Abstract To determine the role of leaf mechanical prop-erties in altering foliar inclination angles, and the nutri-ent and carbon costs of specific foliar angle variationpatterns along the canopy, leaf structural and biomechan-ical characteristics, biomass partitioning into support,and foliar nitrogen and carbon concentrations were stud-ied in the temperate deciduous species Liriodendron tu-lipifera L., which possesses large leaves on long peti-oles. We used beam theory to model leaf lamina as a uni-form load, and estimated both the lamina and petioleflexural stiffness, which characterizes the resistance tobending of foliar elements at a common load and length.Petiole and lamina vertical inclination angles with re-spect to horizontal increased with increasing averagedaily integrated photon flux density (Qint). Yet, the lighteffects on lamina inclination angle were primary deter-mined by the petiole inclination angle. Although the pet-ioles and laminas became longer, and the lamina loadsincreased with increasing Qint, the flexural stiffness ofboth lamina and petiole increased to compensate for this,such that the lamina vertical displacement was onlyweakly related to Qint. In addition, increases and decreas-es in the petiole inclination angle with respect to the hor-izontal effectively reduced the distance of lamina loadfrom the axis of rotation, thereby reducing the bendingmoments and lamina inclination due to gravity. We dem-onstrate that large investments, up to 30% of total leafbiomass, in petiole and large veins are necessary tomaintain the lamina at a specific position, but also thatlight has no direct effect on the fractional biomass in-vestment in support. However, we provide evidence thatapart from light availability, structural and chemical

characteristics of the foliage may also be affected by wa-ter stress, magnitude of which scales positively with Qint.

Keywords Carbon partitioning · Dry mass per unit area ·Flexural stiffness · Support costs · Light interception

Introduction

Plants may enhance whole canopy light interception byincreasing the total foliar area, or by increasing the effi-ciency of unit leaf area for light interception. Changes inbranch and foliar inclination angles provide an importantway to modify the light interception capacity of the fo-liage. As the canopy elements become more horizontal,the interception efficiency of both direct and diffuse irra-diance increases (Heilman et al. 1996; Hikosaka and Hirose 1997; Muraoka et al. 1998; Pearcy and Valladares1999; Utsugi 1999; Valladares and Pearcy 2000). Ac-cordingly, a canopy with horizontal leaves is particularlyadvantageous in understorey low-light environment.However, horizontal leaves may result in large within-canopy shading, because they do not allow light penetra-tion into deeper foliage layers. With increasing lightavailability, steeper inclination angles become increas-ingly profitable, because they allow more uniform distri-bution of light within the canopy, and thus, exposition ofa greater photosynthesizing foliar area to light (Duncan1971; Valladares 1999; Valladares and Pearcy 2000).Studies indicate that plants do have more horizontalleaves in low light environments, and more steeply ori-ented leaves in open environments (Knapp and Smith1997; Muraoka et al. 1998; Valladares and Pearcy 2000;Valladares et al. 2000). Furthermore, there exists a con-tinuous vertical light gradient along the plant canopies,and leaf inclination angles become increasingly verticalwith increasing irradiance along this gradient (Miller1967; van Elsacker and Impens 1984; Hollinger 1989;Heilman et al. 1996; Utsugi 1999).

Despite the frequently observed and ecologically rele-vant correlations between long-term leaf light environ-

Ü. Niinemets (✉ )Department of Plant Physiology, Institute of Molecular and Cell Biology, University of Tartu, Riia 23, 51010 Tartu, Estoniae-mail: ylo@zbi.eeFax: +372-7-366021

S. FleckDepartment of Plant Ecology, University of Bayreuth, 95440 Bayreuth, Germany

Oecologia (2002) 132:21–33DOI 10.1007/s00442-002-0902-z

E C O P H Y S I O L O G Y

Ülo Niinemets · Stefan Fleck

Petiole mechanics, leaf inclination, morphology, and investment in support in relation to light availability in the canopy of Liriodendron tulipifera

Received: 21 February 2001 / Accepted: 11 February 2002 / Published online: 30 April 2002© Springer-Verlag 2002

ment and leaf inclination angle, the mechanistic explana-tions of these correlations are essentially lacking. Asleaves acclimate to the vertical light gradient, not onlythe inclination angles, but also the morphology and sizeof their petioles and laminas change. Light-related modi-fication of the mass of, and the load distribution along,the leaf lamina may alter the bending moment exerted onthe petiole, and thereby change lamina inclination an-gles. Often the area per leaf increases with decreasing ir-radiance (Ducrey 1992; Sala et al. 1994; Niinemets andKull 1999), implying greater lever arms and maximalbending moments exerted on the petiole of the shadedleaves. In other cases, leaf size is independent of irradi-ance (Hollinger 1989; Niinemets and Kull 1999). Giventhat leaf dry mass per unit area invariably and positivelyscales with irradiance (Hollinger 1989; Niinemets andKull 1998, 1999; Niinemets et al. 1999a), for a constantleaf area, the mass of the leaf lamina (Hollinger 1989;Niinemets 1998; Niinemets and Kull 1999), and thebending moments, are larger for the upper than for thelower canopy leaves. Thus, the dependence of lamina in-clination angles on irradiance may result from the lighteffects on lamina and petiole mass, size, and shape.There is evidence that changes in the vertical inclinationangle in the canopy of long-petioled temperate tree spe-cies Populus tremula (Niinemets 1998) and tropical rainforest species Scaphium macropodum (Yamada and Suzuki 1996) may be explained by changes in petiolelength with irradiance. Further evidence of the role ofbiomechanics in determining lamina inclination angles isprovided by leaf age effects on the lamina inclination an-gle. Lamina inclination angles generally decrease withincreasing leaf age, possibly because of simultaneous in-creases in lamina mass and area with increasing leaf age(Gordon and Promnitz 1976; Hamerlynck and Knapp1996).

Petiole mechanical properties may change along thevertical light gradient too, allowing modification of thelamina inclination angle for a common lamina load andpetiole length. Vertical deflection of the leaf lamina maybe reduced by increases in the petiole elastic modulusvia changes of the petiole material properties, and/or bymodifications in the cross-sectional petiole shape and di-mensions, e.g. as the result of larger biomass invest-ments in the petiole (Niklas 1999). There is evidencethat petioles are stiffer at higher irradiance (Niinemets1998), partly counterbalancing the effect of heavier lami-na load on petiole deflection. Yet, the biomass require-ments for support may increase faster than the efficiencyof light capture, indicating that horizontal arrangementof all leaves in the canopy may not be possible. Further-more, mechanical properties of leaf laminas of largeleaves may be equally important in determining leaf in-clination, and meeting the support requirements withinthe leaf lamina may provide an additional constraint forthe leaf inclination angle.

