Leaf dispersion and light partitioning in three-dimensionally digitized tall fescue–white clover mixtures

Authors


Correspondence: H. Sinoquet. E-mail: sinoquet@clermont.inra.fr

Abstract

A three-dimensional digitizing method was used to assess the canopy structure of six Festuca arundinacea (FA)–Trifolium repens (TR) mixtures during the installation stage. Virtual canopy images were synthesized and used to derive light interception and partitioning between species. Computations from images were compared with a simple light model based on Beer’s law, in order to analyse within- and between-species foliage dispersion. The total leaf area index of the mixtures ranged from 0·6 to 4·5. The fraction of FA foliage overtopping TR was 9–30%. The mean inclination of FA and TR was 66 and 57°, respectively. Within-species dispersion parameters of FA and TR were about 0·8 and 1·0, namely clumped and random foliage dispersion, respectively. Although FA was sown in rows, between-species dispersion was random. Lower leaf inclination and lesser clumping in TR compensated foliage overtopping by FA, so that light partitioning between FA and TR (about 80 and 20%, respectively) was similar to the species contribution to total canopy foliage. Since between-species dispersion was random, a simple two-layer light model based on Beer’s law provided correct estimations of light partitioning (RMSE = 0·05), although light interception by FA was slightly overestimated because of its clumped dispersion.

Introduction

Intercropping is a widely used agricultural practice where complementary characteristics between species for resource capture and use is expected (Sinoquet & Cruz 1995). In particular, grass–legume mixtures have been reported to increase land use productivity (e.g. Trenbath 1974; Willey 1979) in both forage quantity and quality (e.g. Cruz et al. 1991)). White clover (Trifolium repens L.) is the most important legume grown with companion grasses in the temperate pastures (Frame & Newbould 1986). Despite an extensive accumulation of agronomic results about their production, the highly unpredictable nature of the equilibrium between legume and grass makes difficult to manage these mixed pastures (Kessler & Nösberger 1994). Understanding of the legume–grass equilibrium needs more information on canopy architecture and light distribution within the sward in relation with the defoliation pattern (Barthram & Grant 1994). Among resources, light partitioning is a crucial issue in multi-species canopies because light is involved in most plant responses (e.g. photosynthesis, transpiration, morphogenesis), and the effects of light reduction on the dominated species may be either negative (e.g. species extinction, Caldwell 1987) or positive (e.g. shelter from water stress, Allen, Sinclair & Lemon 1976; improvement of light use efficiency, Willey 1979; Harris, Natarajan & Willey 1987; Cruz 1995).

Light partitioning between species in a mixed canopy has been characterized by the light interception efficiency (LIE; i) of individual component i, which is the fraction of incident radiation which is absorbed by component i (e.g. Azam Ali et al. 1990). The assessment of light partitioning between species is a rather difficult task. If the foliage of each species occupies separate canopy volumes, the radiation balance of each canopy can be derived from sensors distributed in the canopy (e.g. tree-grass, Tournebize & Sinoquet 1995; row intercropping, Marshall & Willey 1983). If species foliages blend together in the same canopy space, the LIE of individual components could theoretically be derived from small lightweight sensors fixed on the foliage (e.g. Gutschick et al. 1985). However the practical operation is extremely difficult, since sensor installation on leaves may disrupt canopy structure and the number of sensors required for an accurate estimation of the radiation balance is large (Sinoquet et al. 2001). Direct measurement of leaf irradiance in grass–legume mixtures would be all the more difficult, because plant height is low, leaves are small and foliage is dense.

