# When architectural plasticity fails to counter the light competition imposed by planting design: an in silico approach using a functional-structural model of oil palm

Raphael P. A. Perez, Rémi Vezy, Loïc Brancheriau, Frédéric Boudon, François Grand, Merlin Ramel, Doni Artanto Raharjo, Jean-Pierre Caliman, Jean Dauzat

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Raphael P. A. Perez, Rémi Vezy, Loïc Brancheriau, Frédéric Boudon, François Grand, et al.. When architectural plasticity fails to counter the light competition imposed by planting design: an in silico approach using a functional-structural model of oil palm. in silico Plants, 2022, 4 (1), 10.1093/insil-icoplants/diac009. hal-03736274

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# When architectural plasticity fails to counter the light competition imposed by planting design: an *in silico* approach using a functional-structural model of oil palm

Raphaël P. A. Perez<fnref n="1" />,<fnref n="2" />,* , Rémi Vezy<fnref n="3" />,<fnref n="4" />, , Loïc Brancheriau<fnref n="5" />,<fnref n="6" />, , Frédéric Boudon<fnref n="1" />,<fnref n="2" />, ,
François Grand<fnref n="3" />,<fnref n="4" />, Merlin Ramel<fnref n="3" />,<fnref n="4" />, Doni Artanto Raharjo<fnref n="7" />,
Jean-Pierre Caliman<fnref n="7" />, and Jean Dauzat<fnref n="3" />,<fnref n="4" />

Guest Editor: Katrin Kahlen

Editor-in-Chief: Stephen P. Long

**Citation:** Perez RPA, Vezy R, Brancheriau L, Boudon F, Grand F, Ramel M, Artanto Raharjo D, Caliman J-P, Dauzat J. 2022. When architectural plasticity fails to counter the light competition imposed by planting design: an *in silico* approach using a functional-structural model of oil palm. *In Silico Plants* **2022**: diac009; doi: 10.1093/insilicoplants/diac009

## ABSTRACT

Functional-structural plant modelling approaches (FSPM) explore the relationships between the 3D structure and the physiological functioning of plants in relation to environmental conditions. In this study, we present a methodo-logical approach that integrated architectural responses to planting design in an oil palm FSPM, and test the impact of planting design and architectural plasticity on physiological responses such as light interception and carbon assimilation. LiDAR-derived and direct measurements were performed on five planting designs to assess the phenotypic plasticity of architectural traits, and allowed evaluating the variations of the main parameters of an existing 3D plant model. Accordingly, we proposed a neighbourhood index (NI) as a simple explanatory variable of architectural plasticity, and used NI-based allometries to simulate architectural variations in 3D virtual plants. Light interception and carbon assimilation were then simulated on virtual plots reproducing the five studied designs. We found that the main traits affected by plant proximity were leaf dimensions, leaf weight and leaf erectness, whereas other structural traits like the frequency of leaflets along the rachis or biomechanical properties of leaves remained unchanged. Our simulation study highlighted model compliance to reproduce architectural plasticity and illustrated how architectural plasticity improved light interception via leaf area expansion, but how the competition for light imposed by the design can counterbalance this benefit in terms of carbon assimilation at stand scale. We conclude on the importance of planting patterns for plants with low architectural plasticity such as oil palm, and how *in silico* experiments can help in designing innovative planting patterns.

**KEYWORDS:** *Elaeis guineensis*; FSPM; LiDAR; phenotypic plasticity; plant architecture; planting design

<footnote n="1">¹CIRAD, UMR AGAP Institut, F-34398 Montpellier, France</footnote>

<footnote n="2">²UMR AGAP Institut, Univ Montpellier, CIRAD, INRAE, Institut Agro, F-34398 Montpellier, France</footnote>

<footnote n="3">³CIRAD, UMR AMAP, F-34398 Montpellier, France</footnote>

<footnote n="4">⁴AMAP, Univ. Montpellier, CIRAD, CNRS, INRAE, IRD, F-34398 Montpellier, France</footnote>

<footnote n="5">⁵CIRAD, UPR BioWooEB, F-34398 Montpellier, France</footnote>

<footnote n="6">⁶BioWooEB, Univ. Montpellier, CIRAD, CNRS, INRAE, IRD, F-34398 Montpellier, France</footnote>