We studied foliage inclination angles, lamina and pet-iole morphology, and chemical composition in Lirioden-dron tulipifera L. – a wide-spread North American tem-

perate early successional species (Fowells 1965; Loach1967; Barnes 1991; Busing 1995) with large leaves andlong petioles. We addressed the following questions:what is the role of: (1) lamina and petiole morphologyand size, and (2) mechanical properties of the petiole andlamina in determining the light-related variability in lam-ina inclination angles along the canopy; and (3) howdoes light availability alter biomass partitioning betweensupport and physiological tissues within the leaf?

In leaves, the petioles and veins have a dual function.Apart from providing the structural support, they alsoserve as a pathway for water and nutrients, and for trans-location of photosynthates. Because the physiologicallyactive cells like the phloem cells form an integral part ofpetioles and veins, the cost of petioles and veins in termsof limiting resources may be considerably higher thanthat directly required for mechanical support. Therefore,we also asked: (4) what is the nitrogen and carbon costof veins and petioles? Although we focus on static load-ing, petioles also have to resist the dynamic loadings re-sulting from wind. Given that the canopy becomes moreturbulent, and mean wind speeds increase with increas-ing irradiance in the canopy, it is important to realize thatseveral of the relations observed in our study may re-present combined responses to enhanced static and dy-namic petiole loading (Vogel 1989; Ennos 1997).

Materials and methods

Study site and foliar sampling

The study was conducted in July 1999, in the Botanical Garden ofthe University of Bayreuth, Germany (49°55'N, 11°35'E, altitude365 m). According to the direct measurements in the BotanicalGarden, the average annual temperature was 8.3°C with a mini-mum of –0.4°C in January and a maximum of 17.9°C in July, andthe yearly average precipitation was 688 mm over the years1992–1999 (unpublished data of the Chair of Climatology, BITÖK, University of Bayreuth).

Sampled trees were 12–14 years old, and 5–8 m tall with thelive canopy starting from ca. 1 m above the ground. Leaves weresampled throughout the canopy, and the uppermost leaves at theheight of ca. 6.5 m received >75% of the above-canopy irradiance.For each leaf, petiole and lamina inclination angles of the freelyhanging leaf were measured with a protractor and plumb line(Fig. 1). Thereafter, the leaf was removed, put in a plastic bag and

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Fig. 1 Estimation of petiole (ϕP) and lamina (ϕL) inclination an-gles in situ in free-hanging leaves of Liriodendron tulipifera. ϕPwas defined as the angle between the points of petiole attachmentto the shoot and lamina attachment to the petiole. ϕL was mea-sured at the fall line of the lamina

transported immediately to the laboratory for biomechanical andfoliage morphological measurements.

Estimation of potential incident light availability by hemisphericphotography

Hemispherical photographs (Minolta MF camera equipped withSoligor 0.15× fisheye adapter; Soligor, Leinfelden-E., Germany)were taken above each sampled leaf. From the hemispheric imag-es, the fractions of penetrating diffuse solar radiation of open sky(ID, diffuse site factor) and of potential penetrating direct solar ra-diation of open sky (IB, direct site factor) were calculated accord-ing to Evans and Coombe (1959) and Anderson (1964). ID wascomputed from the measurements of relative area of canopy gaps(nine sky bands, 36 radial sectors per sky band) for uniformlyovercast conditions. IB was found as the canopy gap fraction alongsolar tracks between 15 May and 30 June. Both ID and IB calcula-tions took account of the angular distribution of diffuse and directradiation over the sky, and the angular fractions were cosine cor-rected to assess radiation incident on a horizontal plane (Evansand Coombe 1959; Anderson 1964).

Determination of daily integrated incident photon flux density for the leaves

At the site, 200 m distance from the investigated trees, above-can-opy global solar radiation (RG, radiation flux density from thespectral range of 0.3–2.8 µm) was measured continuously with py-ranometer CM-5 (Kipp & Zonen, Delft, The Netherlands), and 10-min averages were stored. We use these estimations of RG to com-pute an integrated value of photosynthetically active photon fluxdensity (Qint, wavelengths 0.4–0.7 µm) over the study period.

Because the fraction of photosynthetically active radiation inRG is different for diffuse and direct irradiance (e.g. Meek et al.1984; Weiss and Norman 1985; Spitters et al. 1986), first the di-rect (RB) and diffuse (RD) components of solar radiation must beseparated. Calculations of diffuse radiation follow Roderick(1999), and essentially require estimation of atmospheric clear-ness. The clearness index (C) is defined as the ratio of actual (RG)to potential (RP, the radiation at the top of the atmosphere) solarradiation. This index can be used to calculate RD/RG using a linearthreshold model (Roderick 1999):

(1)

where A0=Y1–A1X1, and A1=(Y1–Y0)/(X1–X0), and X0, X1, Y0, and Y1are empirical parameters. These parameters were derived frommeasurements of RD and RG in Fichtelgebirge (50°03'N, 11°52'E)during 1 April–30 June 1998. Total solar radiation was measuredwith the pyranometer CM-11 (Kipp & Zonen) and diffuse radia-tion with another pyranometer (Model 8101, Philipp Schenk,Wien & Co., Austria) equipped with a shadow band. The instanta-neous potential solar radiation (W m–2), which depends on lati-tude, day of year, and the solar hour was calculated as (Gates1980):

(2)

where S is the solar constant [1,360 W m–2; Gates (1980)], d1 isthe monthly average and d2 the actual distance between the sunand the earth, δ is the sun declination, φ is the latitude and h is thetime of day expressed as hour angle of the sun. Solar hour wascalculated according to Michalsky (1988), and δ according to Li-nacre (1992). Given that (d1/d2)2 never differs more than 3.5%from 1.0 (Gates 1980), a constant value of 1.0 was employed.