As an alternative way to estimate light partitioning in mixtures, simulation models have been proposed. From our knowledge, all simulation models devoted to light partitioning between species are based on the turbid medium analogy (Monsi & Saeki 1953), namely the classical Beer’s law computing light transmission I as a negative exponential function of the downward cumulated leaf area index (LAI; L)

inline image 1

where I0 is incident radiation and K is an extinction coefficient. The theoretical derivation of Beer’s law for vegetation canopies assumes that leaf size is small with regard to the plot scale and that leaves are randomly distributed in the canopy layer (see Ross 1981). Because it primarily deals with light transmission (i.e. non-intercepted radiation), Eqn 1 cannot be used by itself to estimate light-sharing between species, except if foliages occupy separate canopy spaces (e.g. tree/grass, McMurtrie & Wolf 1983). For foliages blending together in the same canopy volume, Beer’s law has been extended to compute light partitioning from the same basic assumptions (i.e. small leaf size, random leaf dispersion). The LIE (i) of component i in a mixture of two components (i and j) can thus be written (e.g. Rimmington 1984).

inline image 2

In a theoretical work on light partitioning in two-species canopies, Sinoquet & Bonhomme (1991) distinguished within- and between-species leaf dispersion. The two kinds of leaf dispersion, respectively, characterize the rate of foliage overlapping within leaves of a given species, and between leaves of the two vegetation components. Within-species dispersion is the leaf dispersion of the canopy where other vegetation components would have been removed, whereas between-species leaf dispersion accounts for the interactions between species. Sinoquet & Bonhomme (1991) showed that Eqn 2 accounts for the case where within- and between-species leaf dispersion are random. Departure from the random leaf dispersion, namely clumping or regularity (Nilson 1971), have been reported for several monocrops (see the review by Myneni, Ross & Asrar 1989). In contrast, foliage dispersion in actual mixtures has not been documented till now, except in ryegrass–clover mixtures where within-species dispersion has been assessed from point quadrat analysis (Lantinga, Nassiri & Kropff 1999).

Another way to compute light partitioning in multi-species canopies could be light models based on virtual three-dimensional (3-D) plant models. This approach has been applied to several monocrops, with abstracted plant models (e.g. Ross & Marshak 1988), simulated plants (e.g. poplar, Chen et al. 1993) or plants digitized in the field (e.g. Sinoquet et al. 1998), and with light computations ranging from plant projections (Chen et al. 1993) to ray-tracing (Ross & Marshak 1988) and radiosity techniques (Chelle & Andrieu 1998).

The objective of this paper was to estimate light partitioning between species in relation to canopy geometry, and analyse within- and between-species foliage dispersion in grass–legume mixtures. For this purpose, tall fescue–white clover canopies were three-dimensionally digitized in order to provide an accurate description of the canopy geometry. Light computations derived from the 3-D plant models were compared with the Beer’s law approach, in order to assess foliage dispersion and test the ability of a simple light model (Rimmington 1985) to estimate light partitioning.

Materials and methods

A mixture of tall-fescue (Festuca arundinacea Schreb., cv Barcel, denoted FA) and white clover (Trifolium repens L., cv Huia, denoted TR) was sown on 18 March 1999, at the experimental station Le Robillard, near Caen, France (48°55′ N, 0°0′ E, 60 m a.s.l) on a clay–loam soil. FA was sown in rows 0·17 m apart whereas TR was broadcast sown. The canopy structure of the mixture was measured by a 3-D digitizing method on 6–7 May, 19–20 May, and 1–2 June, thus during the canopy installation phase. On each date, two plots of 0·17 m × 0·10 m; that is, integrating FA row spacing, were digitized. The measured plots were randomly sampled on the experimental site at a very early growth phase.

Three-dimensional digitizing of the canopy

The canopy geometry of the FA–TR mixture was measured by a 3-D digitizer (3Space Fastrak; Polhemus Inc., Colchester, VT, USA). This device is based on a magnetic technology. The magnetic source is used as a reference frame, and a pen-like sensor points out cartesian co-ordinates of digitized points. Nominal device resolution is of 8 × 10−4 m for an active volume of 1·2 m × 1·2 m × 0·6 m (Polhemus 1993), and previous studies showed for medium-sized leaves an accuracy better than 10−3 m in the laboratory (Moulia & Sinoquet 1993) and about 10−2 m in field conditions (Thanisawanyangkura et al. 1997). For small TR leaflets, the reported accuracy on linear dimensions was 11–15%, increasing as leaflet size decreases (Rakocevic et al. 2000). Since the FA–TR plots were small and dense, plant organs were digitized independently, the topological relationships between organs were not recorded, and every component was cut immediately after digitizing. Two plant components (organs) for each species were considered in this study: leaf lamina and sheath for FA, petioles and leaflets for TR. The TR stolons were disregarded because they do not significantly contribute to light interception during the installation stage. The FA plants were digitized first, by pointing out three to 20 points along lamina midribs, and two to six points along sheaths, beginning at the distal tip. Two additional points were recorded for the maximum width of each lamina.