<footnote n="7">⁷Sinar Mas Agro Resources Technology Research Institute (SMARTRI), Pekanbaru, Indonesia</footnote>

<footnote>*Corresponding author's e-mail address: raphael.perez@cirad.fr</footnote>
# 1. INTRODUCTION

The way plants are spatially organized in a field constitute one of the major factors of agronomic performance. For food crops, the increase in yield during the green revolution has mainly come from the increase in planting densities together with the selection of genetic material adapted to these densities (Kush 2001; Assefa et al. 2018). The ability to increase agronomic performance by increasing density is species-specific and depends on the capacity of plant to tolerate high density, due to the antagonistic effect between per-plant yield and density tolerance (Assefa et al. 2018). Oil palm (Elaeis guineensis) and coconuts are not an exception to the rule, the spacing between oil palm being considered as a major contributor to oil yield (Bonneau et al. 2014). However, experimentation on perennial crops such as oil palm requires long and expensive agronomic trials, making the testing of innovative practices rather economically risky. Investigation on optimal densities for oil palm has focused so far on the distance between plants, maintaining the conventional equilateral triangle pattern (quincunx design; Rafii et al. 2013; Bonneau et al. 2018).

Incident light is the primary resource affected by planting density, but the evaluation of the effect of density and design on light partitioning is not straightforward. Indeed, the effect of planting densities on agronomic performances is often estimated through yield, which integrates the impact of various factors such as water availability, fertilization and climate conditions. As a result, the confounding factors prevent dissecting the contribution of each factor on plant performance. Modelling approaches are relevant to address such questions since models can quantify the impact of separated processes, notably biophysical processes such as light interception.

Functional-structural plant models (FSPMs) offer the possibility to finely estimate the quantity of light intercepted by virtual 3D representations of plants (Vos et al. 2010). The coupling between 3D structure of plants and radiative models has multiple applications: estimating light availability for intercropping (Lamanda et al. 2008), assessing the influence of planting patterns in crop-weed competition for light (Evers and Bastiaans 2016), evaluating the impact of architecture manipulation on plants (Willaume et al. 2004; Buck-Sorlin et al. 2011) or designing architectural ideotypes (Sarlikioti et al. 2011; Da Silva et al. 2014). More recently, studies have used FSPM to investigate the role of phenotypic plasticity in light capture and partitioning in plant mixtures (Barillot et al. 2014; Zhu et al. 2015) and emphasized the importance of phenotypic plasticity in enhancing resource acquisition.

Phenotypic plasticity is defined as morphological, architectural and physiological responses triggered by resource limitation to cope with environmentally induced stress (Valladares et al. 2007; Pierik and Testerink 2014). For crops growing in open habitats, limitation in light due to competition triggers shade-avoidance syndrome (SAS), a growth response to escape shade (Aphalo et al. 1999; Franklin 2008; Ballaré and Pierik 2017). Architectural responses associated with SAS vary among species, but generally result in stem and leaf elongation, hyponasty and reduced branching (Gommers et al. 2013; Pierik and De Wit 2014). Light conditions determined by neighbouring plants, more precisely the decrease in the ratio of red (R) and far red (FR) light intensity (R:FR), have been characterized as the signal-triggering SAS

(Ballaré et al. 1990). The consequence of SAS on plant performance can be assessed through FSPM by simulating light quality within the canopy and calibrating response curves between R:FR and trait value (Chelle et al. 2007). This modelling approach revealed to be efficient to accurately simulate photo-morphogenesis responses such as internode elongation on cucumber (Kahlen and Stützel 2011) or wheat tillering (Evers et al. 2007). However, such approach can be intense in computational time and raises some methodological questions such as where on the plant and over what period of time the R:FR signal has to be perceived to trigger plant response (Demotes-Mainard et al. 2016; Lecarpentier et al. 2019). Lecarpentier et al. (2019) alternatively proposed a simple proxy of R:FR based on a neighbourhood green area index (GAI) that virtually mimicked the cessation of tillering in wheat.