Initially, following the method of Roderick (1999), we calcu-lated estimates of daily average values of diffuse irradiance. How-

ever, atmospheric clearness measured at a specific earth locationmay change rapidly because of the movement of clouds, and theusage of daily integrated values may occasionally lead to largediscrepancies between the measured and modelled estimates ofdiffuse and direct irradiance. To remedy the integration errors, weexplored the possibility of using the same model for more detailedpredictions with measured 10-min averages of RG. Equation 2 wasintegrated over 10-min time steps:

(3)

yielding the integrated amount of solar radiation incident on a hor-izontal surface (J m–2). Thus, using the 10-min average value ofRG, the ratio RG/RP is given as RG600/JP. The coefficients obtainedwere X0=0.24, X1=0.95, Y0=0.71, Y1=0.21, and fitting the modelby 10-min averages resulted in good agreement between the mea-sured and predicted values of RD integrated over the sky bandsused for evaluation of the hemispherical photographs (r2=0.78 fora linear correlation). Thus, the modification applied was consid-ered appropriate.

Diffuse (QD, µmol m–2 s–1) and direct photon flux densities(QB) were calculated from 10-min averages of integrated diffuseand direct radiation using the conversion factors reported by Rossand Sulev (2000). Different conversion factors for clear and over-cast sky conditions were used (Ross and Sulev 2000).

The daily integrated photon flux density (Qint, mol m–2) for aspecific leaf was computed as:

(4)

where ID is the diffuse site factor, IB the direct site factor for theleaf as defined above, D is the daily integrated above-canopy dif-fuse photon flux density and B the direct photon flux density (Niinemets and Kull 1998). In the current study, we used dailyfractions of potential penetrating diffuse solar radiation (ID,i) andhourly fractions of direct solar radiation (IB,i) for each sky locationestimated from the hemispherical photographs (every sector alongthe sky bands and solar tracks evaluated), and corresponding dailyand hourly integrated values of diffuse and direct photon flux den-sity (Di and Bi) were calculated from the 10-min average values of

QD and QB. For each day, Qint was found as: ,

where n is the number of sky sectors in the hemisphere that wereanalysed for the diffuse light penetration, and k the number ofhourly sectors along the solar track. We use an average value ofQint for the period of 15 May–30 June 1999, which corresponds tothe period of foliar expansion and thickness growth.

Measurements to estimate petiole and leaf lamina biomechanicalproperties

A leaf was held from the lamina close to its attachment point tothe petiole, and the distal end of the petiole was clamped by a vicesuch that the distal-most part of the petiole was horizontal. Afterpetiole fixation, the lamina was released, and the vertical displace-ment resulting from the load of lamina was measured at the junc-tion of the lamina to petiole (wA, m). The inclination angle of thelamina tip (ϕT) was also measured with a protractor, and the de-flection of the free end of the lamina, wL (m) was computed as:

(5)

where LP (m) is the length of the petiole and LL (m) the length ofthe lamina, and

(6)

partly corrects for the decrease in the horizontal projection of totalleaf length that results from downward leaf displacement, but itdoes not account for leaf bending (Appendix I). Before these mea-

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surements, phyllopodium – the inflated base of the petiole – wasalways removed.

Additional weights were attached to the middle of the lamina,and resultant horizontal displacements wA and wL were estimatedanalogously. To be compatible with the Euler-Bernoulli beamequation (Appendix I), the weights were in all cases chosen tokeep the downward deflection small (w<0.25L, Bisshopp andDrucker 1945; Morgan and Cannell 1987). After measurement ofwA and wL for a specific weight, the extra load was removed andthe deflections measured again. If the values differed by >3%from the initial estimates obtained with the load of leaf lamina on-ly, the data for the particular weight were considered to indicateplastic and viscoelastic deformations and were discarded.

After measurements with entire leaves, leaf lamina was re-moved, and petiole deflection under the weight of loads added tothe tip of the petiole was measured separately in the same manneras with the whole leaves.

Calculation of petiole and leaf lamina flexural stiffness

For a point-load P (N) applied at the tip of the non-tapered cantile-ver, the vertical dip displacement is given by (Gere and Tim-oshenko 1997; Niklas 1999):

(7)

where L (m) is the length of the cantilever, E (N m–2) is Young’smodulus of elasticity, and I (m4) is the second moment of area ofthe cantilever. E is determined by the material properties, and I bythe shape of the cross-section and absolute dimensions of the can-tilever. The second moment of area basically indicates the way thematerial is distributed about the axis of bending (Wainwright et al.1976). The product EI is called flexural stiffness, and it character-izes the ability of beam-like structures to resist bending. We usedEq. 7 to calculate EI of the petiole from the measurements withdetached lamina. A value of EI was computed for each measure-ment of w with a specific load, and an average was found for allloads applied.

Contrary to petioles, the mechanical properties of leaf laminashave been poorly studied [see Niklas (1999) for a review]. Despitethe thin (Kirchhoff) plate theory possibly being more appropriate(Gere and Timoshenko 1997; Niklas 1999), beam theory has oftenbeen employed to model complex natural objects such as animalskin (Long et al. 1996) or foliar lamina (Vincent 1982; Niklas1993; Paolillo and Niklas 1996; Moulia and Fournier 1997). Wealso use the beam theory to approximate the load of lamina on thepetiole, and the deflection of the lamina. We model the leaf of Li-riodendron as consisting of two beams – petiole and lamina – andassume that the lamina weight per unit lamina length is a constant,i.e. that the lamina is a uniform load (Appendix I). Using specificboundary conditions, beam equations for petiole and lamina arederived in Appendix I. Substituting x=a, where x (m) is the hori-zontal distance from the clamped end of the petiole, and a (m) thehorizontal distance to the junction of petiole to lamina, we can de-rive the deflection of the attachment point of lamina to petiolefrom Eq. 15 (Appendix I):

(8)

where m is the mass of leaf lamina, g the acceleration due to grav-ity, L the total leaf length, and EPIP the petiole flexural stiffness.Equation 8 was employed to compute the second estimate of EPIP.The values of EPIP derived from Eqs. 7 and 8 were strongly corre-lated (Fig. 2), providing a partial verification of the applied leafmodel. Because of an almost one-to-one relationship, the two esti-mates of EPIP were averaged. For the lamina tip, we substitute x=Linto Eq. 16 (Appendix I):

(9)

where ELIL is the lamina flexural stiffness. Thus, the measure-ments of lamina tip deflection were used to determine ELIL. Im-plicit in these calculations is the assumption that the lamina isflexurally uniform along the entire length. We realize that a leaf isactually elastically non-homogeneous, and that the lateral leaf di-mension may be significant. Nevertheless, previous studies haveshown that the lamina flexural stiffness, which determines the ver-tical displacement of the leaf lamina, is primarily dependent on themechanical properties of major veins (Vincent 1982; Moulia andFournier 1997), and in particular on the mechanical properties ofleaf mid-rib (Moulia and Fournier 1997) that extends through theentire leaf, and approximately halves the leaf. For instance, in Lolium perenne the veins accounted for >90% of the flexural stiff-ness of the leaf (Vincent 1982). Thus, we suggest that our simplifi-cation allows one to derive valuable information about the deter-minants of leaf lamina mechanics.