The digitizing protocol for TR components has been described by Rakocevic et al. (2000). Leaflets were digitized first, from the top of the canopy. For each leaf, 10 points were recorded in a standardized sequence including the common intersection of the three petiolules, the distal tips of leaflet midrib and the widest points of each half-leaflet. Leaves still not completely opened were subjected to the same protocol. The petioles were digitized from the top down after the leaves had been removed, by two to 20 points according to the petiole length and curvature. Further details on TR digitizing are given in Rakocevic et al. (2000).

Virtual canopy reconstruction

Plant organs were represented by a variable number of geometrical components, the size, orientation and spatial position of which were derived from the digitized data. FA lamina were treated as a succession of rectangles. TR leaflets were reconstructed as a set of two quarter-ellipses for the distal part and two triangles for the proximal part (see Rakocevic et al. 2000). The FA sheaths and TR petioles were represented by a series of cylinders. Diameters were set to 2 × 10−3 m for FA sheaths and 7 × 10−4 m for TR petioles, respectively, according to previous observations (Jacquet, unpublished results).

Estimation of canopy geometry parameters

Organ area and inclination was computed as the area and inclination of the geometrical components. Vertical profiles of leaf area density (LAD) and mean inclination angle were then derived for each organ class. The canopy profiles were described as 0·02 m canopy layers, given that 96% of the virtual foliage elements had a vertical projection height lesser than 0·02 m. Mean inclination angle was calculated by weighting the inclination angle of each foliage element by its surface area. Profile-integrated values of LAD and inclination angles were also calculated for each organ class, each species and the whole canopy.

Estimation of light interception from plant images

Directional light interception was computed using graphics software VegeSTAR (Adam, Sinoquet & Donès 2000). VegeSTAR allows one to visualize 3-D digitized plants and to compute light interception from image processing of the virtual plant pictures (Sinoquet et al. 1998). The software computes the values of the ‘silhouette to total area ratio’ (STAR; Stenberg 1995) by counting the coloured pixels corresponding to an organ class on the picture. The computation thus disregards multiple scattering and assumes leaves as black bodies. VegeSTAR input files were obtained from the digitized data by a special program written in FORTRAN, called tritrefle. False colours were attributed to plant organs in order to distinguish them on the virtual plant pictures. A sample of 17 directions was used to approximate the sky vault: the vertical direction and elevation angles of 30, 45, 60 and 75 degrees at 0, 90, 180 and 270 degrees in azimuth angle with respect to the FA row direction. In order to avoid border effects, several duplicates of the 0·10 m × 0·17 m vegetation scene were lined up along the directions perpendicular and parallel to the rows. The sky vault-integrated LIE was estimated by summing up the 17 directional values weighted according to the standard overcast sky (SOC) radiance distribution (Moon & Spencer 1942). Light interception was computed for the whole canopy and for each species in the mixture. The same process was also applied to virtual canopies including only one species (i.e. where the other species was virtually removed), in order to assess the competition -free light interception of each species.

Analysis of light relations in the mixture

  • LIE (ɛ)of a canopy made of black leaves can be written according to Beer’s law as follows

inline image 3

Inversion of Eqn 3 by using LIE measured from the plant images and LAI (L) values derived from plant digitizing allows one to infer an apparent extinction coefficient of the canopy Ka

inline image 4

Extinction coefficients Ka were computed from plant image processing for the two-species mixture (KaMIX) and the one-species canopies (KaFA and KaTR); that is, where the competing species was virtually removed from the 3-D scenes.