In the present study, we wanted to address the question of how planting design modulates oil palm individual and stand performances in term of light interception and carbon assimilation, and what is the contribution of architectural plasticity to these performances. Using comprehensive and destructive data of plant architecture and vegetative biomass measured on five planting designs, we assessed oil palm phenotypic plasticity. The integration of the observed architectural plasticity into an existing FSPM of oil palm (Perez et al. 2016) allowed us conducting a simulation study to test the impact of planting design and architectural plasticity on physiological processes such as light interception and carbon assimilation.

# 2. MATERIALS AND METHODS

## 2.1 Experimental site

Field measurements were performed in experimental plots at the SMART Research Institute (SMARTRI, Smart Tbk.) located near Pekanbaru (Riau Province, Sumatra, Indonesia). This study focused on five plots with different planting density, varying from 136 (conventional) to 272 plants per hectare. Besides variations in planting density, the designs also varied from the conventional quincunx design with anisotropic patterns, i.e. involving non-equivalent distances between plants. Table 1 shows the characteristics of the five designs: isotropic when plants present equivalent distance to all their neighbours and homogeneous when all plants share a unique neighbourhood pattern [see Supporting Information—Fig. S1]. A heterogeneous design means that replicating a single neighbourhood pattern is not sufficient to represent the entire design. As the result, the heterogeneous design C is defined by two groups of plants (p1 and p2). The trial was set up in 2013 and each plot was planted with oil palm plants (E. guineensis) with a genetically uniform material (one progeny) grown in nursery for 18 months after seedling germination.

## 2.2 Phenotyping architectural plasticity

Destructive measurements were conducted in July 2019 (i.e. ~72 months after planting) to estimate plant dimensions and biomass. Six plants per plot, selected in the middle of each plot to avoid any border effects, were entirely dissected to collect structural, geometrical and biomass data for all leaves. Structural data included the number of leaves and the number of leaflets per leaf. Rachis and petiole length, fresh and dry weight were also measured along with the length, maximal width and fresh and dry biomass of a subsample of four leaflets
<table><caption>**Table 1.** Characteristics of the five studied planting patterns. Distance min, mean and max indicate the minimal, the average and the maximal distance between plants, respectively. Design C presents two groups of plants due to the irregular spacing between plants in the plot.</caption><thead><tr><th>Design</th><th>Density (plants per hectare)</th><th>Pattern</th><th>Distance min (m)</th><th>Distance mean (m)</th><th>Distance max (m)</th><th>Polygon area (m²)</th></tr></thead><tbody><tr><td>A</td><td>136</td><td>Isotropic homogeneous</td><td>9.21</td><td>9.21</td><td>9.21</td><td>220</td></tr><tr><td>B</td><td>272</td><td>Anisotropic homogeneous</td><td>4.61</td><td>7.07</td><td>8.31</td><td>110</td></tr><tr><td rowspan="2">C</td><td rowspan="2">272</td><td rowspan="2">Anisotropic heterogeneous</td><td>3.07 (p1)</td><td>5.60 (p1)</td><td>8.13 (p1)</td><td>49 (p1)</td></tr><tr><td>8.12 (p2)</td><td>8.49 (p2)</td><td>9.21 (p2)</td><td>171 (p2)</td></tr><tr><td>D</td><td>200</td><td>Anisotropic homogeneous</td><td>5.00</td><td>8.54</td><td>10.31</td><td>117</td></tr><tr><td>E</td><td>200</td><td>Anisotropic homogeneous</td><td>6.01</td><td>7.07</td><td>10.00</td><td>150</td></tr></tbody></table>

per leaf. For each design, measurements were performed on two replicated plots and data of the two plots were pooled together after checking that plot effect was negligible in comparison to design effect [see Supporting Information—Table S1 and Fig. S2]. As a result, 12 plants per design (even though being pseudoreplicates) were pooled together and considered for the analyses performed on structural data.