Although Eq. 7 has also been used to estimate the petiolar de-flection if the lamina is attached (e.g. Niklas 1991b, 1992b), leaflamina cannot be approximated as a point load affixed at the tip ofthe petiole, because the weight of lamina is distributed over a longdistance away from the axis of rotation, and the effective bendingmoments are larger than those for a point load applied at the junc-tion between the petiole and lamina. Simulations demonstrate thatthe shape of load distribution along the lamina may significantlyalter the maximal bending moment at the petiole attachment to theleaf lamina, and thereby modify the deflection curve for the entireleaf (Appendix I). For equal weights, the deflection of petiole un-der the load of leaf lamina is larger than under the weight of apoint load (Appendix I). Accordingly, evaluation of the role ofleaf biomechanical characteristics in lamina inclination requiresestimation of both lamina and petiole flexural stiffness as well ascharacterization of the lamina load distribution.

Morphological measurements

Leaf area was measured with a portable leaf area meter (CI-202;CID, Vancouver, Canada), and leaf lamina and petiole fresh masswas determined immediately after the biomechanical measure-ments. All veins thicker than 0.4 mm were further separated fromthe rest of the lamina with a razor blade, and dry mass of all leafparts was determined after oven-drying at 70°C for at least 48 h.From these measurements, dry to fresh mass ratios of leaf parts,lamina dry mass to area (MA), and support biomass to area ratioswere calculated. In addition, petiole density (fresh mass per unitvolume) and dry matter concentration (dry mass per unit volume)were calculated from petiole dry and fresh mass, length, and area

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Fig. 2 Comparison of the values of petiole flexural stiffness [EPIP;where E (N m–2) is Young’s modulus of elasticity, and I (m4) is thesecond moment of area of the cantilever] calculated from mea-surements with a detached (Eq. 7), and attached (Eq. 8) lamina. EImeasures the resistance of beam-like mechanical structures tobending, and combines both the material elastic properties and ge-ometry of cross-section into a single characteristic

25

of cross-section. For the latter variable, the radii of essentiallyprismatic petioles with circular cross-sections were estimated bycallipers as an average of three to four measurements.

The second moment of area for the petioles was computed asIP=πr4/4, where r is the radius of the petiole (m). The second mo-ment of area for the laminas was found as IL=T3H/12 (Wainwrightet al. 1976; Niklas 1993), where H is the lamina width (m) and Tthe thickness (m). We assumed that lamina density is constantthroughout the lamina, and calculated leaf thickness from an esti-mate of leaf dry matter concentration (ρB) of 300 kg m–3, which isa representative value for the leaves of temperate deciduous spe-cies (Niinemets 1999, 2001). Having determined the second mo-ment of area, elastic moduli were found for both the petiole andthe lamina from their EI. Although ρB may depend on the long-term light availability conditions in the canopy (Niinemets et al.1999a), modification of ρB with light availability in a manner asobserved in the temperate species in Niinemets et al. (1999a) didnot alter the correlations of IL and EL with integrated photon fluxdensity and with other leaf structural and chemical variables. Giv-en that the largest portion of the effective second moment of areaof the lamina may be attributable to major veins, our approach todetermine IL may have led to an overestimation of effective EL.Nevertheless, previous investigations have demonstrated that theflexural stiffness of the major veins separated from the rest of thelamina is considerably lower than that of the petioles of similarshape and size (Niklas 1991b), indicating that embedding of veinsin the lamina matrix significantly increases the composite leafelastic modulus.

Carbon and nitrogen determination

Nitrogen and carbon concentrations of leaf laminas, petioles, andmajor veins were measured with an elemental analyser (CHN-O-Rapid; Foss Heraeus, Hanau, Germany).

Results

Canopy light climate

The potential fractions of diffuse (ID) and direct (IB) irra-diance incident on the sampled leaves were strongly correlated (r2=0.78, P<0.001 for a liner regression). IDwith a mean±SE of 0.31±0.06 (range 0.017–0.79) wasgenerally larger than IB (mean±SE=0.223±0.039, range0.031–0.69), and the means were statistically different atP<0.005 according to a paired samples t-test. Over theperiod 15 May–30 June 1999, which was used to deter-mine the values of integrated photon flux density (Qint),the average daily integrated direct photon flux densityincident to specific leaves averaged 2.42±0.49 mol m–2

day–1, and the diffuse integrated photon flux density7.5±1.4 mol m–2 day–1, indicating that the leaf light re-gime was dominated by diffuse irradiance.

Light effects on foliage inclination angle

Although the correlations were scattered, both petiole(ϕP) and lamina (ϕL) vertical inclination angles with re-spect to horizontal (Fig. 1) were positively related to in-tegrated photon flux density (Qint, Fig. 3A). In general,leaves were inclined downwards (ϕL<0) in the lowercanopy and upwards (ϕL>0) in the upper canopy. BothϕP and ϕL were strongly correlated (Fig. 4). Thus, the

positive scaling of the lamina inclination angle with Qintprimarily resulted from the positive effects of light onϕP.