In the theoretical case of random leaf dispersion, the extinction coefficient Kr only depends on the leaf angle distribution with regard to the direction of the incident radiation. Values of Kr computed for incident radiation obeying the SOC radiance distribution (Moon & Spencer 1942; Bonhomme & Varlet-Grancher 1977) were fitted to the following relationship, as a function of mean leaf inclination angle α (Sinoquet, Rakocevic & Varlet-Grancher 2000)

inline image 5

According to Nilson (1971), the ratio µ = Ka/Kr can be used as a leaf dispersion parameter since it is equal to, lesser than and greater than 1 for random, clumped and regular foliage dispersion, respectively. This approach was applied to the one-species canopies in order to derive the within-species leaf dispersion parameters µFA and µTR.

In a similar way, the between-species leaf dispersion parameter was defined as the ratio µMIX = KaMIX/KrMIX, where KrMIX equals (Sinoquet & Bonhomme 1991)

inline image 6

KrMIX is a linear combination of KaFA and KaTR weighted by leaf area indices LFA and LTR, respectively. KrMIX is thus the extinction coefficient of a mixed canopy where the two species show their actual within-species leaf dispersion and between-species dispersion is random. As both KaMIX and KrMIX deal with the actual within-species leaf dispersion, parameter µMIX = KaMIX/KrMIX only accounts for the between-species leaf dispersion.

Between-species dispersion parameter describes the rate of leaf overlap between the two species but does not account for the direction of leaf overlap, namely the dominance of the species in the mixture. Additional dominance parameters (νFA and νTR) were therefore defined as the ratio between actual LIE of the species in the mixture (ɛFA and ɛTR) and species LIE where computation of light partitioning between species assumes random within-species leaf dispersion and uniform distribution of leaf area of both species in the mixture profile (see Eqn 2), for example:

inline image 7

where ɛMIX is the actual LIE of the mixture. Indeed the dominance parameter ν is one if any species does not overtop the other species, otherwise the overtopping species would show a value of ν greater than one.

Test of a simple light model

The LIE values estimated from plant image processing were compared at canopy and species level to LIE values simulated by a simple model of light partitioning in horizontally homogeneous two-species canopies (Rimmington 1985). In this model, the canopy is divided into two layers, in which the bottom of the upper layer is defined by the height of the smaller component. As FA overtopped TR in the mixtures, the upper layer only contained overtopping FA leaf area, whereas the lower one included foliage of both species. The LIE of the FA component in the upper layer was computed after Eqn 3. The LIE of the two species in the lower layer was derived from Eqn 2, weighted by the transmittance of the upper layer. In a first simulation run, we used FA and TR extinction coefficients for random leaf dispersion (namely Kr given in Eqn 5). Then, actual coefficients of the two species (i.e. Ka given by Eqn 4 applied to the one-species canopies) were used in a second run in order to separate the effect of between-species leaf dispersion.

Results

Canopy structure

Figure 1 shows views of 3-D virtual mixtures at stages of whole canopy plant area index (PAI) of 0·6, 1·7 and 4·5. Canopy images are presented in the horizontal direction parallel to the FA rows. At any stage, FA clearly overtopped TR and showed a marked row structure.

Figure 1.

Horizontal views in the FA row direction of reconstructed 3-D scenes of FA–TR mixtures, at whole canopy PAI stages of 0·6, 1·7 and 4·5. Colour luminance depends on species, organ type and altitude in the canopy profile.

Table 1 gives canopy structure parameters of the six digitized plots. PAI at canopy level showed a large range, with values between 0·6 and 4·5. At all three digitizing dates, the two replicates showed large differences in total PAI. That is the reason why variations as a function of date were hereafter disregarded, with the six digitized plots being regarded as replicates changing by PAI. The PAI of FA and TR ranged between 0·50 and 3·40, and between 0·13 and 1·13, respectively. The contributions of FA and TR to total PAI was 79 ± 2·6% and 21 ± 2·3%, respectively. Species contribution to total PAI was thus very stable, but FA contribution was about 3·7 times higher than that of TR. The contribution of sheaths to total PAI and to PAI of FA was 13·5 ± 2% and 17 ± 2·5%. Similarly the contribution of petioles to total PAI and to PAI of TR was 5·5 ± 1% and 26 ± 3%. Thus, support organs of both species significantly contributed to the mixture PAI, with very stable values. At any stage of mixture PAI, the FA contribution was 2–2·5 higher than that of TR (Fig. 2). The absolute and relative PAI of FA located above TR height ranged between 0·15 and 0·68, and 9 and 30%, respectively. The maximum leaf area density in the canopy profile was located at mid-TR height for FA, and slightly higher for TR.