Dedicated measurements for estimating the biomechanical properties of the leaves were collected on December 2019 on one of the two plots. Three plants per plot were selected on which three leaves located at the top, middle and bottom of the crown were sampled. For each leaf, the length and declination, i.e. the angle from the vertical plane at leaf insertion on the stem, were measured, and remarkable points on the leaf nerve were identified (see Supporting Information—Fig. S3; Perez 2017). The 3D coordinates of these points along the rachis were manually reported for describing leaf bending and deviation (Perez 2017 Appendix A for the methodology). Each leaf was then cut into four segments between each remarkable point, and provided the following information at each section/segment: cross-sectional shape (width and thickness), length and fresh weight of the rachis segment, fresh weight of the leaflets on segment. These geometrical and biomass attributes were subsequently used to calibrate the biomechanical modulus of the leaves (cf. next section).

Field measurements of leaf architecture, mainly leaf angles and 3D coordinates, were hardly feasible on a high number of plants and may be very sensitive to manipulators. Here we tested how LiDAR-based measurements could overcome those phenotyping constraints. Terrestrial LiDAR (TLS) scans were thus collected on five palm trees to derive phenotypic traits of leaf geometry that were compared to labour-intensive measurements. Reflective balls and stripes were placed on rachis base (point C) and tip (point A) to easily identify these points on the TLS scans. On average, four scan positions were needed around each plant to isolate and clean co-registered 3D points of leaves. The PlantScan3D software (Boudon et al. 2014) was used to manually retrieve the 3D coordinates on the collected point clouds along the rachis and determined rachis length, bending and deviation (Fig. 1). Comparison of TLS-derived data and handmade direct measurement were assessed through root mean square error (RMSE), normalized root mean square error (NRMSE) and bias defined as:

$$RMSE = \sqrt{\frac{\sum_{i=1}^{n} (t_i - m_i)^2}{n}}$$

$$NRMSE = \frac{\sqrt{\frac{\sum_{i=1}^{n} (t_i - m_i)^2}{n}}}{\sum_{i=1}^{n} m_i / n}$$

$$bias = \frac{\sum_{i=1}^{n} (t_i - m_i)}{n}$$

where $t_i$ and $m_i$ are TLS observations and handmade observations, respectively, and $n$ represents the number of observations.

## 2.3 Leaf biomechanical model

The biomechanical model of leaf aimed at simulating leaf deformation (due to bending and torsion) according to leaf geometry, biomass and its biomechanical properties. Leaf geometry inputs (rachis length and cross-section width and thickness) were modelled using the existing VPalm allometries (Perez et al. 2016, 2018) and updated to take into account the architectural plasticity with planting density. New allometries were defined to link leaf length and leaf biomass, and allowed the estimation of rachis biomass properties required in the biomechanical model.

Due to the slenderness of the rachis (ratio length to cross-section dimensions), the biomechanical model considered the rachis as a beam subjected to two combined stresses: a bending stress and a torsion stress. The transverse shear deformation in the cross-section was neglected (slender beam). The constitutive equations of the beam theory (Euler-Bernoulli beam theory) in mechanics of solids can be applied in their integral forms, which allow varying the modulus of elasticity within the cross-section and along the length, as the inertia along the length of the beam. Furthermore, considering the integral forms, the initial shape of the beam can be curved. These equations are valid only for small displacements, but can be used to obtain large displacements via a decomposition of the total loading in successive elementary loadings.

To simplify the model (and to allow a determination of the modulus of elasticity), the shear modulus (G) and the modulus of elasticity (E) were considered constant along the rachis and were used to model the torsion and the bending of the rachis, respectively. Besides, we assumed that biomechanical properties were independent of leaf age. The material was assumed to be homogeneous and isotropic in the cross-section. Bending and torsion inertia were estimated for each of the five remarkable points using simple geometrical cross-sectional shapes (C: down triangle, CB: rectangle, B: up triangle, BA: ellipse, A: circle).
<figure><img src="image_2.png" /><figcaption>Figure 1. Processing terrestrial LiDAR scans on PlantScan3D software to retrieve 3D coordinates along the rachis.</figcaption></figure>

The rachis was discretized in 100 segments to solve numerically the integral forms of the constitutive equations (the cross-sections were discretized in 100 × 100 pixels and the inertia values were interpo- lated between the five remarkable points). The total loading (due to the segment weights and leaflet weights) was decomposed in a sum of ‘elementary loadings’, so that each elementary loading induced small displacements (the assumption of small displacement is checked at each computation step all along the beam). A computation step cor- responded to the application of an elementary loading on the previous deformed shape of the beam (deformed shape obtained at the previ- ous step). This iterative method on the loading allowed obtaining large displacements of the rachis. The final deformation was thus the result of a successive number of combined bending and torsional elementary deformations resulting from the segment mass and inertia.