When the lamina angle of attached leaves was calcu-lated with respect to the petiolar angle (ϕR,1=ϕL–ϕP), itwas only weakly correlated with the integrated photonflux density (Fig. 3B). Similarly, a poor correlation wasfound between Qint and the lamina angle of leavesclamped by a vice such that the fixed end of the petiole

Fig. 3 Effects of daily integrated photon flux density (Qint) on (A)ϕL and ϕP (Fig. 1), and on (B) ϕL relative to the petiolar angle (ϕR)for attached (ϕR,1=ϕL–ϕP) and detached leaves (ϕR,2). Detachedleaves were clamped by a vice such that the distal end of the peti-ole was horizontal, and the lamina inclination angle resulting fromthe bending of the leaf under its own weight was measured at thelamina tip (ϕT). The inclination angle of the leaf at the junction oflamina to the petiole (ϕA), was computed as arcsin(w/LP), where w(m) is the vertical deflection of the leaf at the junction, and LP isthe length of the petiole. The angle ϕR for this situation was de-fined as ϕR,2=ϕT–ϕA. Qint was found as an average value over 15 May–30 June 1999. The data were fitted by linear regressions.The non-significant regression (P>0.05) is given by a dashed line

Fig. 4 Scatterplot of ϕL versus ϕP (Fig. 1). Data were fitted by alinear regression

26

was horizontal (ϕR,2, Fig. 3B). Nevertheless, accordingto a separate samples t-test (P<0.05) the leaves from thelower canopy (Qint<10 mol m–2 day–1) still had a lowerϕR,2 (average±SE=–29±4) than the ϕR,2 (–16±4) of theleaves from the upper canopy (Qint≥10 mol m–2 day–1).

The lamina angles ϕR,1 and ϕR,2 were strongly corre-lated (r2=0.56, P<0.001). Thus, apart from the petiolarangle, lamina angle of attached freely hanging leaveswas dependent on the gravitational effects on lamina andpetiole bending.

Variability in foliage morphological characteristics along the canopy

Lamina dry mass (major veins removed) per unit area(MA) as well as the dry mass of support biomass per unitarea were strongly correlated with Qint (Fig. 5A). Laminaload (P, fresh mass×acceleration due to gravity; Fig. 5B)and dry mass (r2=0.82, P<0.001 for a power function asdescribed in the legend of Fig. 5), and lamina area(Fig. 5B) were also positively related to integrated pho-ton flux density. However, the mass increased faster thanarea (Fig. 5B), leading to the positive scaling of MA withlight. The ratio of leaf width to length was independentof irradiance (r2=0.00, P>0.9), suggesting that light didnot affect leaf shape.

Although the ratio of support biomass to lamina areawas positively related to light availability (Fig. 5A), thedry mass ratios of major veins (MV) to lamina (ML), andpetiole (MP) to lamina were independent of Qint(Fig. 5C). The average±SE MV/ML ratio was0.0818±0.005 kg kg–1 (range 0.027–0.152 kg kg–1), andaverage±SE MP/ML ratio was 0.107±0.005 kg kg–1

(range 0.066–0.187 kg kg–1). For the sum MV/ML+

MP/ML, the mean was 0.189±0.048 kg kg–1 (range0.115–0.304 kg kg–1), indicating that a large fraction offoliar biomass was invested in mechanical support. TheMV/ML ratio scaled positively with total leaf length(r2=0.18, P<0.05), area (r2=0.29, P<0.001), and petiolelength (r2=0.18, P<0.05). The MP/ML ratio was positive-ly related to petiole length (r2=0.46, P<0.001).

Neither the petiole density (fresh mass to volume ra-tio) with a mean±SE of 1170±39 kg m–3 nor the petioledry matter concentration with a mean of 337±11 kg m–3

were correlated with Qint (r2<0.04, P>0.3 for both). Nev-ertheless, petiole and lamina (without major veins) dry tofresh mass ratios scaled positively with Qint (Fig. 5D),suggesting that the fraction of physiologically active tis-sues decreased with increasing light availability in bothpetioles and in the lamina.

Contents of foliar carbon and nitrogen in leaves of various morphological structure

Carbon contents (Cm) of all leaf fractions increased(Fig. 6A), and nitrogen contents (Nm) of major veins andthe rest of the lamina decreased (Fig. 6B) with increas-ing Qint. Because of increases in MA with increasing Qint(Fig. 5A) lamina nitrogen contents per unit area(Nm×MA) were strongly and positively related to Qint(r2=0.80, P<0.001).

According to a common slope analysis of covariance(ANCOVA) (Wilkinson 1990) followed by the Bonfer-roni test (interaction term was insignificant in the fullANCOVA model), lamina and petiole carbon contentsdid not differ (P>0.8). However, the Cm of the majorveins was significantly lower than that for lamina or forpetiole (P<0.001), suggesting that the material properties

Fig. 5 Lamina dry mass to ar-ea, and support dry biomass(major veins and petiole) tolamina area (A), lamina load(fresh mass times the accelera-tion due to gravity), and area(B), dry mass ratios of majorveins (MV) to lamina (ML), andpetiole (MP) to ML (C), and dryto fresh mass ratios of laminaand petiole (D) in relation toQint. The data were fitted bylinear regressions in A, and bypower functions in the form ofy=a.xb in B and D. No trend-lines are provided for C be-cause of low fractions of ex-plained variance (for linear re-gressions, r2=0.03, P>0.4 forMP/ML and r2=0.00, P>0.7 forMV/ML)

27

of major veins differ from those of the petiole. Laminanitrogen contents were the largest, those for major veinsintermediate, and those for petioles the lowest (P<0.001for all comparisons according to the Bonferroni test),suggesting a similar gradation in physiological activity.

Given that structural polysaccharides such as cellu-lose, which make up a large fraction of foliar biomass,contain only 44.4% carbon, Qint effects on Cm of onlymajor veins can be explained by increases in structuralpolysaccharides. A decline in nitrogen content (Fig. 6B),which is mainly present in proteins with high carbonconcentrations [53.5% carbon, Vertregt and Penning deVries (1987)], further indicates that certain carbon-richprotective compounds such as tannins or structuralchemicals such as lignin must have accumulated in thefoliage to compensate for decreases in Cm because of de-creases in the protein contents.

Dependence of foliage biomechanical properties on canopy light availability

Both the lamina and petiole flexural stiffness, EI, in-creased with increasing Qint (Fig. 7A), and thus, the peti-ole and lamina bent less at a common load and length(Appendix I) in greater irradiance. The relationshipswere linear when both variables were log-transformed,indicating large modifications in foliar variables withmoderate changes in light availability (s. also Fig. 5B).ANCOVA demonstrated that EI of petioles was larger,on average ca. sevenfold, than that of laminas at a com-mon integrated photon flux density (P<0.01).