Table 1.   Canopy structure parameters of the Festuca arundinacea (FA)–Trifolium repens (TR) plots: plant and organ area indices and mean leaf inclination angle
Plot no.123456
Days after sowing494962627575
Area indices (m2 m−2)
Whole canopy1·40·64·51·73·94·5
Festuca arundinacea1·070·503·531·403·093·40
 Sheath (% of total PAI)10·914·815·610·816·412·4
 Lamina (% of total PAI)64·864·862·871·463·662·6
Trifolium repens 0·34 0·13 0·97 0·30 0·77 1·13
 Petiole (% of total PAI) 5·4 5·1 5·0 4·56·6 7·1
 Leaflet (% of total PAI)18·915·316·613·213·417·9
Mean foliage inclination angle (°)
Whole canopy656963616465
Festuca arundinacea687265616567
 Sheath787986727875
 Leaf lamina667062606266
Trifolium repens545757575957
 Petiole686571717272
 Leaflet505552525252
Figure 2.

Vertical profiles of plant area density (PAD) for each species (FA on the right, TR on the left side), at whole canopy PAI stages of 0·6, 1·7 and 4·5. Values correspond to 0·02 m thick layers.

At canopy level, the mean leaf inclination angle ranged between 61 and 69° (Table 1); namely the mean value of erectophile canopies. The mean inclination of FA organs was slightly higher as it ranged between 61 and 72° with an average value of 66°, whereas TR organs showed lower mean inclination, namely between 54 and 59°, averaging at 57°. In both species, the inclination of support organs was higher than that of lamina, namely +14° and +18° for FA and TR, respectively. In particular, the sheaths were very close to vertical. Vertical profiles do not show any clear variation in mean organ inclination as a function of canopy height (Fig. 3).

Figure 3.

Vertical profiles of mean foliage inclination angles for each species (FA on the right, TR on the left side), at whole canopy PAI stages of 0·6, 1·7 and 4·5. Mean inclination angles were computed for 0·02 m thick layers.

Light interception and partitioning

At canopy level, the LIE of the one-species canopies and the whole mixture verified Beer’s law, namely Eqn 3 (Fig. 4). Non-linear regression analysis between LIE and PAI showed r2 coefficients of 0·96 for the one-species FA canopy, and 0·99 for the one-species TR canopy and the whole mixture. For the one-species canopies, the apparent extinction coefficient inferred from regression analysis was much lower for FA (KaFA = 0·49) than for TR (KaTR = 0·69). The apparent extinction coefficient for the whole mixture was in-between (KaFA+TR = 0·56). The LIE of species in the mixture poorly matched Beer’s law since Eqn 3 does not account for light competition. Difference between competition-free LIE and species LIE in the mixture allowed us to assess the effect of the companion species on light competition. Shortage in species LIE due to the presence of the other component was much larger for the TR component: it ranged from 0·00 to 0·12, and from 0·01 to 0·32, for FA and TR, respectively (Fig. 4). The LIE reduction due to light competition was thus 2–14 and 16–60% of the competition-free LIE, for FA and TR, respectively. LIE reduction – both in absolute and relative values – strongly depended on the stage of the mixture PAI (r2 = 0·90–0·98). Despite the asymmetry of light competition in the FA–TR mixture, the contribution of each species to the mixture LIE was similar to their contribution to PAI, namely 76 ± 4·5 and 24 ± 4·5% for FA and TR, respectively (Fig. 5). Within the two species, contribution of the support organs – namely FA sheaths and TR petioles – to LIE was slightly lesser than their contribution to PAI (Fig. 5).