The shear modulus (G) was experimentally estimated with a dedicated device [see Supporting Information—Appendix S1; Fig. S4] and an average value was calculated for each density. The modulus of elasticity (E) was estimated from an optimization process on the 3D coordinates derived from field measurements. The optimization processes to estimate the value of E for each leaf used the value of G obtained experimentally, and the measurements of rachis segment biomass, length and cross-sectional shapes. Using the Nelder–Mead simplex algorithm (Nelder and Mead 1965; Lagarias et al. 1998), the optimization consisted in finding the value of E that minimized the quadratic error (EQ) between simulated coordinates and the experiment [see Supporting Information—Fig. S5].

$$
EQ = \sqrt{\frac{\sum_{k=1}^{N_{pts}} (X_{Exp} - X_{Sim})^2}{N_{pts}}} + \sqrt{\frac{\sum_{k=1}^{N_{pts}} (Y_{Exp} - Y_{Sim})^2}{N_{pts}}} + \sqrt{\frac{\sum_{k=1}^{N_{pts}} (Z_{Exp} - Z_{Sim})^2}{N_{pts}}}
$$

where:

$N_{pts}$: the number of experimental points (five points)

X, Y, Z<sub>Exp</sub>: the observed coordinates in field

X, Y, Z<sub>Sim</sub>: the simulated coordinate for given E and G values

The initial solution to start the simplex was set to a value of 1000 MPa (this value was chosen after static tests performed on some rachis sam- ples to determine the modulus of elasticity). The optimization was per- formed on each of the 15 leaves studied per density and the average value of E was calculated for each density.

2.4 Defining a neighbourhood index to model archi-
tectural plasticity

Changes in architectural attributes in response to planting design were
considered at a given developmental stage (6 years after planting). The
integration of plasticity in the VPalm 3D model required the develop-
ment of allometries based on a variable as generic as possible able to
decipher each of the designs considered in our study. In this study,
some designs presented similar density with varying pattern (Table
1). As a result, planting density was not alone informative enough to
decipher the designs.

Various neighbourhood indices, derived from distances between
plants, were tested to establish the existence of simple allometries
with VPalm parameters. The indices tested were the minimal, aver-
age and maximal distance between plants and the polygonal area
around the central plant defined by the closest surrounding plants
(see Supporting Information—Fig. S1; Table 1). As for planting
density, the average and the maximal distances between plants did
not allow to properly decipher the studied designs. Contrarily, the
minimal distance between plants proved to be unique for each pat-
tern and was thus considered as the explanatory variable of plastic
responses. Polygonal area and the minimal distance between plants were highly correlated [see Supporting Information—Fig. S6], therefore involving comparable allometries. We investigated the existence of simple relationships between the minimal distance (hereafter called neighbourhood index [NI]) and the variations of VPalm parameters with designs. VPalm allometries (Perez et al. 2016) were fitted on the observed data for each plant (Fig. 2A and B) and regression analyses were performed to evaluate if NI was a significant factor in the adjustment of allometric parameters. When significant differences were found, i.e. when the coefficient associated to NI was significantly different from zero (P-value of the t-test < 0.05; Table 2), NI was selected as the explanatory variable for rendering architectural plasticity and NI-based allometries were defined to simulate VPalm parameter values (Fig. 2C and D). Architectural plasticity was estimated for each parameter as the

relative variation of the parameter from its value on the reference design (NI = 9.21 m).