Similarly to EI, one of its components – the secondmoment of area (I) – was positively related to Qint forboth the lamina and the petiole (Fig. 7B). In contrast, thefoliar elastic moduli (E) were only weakly related to thephoton flux density (Fig. 7C). A larger flexural stiffnessof petioles was primarily achieved by their greater sec-ond moment of area (Fig. 7B). Given that the laminaload (Fig. 5B), and petiole and leaf lengths (Fig. 7D)

Fig. 6 Relationships of Qintwith (A) the carbon and (B) thenitrogen contents of variousleaf fractions. Data fitting as inFig. 3. The non-significant re-gression is given by a dashedline

Fig. 7 Petiole and lamina flex-ural stiffness (A, Eqs. 7, 8, 9),second moment of area (B),elastic modulus (C), and length(D) in relation to Qint. The rela-tionships were linearized bylog10 transformation. Thus, thefitting of original data by pow-er functions (Fig. 5) gives simi-lar fractions of explained vari-ance as the linear fits to thelog-transformed data(log10y=log10a+blog10x)

28

scaled positively with irradiance, but the lamina horizon-tal angle relative to the petiolar angle was only weaklyrelated to Qint (Fig. 3B), light-related adjustments in foli-ar flexural stiffness were sufficient to keep the gravita-tional effects (Eqs. 7, 8, 9) on foliar inclination angleconstant throughout the canopy.

The elastic modulus of petioles scaled positively withthe length of the petiole (Fig. 8A) and petiole dry tofresh mass ratio (Fig. 8B). The elastic modulus of thelamina was poorly correlated with these characteristics(Fig. 8A, B), but was primarily related to the mass ratioof major veins to the rest of the lamina (Fig. 8C) demon-strating that an increase in the fraction of veins in thelamina matrix increases the mechanical strength of theentire lamina.

Discussion

Variability of foliage inclination angles along the canopy

As observed previously (cf. Introduction), we also found(Fig. 3A) a positive correlation between lamina and peti-ole inclination angle and integrated photon flux density(Qint). However, the leaves in both the upper and lowercanopy were vertically inclined, suggesting that the lightinterception efficiency did not necessarily increase withdecreasing light availability, possibly because of a limit-ed investment of biomass in mechanical support.

Although most of the light is generally intercepted bythe upper leaf surface, the fraction of light intercepted bythe lower surface increases with increasing vertical leafinclination angle, and may occasionally be >30% of totallight intercepted (James and Bell 2000). Especially in theupper canopy, where there is less shading by neighbour-ing branches and leaves, light interception by the lowersurface may significantly increase the efficiency of thevertical leaves. However, the fraction of light intercepted

by the lower side of the leaf may be considerably less forthe leaves inclined downwards in the bottom of the cano-py (Fig. 3A), because such leaves are located closer to,and are more aggregated on, the supporting twig than theleaves inclined upwards (Takenaka 1994).

Because of the prevalence of vertical inclination an-gles, the canopy of Liriodendron tulipifera does not castdeep shade (Horn 1971), and also harvests light less effi-ciently than a canopy with more horizontal leaves. In ourstudy, the lowermost leaves of the trees grown in a non-competitive environment were found at a light level ofabout 2% of incident irradiance. This contrasts to obser-vations in natural mixed canopies, where the live canopyof ca. 50-year-old L. tulipifera extended from 16 m to30 m, and the lowest leaves at 16 m were encountered atirradiances of about 16% of above-canopy irradiance(Hutchinson and Matt 1977). In the same natural stand,the short-petioled shade-tolerant species Cercis canaden-sis and Cornus florida occupied lower canopy positionsdown to ca. 1.7% of above-canopy irradiance (Hutchin-son and Matt 1977). As our measurements demonstrate,leaves of L. tulipifera are close to horizontal at aboutabove-canopy irradiances of 15–20%, which correspondto a Qint of ca. 6–10 mol m–2 day–1 (Fig. 3A). Thus, in-ability to keep the large shaded leaves horizontal may re-duce the competitive ability of L. tulipifera in low-lightenvironments.

Modification of foliage morphological characteristics by irradiance

Although both the lamina mass and area (Fig. 5B) in-creased with increasing Qint, foliage dry mass increasedmore with increasing irradiance than area, leading to astrong positive correlation between Qint and lamina drymass per unit area (MA, Fig. 5A). As observed previous-ly in numerous studies, scaling of MA (Baldocchi andHarley 1995) and nitrogen content per unit area (Antenet al. 1995) with Qint leads to a vertical gradient in fo-liage photosynthetic capacity along the canopy, therebymaximizing the whole canopy photosynthesis for a givenbiomass (Gutschick and Wiegel 1988) and nitrogen (Hirose et al. 1988) investment in leaves. Light-relatedchanges in MA were also accompanied by modifications

Fig. 8 Correlations of lamina elastic modulus with lamina length(A), dry to fresh mass ratio of lamina (B), and with the dry massratio of major veins to lamina (C); and correlations of petiole elas-tic modulus with petiole length (A), petiole dry to fresh mass ratio(B) and with petiole to lamina dry mass ratio (C). Data fitting asin Fig. 7

of vascular tissue content per unit area (Fig. 5A) indicat-ing that physiologically more active leaves also had agreater potential supply of water and nutrients.

Apart from foliage inclination angles, increases in themean internode distance, leaf length and petiole lengthprovide other important ways to reduce within-canopyshading (Takenaka 1994; Valladares and Pearcy 2000).Often, leaves in shaded environments have longer peti-oles and greater internode distances than plants in openhabitats (Leeflang et al. 1998). However, as the petiolesand lamina increase in length, the lamina biomass be-comes located farther away from the axis of rotation, andthis may lead to lower foliar inclination angles (Eqs. 7,8, 9) unless modifications in petiole and lamina flexuralstiffness, EI, do not compensate for the increases inlength. Contrary to the patterns observed in herbaceousspecies, both the petiole and lamina length increasedwith increasing irradiance in L. tulipifera (Fig. 7D), ashas been demonstrated in some other woody species(Schultz and Matthews 1993; Niinemets 1998). Becausethe leaves were inclined upwards in the upper canopyand foliage biomechanical properties scaled with irradi-ance, increases in the length of foliage elements likelyresulted in decreases in foliage clumping, and allowedmore efficient light harvesting. In addition, Vogel (1989)noted that leaves with long petioles have lower drag instrong wind. Given that the mean wind speeds increasewith height in the canopy, modifications in petiole lengthmay also represent an adaptive response to the verticalgradient of wind speed (but see Niklas 1996).