Figure 4.

Light interception efficiency () derived from 3-D plant image processing, as a function of PAI. MIX, whole mixture; FA, FA in the mixture; TR, TR in the mixture; FA1, one-species FA canopy; TR1, one-species TR canopy. Curves are non-linear regression fitting of Beer’s law (Eqn 3).

Figure 5.

Partitioning of light interception efficiency (relative ) between species (FA, TR) and species organs (FA sheaths and lamina, TR petioles and lamina) as a function of their contribution to the total mixture PAI.

Foliage clumping and dominance

The within-species foliage dispersion of FA was markedly clumped, since µFA was 0·76 ± 0·05 (Fig. 6). In contrast, TR foliage was slightly clumped as µTR equalled 0·94 ± 0·02. As µTR was significantly different from one, within-species dispersion of TR could not be considered as random. Parameter µMIX equalled 1·03 ± 0·03 and was not significantly different from unity. Thus between-species foliage dispersion was clearly random. Within-species dispersion of both species and between-species dispersion parameters did not show any clear variation with PAI (Fig. 6).

Figure 6.

Within-species (FA, TR) and between-species (MIX) dispersion parameters (µ) as a function of species and the whole mixture PAI, respectively.

FA was the dominant species in the mixture as the dominance parameter νFA was greater than unity and ranged between 1·02 and 1·11 (Fig. 7). Reciprocally TR was markedly dominated, with parameter νTR between 0·74 and 0·92. Dominance relationships between FA and TR significantly increased as the mixture developed.

Figure 7.

Dominance parameter (ν) of each species in the mixture as a function of the species PAI.

Test of the simple light partitioning model

When the extinction coefficients Kr (i.e. for random leaf dispersion, see Eqn 5) were used in the simulation, the root mean square error of prediction (RMSEP) of Rimmington’s model (1985) was 0·0674 and 0·0226, for the FA and TR components, respectively (Fig. 8a). Moreover, simulation of TR LIE by the simple model was unbiased, whereas that of the FA component was overestimated by 0·065 ± 0·019, that is 14·4 ± 7·2% of FA LIE measured from the plant images. For a second run in which the extinction coefficients Ka (i.e. the actual coefficients of the one-species canopies) were used, RMSE decreased to 0·0133 and 0·0125, for the FA and TR components, respectively, and simulated values of species LIE were unbiased (Fig. 8b). This means that discrepancies observed in the first run were due to the departure from foliage dispersion randomness in the one-species canopies; that is, due to non-random within-species leaf dispersion. In contrast, the correct simulations obtained in the second run can be related to the random between-species leaf dispersion.

Figure 8.

Figure 8.

Comparison between light interception efficiency coefficients () derived, respectively, from a simple turbid medium model (Rimmington 1985) and from 3-D plant image processing. Values correspond to each species in the mixture. (a) Rimmington’s model was run with theoretical extinction coefficients (Kr, Eqn 5) derived from mean foliage inclination angle assuming random within-species dispersion. (b) Rimmington’s model was run with apparent extinction coefficients (Ka, Eqn 4) of each species; that is, taking into account actual within-species dispersion.

Figure 8.

Figure 8.

Comparison between light interception efficiency coefficients () derived, respectively, from a simple turbid medium model (Rimmington 1985) and from 3-D plant image processing. Values correspond to each species in the mixture. (a) Rimmington’s model was run with theoretical extinction coefficients (Kr, Eqn 5) derived from mean foliage inclination angle assuming random within-species dispersion. (b) Rimmington’s model was run with apparent extinction coefficients (Ka, Eqn 4) of each species; that is, taking into account actual within-species dispersion.

Discussion

Methodology

This study proposes a method for the assessment of light relations in intercropping systems. The method integrates (i) 3-D digitizing of the canopy structure of the vegetation mixture; (ii) the estimation of light partitioning between vegetation components from the processing of 3-D plant model images; and (ii) a framework to identify the determinants of the light competition in the mixture.