## 2.5 Evaluating the effect of planting design and architectural plasticity on light interception and carbon assimilation

Three-dimensional mock-ups were generated from a set of VPalm parameters derived from the NI-based allometries. Replicates of the same mock-up were placed in virtual scenes with periodic boundary conditions to reproduce the planting designs with endless canopies (Perez et al. 2018). Inter-individual variability was generated thanks to the dedicated variance parameters in VPalm rendering variations in the allometric relationships (Perez et al. 2016). Subsequently, for each design, variations in leaves geometrical attributes (length, declination and number of leaflets) and leaflets dimensions (length and width)

<figure><img src="image_3.png" /></figure>

**Figure 2.** Allometries derived from neighbourhood index to model architectural plasticity. Observations and VPalm allometries fitting for rachis length (A) and rachis base declination (B) used for estimating the variation in model parameters with NI (points indicate average value per rank and design, vertical lines standard deviations between individuals). Allometries were fitted for each design with one of the two parameters constant (here the slope), the other parameter being used to define the NI-based allometric relationships (C and D). Rachis length plasticity (C) and declination plasticity (D) represent the percent of variation of rachis length intercept and the declination intercept (relatively to the control design NI = 9.21 m), respectively.
<table><caption>Table 2. Calibration of VPalm parameters in response to NI. When significant relationships between a parameter and NI are stressed, the allometric equation is written in the parameter value. Level of significances correspond to the P-value of t-test (ns, non-significant; **P < 0.01; ***P < 0.001).</caption><thead><tr><th>Predicted variable</th><th>VPalm equation</th><th>Parameter</th><th>Significance level with NI</th><th>Parameter value</th></tr></thead><tbody><tr><td>Rachis length</td><td>L<sub>rac</sub> = L<sub>rac int</sub> + L<sub>rac slp</sub> × rank</td><td>L<sub>rac int</sub></td><td>***</td><td>L<sub>rac int</sub> = {505 × (1.35 – 0.058 NI), NI < 6.14<br>505, NI ≥ 6.14</td></tr><tr><td>Petiole length</td><td>L<sub>pet</sub> = L<sub>rac</sub> × ratio<sub>L</sub></td><td>L<sub>rac slp</sub><br>ratio<sub>L</sub></td><td>ns</td><td>L<sub>rac slp</sub> = -1.45<br>ratio<sub>L</sub> = 0.25</td></tr><tr><td>Relative position of point B on rachis</td><td>Nb<sub>Lft</sub> = <sup>Nb<sub>int</sub></sup>&frasl;<sub>1 + e<sup>-Nb<sub>slp</sub>(Nb<sub>int</sub> - L<sub>rac</sub>)</sup></sub></td><td>Nb<sub>slp</sub><br>Nb<sub>int</sub></td><td>ns<br>ns</td><td>PosB<sub>rel</sub> = 0.66<br>Nb<sub>max</sub> = 172</td></tr><tr><td>Number of leaflets per leaf</td><td>L<sub>Lft B</sub> = L<sub>B int</sub> + L<sub>B slp</sub> × L<sub>rac</sub></td><td>Nb<sub>slp</sub><br>Nb<sub>int</sub></td><td>ns<br>ns</td><td>Nb<sub>slp</sub> = 0.0025<br>Nb<sub>int</sub> = 241</td></tr><tr><td>Leaflet length</td><td>W<sub>Lft B</sub> = W<sub>B int</sub> + W<sub>B slp</sub> × L<sub>rac</sub></td><td>L<sub>B int</sub><br>L<sub>B slp</sub></td><td>ns<br>ns</td><td>L<sub>B int</sub> = 77.7<br>L<sub>B slp</sub> = 0.016</td></tr><tr><td>Leaflet width</td><td>W<sub>Lft B</sub> = W<sub>B int</sub> + W<sub>B slp</sub> × L<sub>rac</sub></td><td>W<sub>B int</sub><br>W<sub>B slp</sub></td><td>ns<br>ns</td><td>W<sub>B int</sub> = 4.06<br>W<sub>B slp</sub> = 0.00097</td></tr><tr><td>Declination at C point</td><td>δ<sub>C int</sub></td><td>δ<sub>C slp</sub></td><td>ns</td><td>δ<sub>C int</sub> = 10.1 × (0.17 + 0.09NI)<br>δ<sub>C slp</sub> = 1.33<br>G = 125<br>E = 3026</td></tr><tr><td>Shear modulus</td><td>FW<sub>rac</sub> = FW<sub>rac int</sub> + FW<sub>rac slp</sub> × L<sub>rac</sub></td><td>FW<sub>rac int</sub></td><td>***</td><td>FW<sub>rac int</sub> = {354 × (1.31 – 0.054 NI), NI < 5.75<br>354, NI ≥ 5.75</td></tr><tr><td>Elastic modulus</td><td></td><td>FW<sub>rac slp</sub></td><td>ns</td><td>FW<sub>rac slp</sub> = 0.00571</td></tr><tr><td>Rachis fresh weight</td><td></td><td></td><td></td><td></td></tr></tbody></table>
were simulated to obtain seven individual mock-ups, each randomly deriving from an average individual. Seven plots were simulated per design to reproduce inter-individual variability and its impact on physiological processes. The number of simulations (seven) was chosen to allow the estimation of the mean and standard deviation of physiological outputs, with the concern of limiting the computational time to one night. The low coefficient of variation on simulation outputs [see Supporting Information—Table S2] also supported the choice to conduct only few simulation repeats. Simulation of physiological processes were computed in Archimed-φ (https://archimed-platform.github.io/) using meteorological and light conditions (sun position and day length) with a 30-min time step on a sunny day in the experimental site (Pekanbaru, Sumatra). Light interception of each object (leafletlet, rachis, petiole, snags and soil) was estimated on the 3D explicit stands considering 16 hemispherical directions. Direct incident light was computed for each triangle in the scene and scattered light assuming that each leaf intercepts scattered radiation proportionally to its apparent surface area in the direction of the incoming radiative flux (Dauzat et al. 2001).