Light effects on foliage mechanical properties

Although the lamina load on petiole increased with in-creasing light availability, coordinated modifications inpetiolar angle (Fig. 3A), and foliage mechanical proper-ties (Fig. 7) led to only weak gravity effects on leaf lami-na bending (Fig. 3B). Niklas (1992a) suggested that lighteffects on petiole translation, bending and twisting,which collectively determine the inclination angle ofnon-loaded petiole, are combined gravi- and photomor-phogenetic responses. Like in L. tulipifera, petiole incli-nation angle was the primary determinant of lamina ver-tical inclination in Acer saccharum (Niklas 1992a). Giv-en that the effective bending moments are lower for ver-tically oriented leaves (Gere and Timoshenko 1997),leaves with vertical orientation require less mechanicalsupport than those oriented horizontally (King and Loucks 1978; Cannell et al. 1988). Despite the econom-ics of light harvesting which favours horizontal leaves inthe lower canopy (cf. above), limited carbon availabilityfor support may have resulted in leaves which were in-clined downwards at low light levels in L. tulipifera.

The positive effects of Qint (Fig. 7A) on lamina andpetiole flexural stiffness, which is the product of Young’smodulus of elasticity (E), and the second moment of area(I) were mainly governed by light effects on I (cf.Figs. 7B, C). Thus, changes in the thickness of foliage

elements with irradiance were the primary determinantsof modifications in EI. Ample evidence from previousstudies demonstrates that petiole flexural stiffness scalespositively with lamina load and petiole length, but alsothat both E and I may depend on foliage size (Niklas1991b, 1992a, 1992b, 1996).

Biomass investment in support elements in relation to foliage mechanics

The leaf lamina may be approximated (Vincent 1982;Paolillo and Niklas 1996) as a composite beam that con-sists of elastic fibres with a higher modulus of elasticityinserted into a matrix with a lower modulus of elasticity,assuming that the fibres are long enough such that theforce is equally distributed between the fibres and thematrix [Voigt model, Wainwright et al. (1976)]. Accord-ing to the Voigt model, the total modulus of elasticity islinearly dependent on the volume fraction of the fibresin the composite beam (Wainwright et al. 1976). Thus,there should be a positive correlation between the frac-tion of major veins in the lamina and the elastic modu-lus of the lamina as was found in the current study(Fig. 8C).

Although the fractional biomass investment in majorveins did not depend on irradiance (Fig. 5C), there is ev-idence that the number of minor veins per unit area mayincrease with increasing Qint (Wylie 1949; Högermann1990), apparently strengthening the lamina between themajor veins. An increase in the matrix elastic modulusavoids pulling the fibres out of the matrix and longitudi-nal failure at the interface (Wainwright et al. 1976).Moreover, the thickness of the leaf epidermis, which isalso an important stiffening tissue (Niklas and Paolillo1997), increases with increasing irradiance (Myers et al.1987) further suggesting that the stiffness of the interve-inal area scales positively with Qint. Given that the maxi-mum bending stresses occur in the upper (tension) andlower (compression) lamina surfaces (Wainwright et al.1976), thickening of the epidermis cells may stronglyadd to the flexural stiffness of the lamina.

Influences of light on lamina carbon and nitrogen concentrations

There is evidence that water stress increases with in-creasing height in the canopy (Niinemets and Kull 1998;Niinemets et al. 1999b). Greater rates of transpirationand lower water potentials in the upper canopy leavesmay imply that leaf turgor potentials are also lower ingreater irradiance in most intensively transpiring leaves.This is relevant for the interpretation of within-canopypatterns in foliage chemistry and mechanics, because themechanical properties of petioles (Niklas 1991a) andother plant tissues (Niklas 1989, 1999) are largely deter-mined by their hydrostatic pressure. Decreases in tissueturgor may both decrease the tissue elastic modulus, but

29

also the second moment of area because of tissue shrink-age (Niklas 1991a; Spatz et al. 1998). Given that in L.tulipifera the light effects on EI were primarily deter-mined by the second moment of area, i.e. by the petioleand leaf thickness, large volume changes may consider-ably alter foliage inclination angles in this species [seealso Niklas (1992b) for dehydration effects on light in-terception efficiency of the lamina].

Nevertheless, carbon contents (Cm; Fig. 6A) as wellas dry to fresh mass ratios (Fig. 5D) of leaves generallyincrease with increasing irradiance in temperate species(Niinemets and Kull 1998; Niinemets et al. 1999a) sug-gesting that leaf material properties as well as the frac-tion of structural leaf constituents change throughout thecanopy. Previous investigations show that the increase inCm with Qint primarily results from increases in carbon-rich lignin [63.3% carbon, calculated from Nimz (1974)for hardwood lignin] contents (Niinemets and Kull 1998;Niinemets et al. 1999a). Because the content of proteins,which are also rich in carbon, decreased rather than in-creased with Qint (Fig. 6B), it is likely that light effectson Cm in L. tulipifera resulted from changes in lignincontents in our study as well. Increased lignification re-duces the water stress-related volume change of leaf ele-ments, and renders leaf flexural and elastic propertiesless sensitive to changes in the turgor pressure (Niklas1989). Lignification also decreases the degree to whichcellulose fibrils can hydrate, and accordingly decreasesthe sensitivity of the leaf elastic modulus to water con-tent changes (Niklas 1991a). Thus, modification in foliarlignin contents may be an important factor for the me-chanical stability and light interception of the leaves, es-pecially when water limitations scale with light avail-ability in the canopy.

Given the large carbon requirements for mechanicalsupport within the lamina as well as for petiole construc-tion, our results collectively suggest that carbon avail-ability for mechanical support may be a relevant factorconstraining foliar inclination angles, especially in low-light environments. However, our study also highlightsthe importance of gravi- and morphogenetic responsesduring leaf development, which alter the non-loaded pet-iole inclination angle from the horizontal.