Three-dimensional digitizing of foliage has been used for a number of years (Lang 1973; Sinoquet, Moulia & Bonhomme 1991; Sinoquet et al. 1998). At the present time, the magnetic technology used in this study is likely to be the most appropriate. The alternative mechanical devices (Lang 1990; Takenaka, Inui & Osawa 1998) are more cumbersome and their arms can disrupt canopy structure; whereas ultrasonic devices (Sinoquet et al. 1991; Room, Hanan & Prusienkiewicz 1996) are extremely sensitive to microclimatic conditions, especially wind fluctuations. However, the magnetic device can be sensitive to the presence of metal in the measurement volume. Magnetic 3-D digitizing has been assessed from a qualitative comparison between 3-D plant images and actual plant photographs (e.g. Sinoquet & Rivet 1997). In the case of TR, Rakocevic et al. (2000) quantitatively assessed 3-D digitizing accuracy. On one hand, leaflet length and width measured with a ruler and derived from the 3-D digitizing data showed a RMSE of 1·5 × 10−3 m. On the other hand, estimates of ground cover from both 3-D canopy images and canopy photographs was very similar. This suggests that magnetic 3-D digitizing is suitable for the assessment of the geometrical structure of small and dense canopies such as forage crops. From our knowledge, this paper is the second attempt to apply 3-D digitizing to two-species canopies, as Drouet, Sonohat-Popa & Nijs (2000) used it for Lolium perenne–Taraxacum officinale and Poa pratensis–Bellis perennis mixtures.

Using 3-D plant models is a powerful method for the estimation of light interception in vegetation canopies. Indeed, its use overcomes the assumptions commonly used in the light models based on Beer’s law, namely small leaf size and random leaf dispersion (see Ross 1981). Light computation from virtual plant images has been previously used in several monocrops (Chen et al. 1993; Thanisawanyangkura et al. 1997; Farque, Sinoquet & Colin 2001). This disregards scattering and thus assumes plant elements as black bodies, but it is especially suitable for the analysis of foliage dispersion within canopies. This approach is particularly useful when applied to 3-D digitized plants in which the shape, size, orientation and location of each plant element is taken into account (Takenaka et al. 1998; Valladares & Pugnaire 1999). In contrast, the theoretical construction of 3-D plants could miss features of the canopy geometry which could be determinant for light interception properties; for example, exposition of new leaves in light microsites (Caldwell 1987). For the present FA–TR mixtures, light computation from plant images allowed us to estimate light partitioning between species. The only other possible method to assess light partitioning in mixtures is the point quadrat method (Warren Wilson 1965), as the radiation balance of any vegetation component cannot be inferred from radiation sensor measurements when the vegetation components are mixed in the same canopy volume. Lantinga et al. (1999) used the point quadrat method on rye grass–clover mixtures. The point quadrat method allowed them to get the sequence of contacts with the plant elements of both species for a limited number (40) of beams sampled in the canopy in a single direction. In contrast, 3-D plant image processing deals with the first contact between light beams and the vegetation, for a larger sample of beams of any direction, as each pixel represents a light beam. Moreover notice that ray-tracing algorithms could easily compute the point quadrat information from the 3-D digitized data (see, e.g. Haines 1989).

The conceptual framework used to analyse light relations in the mixture is derived from Sinoquet & Bonhomme (1991). It allows one to separate the effects of light interception ability of individual species and the interactions between species on light partitioning. On one hand, the determinants of light capture ability of each species are component PAI, inclination (through the extinction coefficient Kr, see Eqn 5) and intraspecies dispersion. On the other hand, interactions between species depend on the rate and the direction of leaf overlapping between species, namely the within-species dispersion and dominance parameters, respectively. In this study, dispersion parameters were derived from the comparison between the apparent extinction coefficient and the theoretical extinction coefficient for a random dispersion. Within-species leaf dispersion can also be derived from point quadrat analysis (Lantinga et al. 1999). As mentioned by Sinoquet & Bonhomme (1991), between-species leaf dispersion could also be assessed from point quadrat data as the coefficient of correlation between the numbers of contacts with both species: a correlation coefficient of zero shows random between-species leaf dispersion, whereas negative and positive correlation relates to regular and clumped dispersion, respectively.