Carbon assimilation was simulated using the model of Farquhar et al. (1980) coupled to the stomatal conductance model from Medlyn et al. (2011), and the leaf temperature by closing the energy balance (Monteith and Unsworth 2008). The long-wave radiation exchanges between the leaves and the environment were computed using a sky view angle, considering the system as isotropic except for the sky considered at air temperature (Dauzat et al. 2001) with constant parameters estimated on oil palm (Table 3). The model was run at a 30-min time step considering changing climate conditions over the day. The last variable was water-use efficiency (WUE), defined as the ratio between carbon assimilation and water transpiration. See Perez et al. (2022) for an example of the input files used for simulating design A.

The total light interception, carbon assimilation and mutual shading were compared for each design at plant and plot scale. Mutual shading was evaluated as the difference between the amounts of light intercepted by a single plant in a stand and the amounts intercepted by the same plant in isolated conditions, under similar incident radiation (Perez et al. 2018).

<table><caption>Table 3. Parameter values of Farquhar model and Medlyn model used for oil palm.</caption><thead><tr><th>Model</th><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td rowspan="5">Farquhar</td><td>J<sub>max</sub></td><td>250 µmol<sub>electron</sub>·m<sup>-2</sup>·s<sup>-1</sup></td></tr><tr><td>V<sub>cmax</sub></td><td>200 µmol<sub>CO2</sub>·m<sup>-2</sup>·s<sup>-1</sup></td></tr><tr><td>R<sub>d</sub></td><td>0.6 µmol<sub>CO2</sub>·m<sup>-2</sup>·s<sup>-1</sup></td></tr><tr><td>Θ</td><td>0.853</td></tr><tr><td>TempC ref</td><td>25 °C</td></tr><tr><td rowspan="2">Medlyn</td><td>g<sub>0</sub></td><td>-0.03 mol<sub>CO2</sub>·m<sup>-2</sup>·s<sup>-1</sup></td></tr><tr><td>g<sub>1</sub></td><td>12</td></tr></tbody></table>

The effect of architectural plasticity on physiological processes was estimated for each design by comparing the simulation outputs obtained from the mock-up integrating changes in architecture with the simulation outputs obtained without considering these changes, i.e. using a mock-up from the control design (Fig. 3).

