations from sunny, open sites inMediterranean-type ecosystems �Valladares andPearcy 1998�. Measurements of the stem geometricproperties required for running Y-plant were made on20 shoots from each of five individuals of each spe-cies. Divergence angle between successive leaves�also called phyllotactic angle� was estimated on eachshoot by counting the number of turns around thestem from one leaf to the next one most approxi-mately overtopping it, dividing this number by thenumber of leaves within this stem section to obtainthe phyllotactic fraction of the genetic spiral, whichwas then multiplied by 360° �Valladares 1999�. Thismethod is less accurate then those using transversalslides of the apex but is acceptable for the morpho-logical scale of the study. For each shoot, the anglesand azimuths of the petiole and surface of any leaforiginating from a node were recorded with a com-pass-protractor. In addition, the azimuth of the mid-rib, the lengths of internodes, petioles and leaves, and

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the diameters of the petioles and internodes were re-corded. Nodes were numbered proceeding from thebase to the top of the stem. By recording the mother-

node �the node from which a subsequent node arises�for each node, the proper topology of the stem couldbe reconstructed by Y-plant. Leaf shape was estab-

Figure 1. Lateral view of a vertical stem of Arbutus unedo with 85 leaves �3-D reconstruction with Y-plant� and three apical views of thesame stem with three different divergence angles between successive leaves: 135°, 137.5° �golden angle�, and 100°. The first two anglesresult from Fibonacci or ordinary systems, while the last one results from Lucas or accessory systems �Rutishauser, 1998�. Note that whilewith divergence angles of 135° and 100° only 8 and 18 leaves can be seen from above respectively, all leaves can be seen at least partiallyin the case of the golden angle.

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lished from x, y coordinates of the leaf margins. Leafsize was then scaled from the measured leaf length.More details on Y-plant can be found in �Valladaresand Pearcy 1998; Valladares, Skillman and Pearcy2002�. Following reconstruction of the three-dimen-sional plant image, Y-plant was then used todetermine the interception of diffuse photosyntheticphoton flux density �PFD� from 160 sky sectors cov-ering the entire hemisphere, and direct PFD fromspecific angles and azimuths corresponding to the so-lar track of a given day �June 21st, the day with themost vertical sunpath� at a latitude of 42° N �meanlatitude for Mediterranean-type ecosystems in theNorthern hemisphere�. Standard overcast conditionswere used for the simulations of diffuse light capture.Diffuse incoming radiation was set as 10% of totalincoming radiation, which is a realistic assumptionfor clear sky conditions in Mediterranean-type eco-systems �Alados et al. 2003 �. Standard equationswere used to simulate the radiation available on acompletely clear day �Pearcy 1989�. The simulatedinterception of PFD by the plant was then determinedwith a simple ray tracing technique �Pearcy and Yang1996�. Summation over all sectors gave the total dif-fuse PFD intercepted. A similar approach was usedfor direct PFD. Light interception efficiency �Ea� wascalculated with Y-plant as a fraction of the lightavailable for a horizontal surface without any shad-ing intercepted by the foliage, including both diffuseand direct PFD. Ea takes into account the effects ofleaf angle projection, leaf overlap, and the effects oflight absorptance, transmittance, and recapture bylower leaves. Since plant size affects light harvestingdue to increasing mutual shading among leaves withincreasing number of leaves, the calculations for eachspecies were run with shoots of increasing number ofleaves, keeping the internode length constant, until Eadid not decrease any further.

Results and discussion

A wide range of divergence angles between succes-sive leaves �from 100° to 154°� was observed withineach species, with 144° being the most frequent�Table 1�. Slight changes in the divergence angle ren-dered very different vertical projections of the shootdue to contrasting patterns of leaf overlap as seenfrom above: the change of only 2.5° from 135° to137.5° led to 8 vs. 85 ��total number of leaves ofthe shoot examined� orthostichies �i.e., vertical rowsTa