Foliage dispersion in grass–legume mixtures

In this paper, the conceptual framework was applied to 3-D digitized grass–legume mixtures during the installation stage. TR had a higher individual ability for light interception, because of lower foliage inclination angle and dispersion close to random. The TR inclination angle of about 50° was however, markedly greater than values previously reported (e.g. 25°, Nichiporovich 1961). Indeed TR has been assumed to be a planophile species. This could be the case when TR leaflets are plane, since Rakocevic et al. (2000) reported that midrib inclination of TR leaflets shows a planophile distribution. However TR lamina angles can depart from the planophile distribution because of the angle between the two half-leaflets. TR leaf dispersion was slightly clumped (µTR = 0·94 ± 0·02). In a rye grass–TR mixture, Lantinga et al. (1999) reported vertical profiles of TR leaf dispersion where dispersion ranged from regular at the top of the canopy to clumped in the lower layers. The overall leaf dispersion was, however, close to random, with µTR about 0·92–1·01. Individual ability of FA for light interception was lower. On one hand, FA foliage was erectophile with mean inclination about 65°, as commonly reported for grasses in monocrops (de Wit 1965; Ross 1981) and mixtures (Faurie, Soussana & Sinoquet 1996). On the other hand, FA dispersion was markedly clumped (µFA = 0·76 ± 0·05). Grass foliage dispersion is usually clumped (e.g. Warren Wilson 1965; Nouvellon et al. 2000). However the only data available for grass–TR mixtures show that grass dispersion is random (Lantinga et al. 1999). The significant grass clumping found in our study is probably due to the marked row structure during the installation stage.

In the studied mixtures, the lower individual ability of FA for light interception was counterbalanced by its dominance in the vertical profile of leaf area (Fig. 2). As a result, light partitioning between FA and TR was close to the species contribution to the mixture PAI. Grass dominance observed during the installation stage is probably not the general case as several authors have reported similar heights and/or vertical profiles of leaf area for the two species (e.g. Woledge, Davidson & Dennis 1992; Faurie et al. 1996).

Surprisingly between-species dispersion was random. Indeed one could have expected regular between-species dispersion as FA was sown in rows. However random dispersion probably results from broadcast sowing of TR seeds. Random between-species leaf dispersion was also indirectly found by Lantinga et al. (1999) on rye grass–TR mixtures, as they reported an unbiased agreement between measured transmittance data and values simulated with a turbid medium model where actual intraspecies leaf dispersion was included and random between-species dispersion was implicitly assumed. Notice that between-species dispersion could not be assessed from the comparison between measured and simulated transmittance data if intraspecies and within-species foliage dispersion are both assumed to be random in the models (e.g. Faurie et al. 1996). This is because of possible trade-offs between the two kinds of dispersion. Random between-species dispersion has been assumed in all turbid medium models devoted to the estimation of light partitioning in multiple-species canopies (e.g. Rimmington 1984; Ryel et al. 1990; Sinoquet et al. 2000) whereas the validity of this assumption has never been explicitly assessed. Experimental evidence for random within-species leaf dispersion could reassure modellers about their computations of light partitioning in mixtures, even if this should be assessed on a larger range of grass–legume combinations. Moreover the comparison between species LIE estimated from virtual plant image processing and simulated from the simple Rimmington’s model (1985) showed that biases in light partitioning computations were related to the non-randomness of the within-species foliage dispersion. This is also in agreement with the results of Lantinga et al. (1999). Unbiased modelling of light partitioning should thus take within-species dispersion into account. This is especially crucial in growth analysis studies of mixtures based on LIE and light-use efficiency, in which uncontrolled biases in LIE can result in large light-use efficiency errors (Sinoquet & Cruz 1993; Bonhomme 2000).

Acknowledgments

The authors are grateful to Marie-Laure Decau, Christophe de Berranger, Dominique Perrin and Emmanuel Gautier for their technical support.

Ancillary