Acknowledgements We thank Triin Niinemets for skillful techni-cal assistance, and Dr Otto Klemm (BITÖK, Universität Bayreuth,Germany) for providing the global solar radiation data for the fieldsite. The study was supported by the Estonian Science Founda-tion (grant 4584), the Estonian Minister of Education (grant0180517s98), and by the German Federal Minister of Researchand Technology [BMFT, grants BEO 51-0339476A (BITÖK) andEST 001-98].

Appendix I. Derivation of formulas for petiole and leaf lamina deflection using beam theory

Integration of the Euler-Bernoulli beam equation

If the vertical displacement of a beam, w, is small rela-tive to total beam length, L [w<0.25L, Bisshopp and

30

Drucker (1945); Morgan and Cannell (1987)], and thebeam elastic modulus (E, N m–2) and second moment ofarea of the beam cross-section (I, m4) do not vary alongthe beam length, the Euler-Bernoulli beam equation(Young and Roark 1989) may be used to describe thebeam deflection. For a prismatic beam:

(10)

where p(x) is a function describing the distribution ofacting force per unit beam length (N/m). IntegratingEq. 10, and using the appropriate boundary conditions todetermine the integration constants, leads to formulaedescribing the beam deflection with dependence on theapplied load and the distance x from the support. For acantilevered beam, Eq. 10 is solved for the followingboundary conditions: d3w/dx3(x=L)=0 (there is no shearat the tip of the beam), d2w/dx2(x=L)=0 (there is nobending moment at the free end of the cantilever),dw/dx(x=0)=0 (the beam is horizontal at the point of fix-ture), and w(x=0)=0 (there is no deflection at the base ofthe cantilever, Fig. 9).

However, a leaf cannot generally be approximated asa prismatic beam with constant flexural stiffness alongthe entire leaf. Therefore, we model the Liriodendronleaf as a composite of two beams – lamina (a≤x≤L) andpetiole (0≤x≤a) – both of which may have different elas-tic (EL for lamina and EP for petiole) and cross-sectional(IL for lamina and IP for petiole) properties. We furtherassume that the leaf lamina is a uniform load, i.e. that theforce exerted by the lamina is equal at each point alongthe lamina (Fig. 9). The latter assumption is critically de-pendent on leaf shape that determines the mass distribu-tion along the leaf mid-rib. Although the assumption ofuniform mass distribution is appropriate for Lirioden-dron, different load functions may be required for otherspecies.

Replacing p(x) in Eq. 10 with the expression for auniform load [mg/(L–a)], integrating, and determiningthe constants of integration from the boundary condi-

Fig. 9 Mechanical model of a Liriodendron tulipifera leaf with apetiole length of a, lamina length of L–a, and lamina weight ofmg, where m is the lamina fresh mass and g the acceleration due togravity (9.81 m s–2). Assuming that the lamina mass is uniformlydistributed along the lamina length, the force per unit laminalength is given as p(x)=mg/(L–a). In the current study, the leaf isapproximated as a non-prismatic beam with different values offlexural stiffness for the petiole (EPIP) and the lamina (ELIL)

tions d3w/dx3(x=L)=0, and d2w/dx2(x=L)=0 we obtain forthe lamina:

(11)

(12)

Equation 11 defines the shear force and Eq. 12 the bend-ing moment at x=a (Fig. 9), and these derivatives arefurther used as boundary conditions for the petiole. As-suming that the mass of petiole is negligible, d4w/dx4=0for the petiole. Thus, the shear force integrated from L toa (Eq. 11) is equal to mg (Eq. 11), i.e. d3w/dx3=mg/(EPIP). Integrating this expression and determiningthe constant of integration using Eq. 12 and consideringthat leads to:

(13)

Further integration with the boundary conditions ofdw/dx(x=0)=0 and w(x=0)=0 yields for the petiole:

(14)

and

(15)

Integrating Eq. 12 in the similar manner, and usingEqs. 14 and 15 as the boundary conditions at x=a, thedeflection of the lamina becomes:

(16)

The vertical deflection along the entire leaf will be cal-culated using Eq. 15 for 0≤x≤a, and Eq. 16 for a≤x≤L.

Performance of the leaf biomechanical model

Replacing EPIP=ELIL=EI, Eq. 16 describes the deflectionof a prismatic beam subjected to an identical load mg(Fig. 9; Gere and Timoshenko 1997):

(17)

Further, if the petiole length is nil, a=0, and Eq. 17 sim-plifies to the beam equation for a uniform load:

(18)

31

which gives the tip deflection (x=L) as:

(19)

Thus, Eqs. 17, 18, 19 indicate that the equations we havedeveloped (Eq. 15, 16) recover known results.

Although the load of leaf lamina is often simulated asa point load (Niklas 1991b, 1992b), a comparison of thepredictions of petiole deflection for a point load, or for aload simulating the lamina of Liriodendron tulipifera

Fig. 10 Comparisons of (A) petiole tip deflections for a concen-trated load applied at x=a (open symbols, Eq. 7) and for a uniformload with a length of (L–a) applied at x=a (filled symbols, Eq. 15),(B) lamina (L–a) deflection without (open symbols, Eq. 18) andwith petiole (filled symbols, Eqs. 15, 16), and (C) leaf deflections(Eqs. 15, 16) for varying values of flexural stiffness of the lamina.Average values of a, L, EPIP, ELIL observed across the whole set ofLiriodendron leaves were applied in A and B. In C, the solid linegives the estimate for average measured values. The bending ofpetiole depends only on petiole flexural rigidity and lamina load(Eq. 15), whereas lamina deflection is related to both the flexuraland elastic properties of petiole and lamina as well as the load dis-tribution along the lamina

(Fig. 10A), indicates that the leaf lamina cannot be ap-proximated as a point load attached at the end of the pet-iole in this species. Because the mass causing petiolebending is distributed over a wide distance from the peti-ole tip, the acting bending moment is considerably largerthan that in the case of a concentrated load at the end ofthe petiole, resulting in a significantly larger tip deflec-tion (Fig. 10A). An analogous comparison of the situa-tions of lamina directly attached to the twig (w=0 atx=a) or to the petiole (w≠0 at x=a), indicates that the de-flection of lamina is much greater when the lamina is at-tached to the petiole (Fig. 10B). As the simulations fur-ther indicate, changes in lamina flexural stiffness, ELIL,may significantly alter leaf inclination for common lami-na load and size, and constant petiole flexural rigidity(Fig. 10C).

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