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of leaves, Figure 1�. However, these different diver-gence angles rendered indistinguishable light inter-ception efficiencies �Ea, Figure 2�. This result is inagreement with the simulations of Sekimura �1995�and Niklas �1998�, but not with the study of lightharvesting in an epiphytic bromeliad by Zotz,Reichling and Valladares �2002�. Results from thelatter paper showed that changing the real divergenceangle of the leaves of each plant to the golden angle�137.5°� significantly increased light interception by5%, leading to an increase in whole plant potentialcarbon gain of 2%. These discrepancies can beexplained by the different growth form of the plantsstudied in each case. While plants studied here andthose simulated by Niklas have the architecture ofmost dicots with relatively narrow, short, ellipticalleaves arranged along stems and branches at measur-able internode lengths, the bromeliad studied by Zotset al. �2002� had long, arced, and relatively wideleaves arranged in a whorl of internodal distancesclose to zero. Thus, the proximity of the leaf surfacesof the bromeliad caused significant self-shading,which was partially, but significantly, alleviated by aprecise arrangement of leaves according to a goldendivergence angle.

By contrast, Ea decreased significantly when leaveswere arranged according to an opposite-decussatepattern �divergence angle of 90° since each pair ofopposite leaves is rotated 90° from the previous pairrendering a total of four ortostichies�. Setting theleaves with a decussate pattern led to a 40–50% de-crease of Ea in the four species studied �Figure 2�,which pointed out that certain phyllotaxis might befunctionally inefficient under certain combinations ofmorphological variables. The interplay of internodelength, leaf size and shape, and leaf elevation angleled to significant species differences in Ea, withDaphne gnidium, the species with shortest internodeshaving the lowest and Quercus ilex, a species withrelatively long internodes and small leaves, havingthe highest Ea for a given leaf area of the shoot �Fig-ure 2�. These differences in light interception amongevergreen plants from Mediterranean-type ecosys-tems is in contrast with the remarkable convergencein Ea found in a comparative study of 24 species ofcontrasting architectures co-occurring in the under-story of a tropical rainforest �Valladares et al. 2002�.Thus, the many morphological variables that deter-mine the light capture efficiency of a shoot can beplastically modified according to the particular lightenvironment experienced by the plant, leading to

functional convergence when light is either limitingor excessive, or to species divergence at optimal lightintensities �Valladares 1999�. This morphologicalplasticity can compensate for inefficient phyllotacticpatterns �Niklas 1988; 1998�, which are under rela-tively tight genetic control. Species divergence inlight capture when light is optimal is the logic resultof the wide range of mutually conflicting tasks that acrown must simultaneously perform.

Light capture efficiency of a crown is the final re-sult of a number of hierarchical set of factors, fromleaf morphology, to branching pattern and crown ar-chitecture. The species studied here exhibited rela-tively similar values for the most frequent divergenceangle, so the results could be influenced by the factthat these species have a leaf morphology and crownarchitecture evolved to fit divergence angles close tothe ‘golden angle’. However, we have shown thateven small changes in divergences angles �within theranges of observed natural variability� lead togeometrically contrasting patterns of leaf overlap�Figure 1�. Thus, our finding that a reduced leaf over-lap does not necessarily translate into an enhancedlight capture efficiency can be held although we haveonly studied a small set of numerically similar diver-gence angles.

The intriguing mathematical properties and the in-trinsic beauty of plant geometry is likely to attractmore research efforts in the future. However, not allthe efforts are equally justified by the existing knowl-edge. From the three evolutionary drivers andconstraints of spiral phyllotactic patterns in plants�leaving whorled and opposite phyllotactic patternsaside�; one, natural selection of spiral arrangementsoptimising light capture, has been proved of onlymarginal importance �Niklas 1998, and present studyshowing minor functional differences of geometri-cally contrasting spiral leaf arrangements�; anotherone, the morphogenetic processes that render the ob-served phyllotactic pattern, is under intense debate�see Klar 2002, and the reply by Fleming 2002�;while the third one, the biomechanic and allocationtrade-offs involved in the different phyllotacticpatterns, has been remarkably less explored.

Acknowledgements

Thanks are due to Robert W. Pearcy for generous ad-vice on Y-plant and fruitful discussions, to AngelDeleito for inspiring ideas, and to Cristina Maguas,

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Otilia Correia, Amelia Louçao, and Luis Balaguer forhelp and support. Financial support was provided bythe Spanish MCYT �REN2000-0163-P4, ECOFI-ARB, and REN2001-2313, TALMED�.

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