## 3. RESULTS

### 3.1 LiDAR-based measurements are promising for fast and accurate phenotyping of oil palm architecture

The TLS scans were processed to extract leaf 3D coordinates and derived rachis length (Fig. 1). Rachis length estimated from LiDAR data showed high accuracy in comparison with the length recorded manually, with an average error around 5 cm (NRMSE = 1%; Fig. 4A). Terrestrial LiDAR data were also used to compare the quality of manual measurements relative to the 3D coordinates along rachis required for estimating the biomechanical modulus of elasticity (E). On average results highlighted a close match between the coordinates recorded manually and the one extracted from TLS data, but some discrepancies were revealed for some leaves [see Supporting Information—Fig. S7]. These differences could be explained by the impact of wind during measurements, but most probably because of leaf manipulation during manual measurements that could deform the leaves. To better estimate the effect of these differences on model calibration, both set of coordinates were used to optimize the value of elastic modulus (E), input data related to biomass remaining unchanged. Results emphasized the consistency of E between the two methodologies with an NRMSE of 8% (Fig. 4B), and clearly showed that manual measurements have an acceptable accuracy compared to TLS.

### 3.2 Plant proximity increased rachis length and erectness while structural components remained unchanged

Change in architectural traits with NI was mainly observed on the rachis (rachis length, rachis fresh weight and declination at point C) while the other architectural traits remained unchanged in comparison with the conventional planting density (design A). Rachis length significantly decreased with increasing NI until a plasticity threshold estimated at NI = 6.14 m (Fig. 2C; Table 2). At the minimal NI (3.07 m; design C-p1), rachis length increased by 18% comparatively to the reference design. With increasing plant proximity, rachis were also lighter than rachis at the conventional density (up to 27% of decrease in rachis fresh weight), suggesting that the increase in rachis growth was at the expense of rachis fresh weight. Response to plant proximity was also revealed by an increase in plant erectness (up to 20% reduction in declination at point C for the top crown leaves), which could be explained by lower rachis fresh weight for comparable biomechanical properties. Indeed, no significant change in elastic and shear modulus was observed among designs, revealing that change in architecture was driven by change in biomass allocation rather than in biomechanical properties.

The number of leaflets per leaf increased with increasing rachis length, but no significant effect of NI was found, suggesting that relationships between leaf dimension and leaf structural characteristics
<figure><img src="image_4.png" /><figcaption>Figure 3. Simulation strategy to estimate the impact of architectural plasticity and planting design on physiological processes. Mock-up of the reference design (design A) corresponds to the model without plasticity, and is thus taken as point of comparison for estimating the impact of plasticity on physiological processes. Colours on 3D mock-up on left represent light irradiance at noon.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4. Comparison of manual and LiDAR-based measurement of rachis length (A) and elastic modulus *E* (B). Values of *E* are estimated using the optimization processed from 3D coordinates recorded manually or extract from LiDAR point clouds (*n* = 14 observations). Grey line represents the 1:1 line.</figcaption></figure>
remained unchanged. Regarding leaflets dimensions, allometries
depending on rachis length were also conserved highlighting negligi-
ble effect of NI on leaf structure.

**3.3 NI-based allometries correctly render architectural plasticity among planting designs**

Statistical analyses allowed the evaluation of the architectural parame-
ters significantly affected by NI, and NI-based allometries were derived
to predicted parameter values depending on design (Table 2). No sig-
nificant effect of NI was found on leaflet attributes (number, length
and width). Given that leaflets were modelled thanks to allometries
based on rachis length, it was likely that the effect of NI on leaflets was
already integrated through the differences in rachis length. In other
words, the relation between rachis length and leaflets attributes was not
modified depending on design. The potential errors resulting from the
successive assembly of NI-based allometric relationships with VPalm
allometries were then assessed through the comparison of trait values
simulated and measured in field. Simulations were performed using
the average parameters estimated for each design, setting to zero all
the variances parameters used to generate inter-individual variability
in VPalm (Perez et al. 2016). Results highlighted model compliance

to reproduce architectural plasticity through NI-based allometric rela-
tionships (Fig. 5). The model allowed the simulation of the increase in
rachis length and the decrease in rachis fresh weight with plant prox-
imity (Fig. 5A and B). The comparison of the VPalm model with and
without NI-based allometries showed the benefits of the integration of
plasticity on the model. For instance, prediction errors (NRMSE) for
rachis length decreased from 10 to 3 %, from 21 to 9 % for rachis fresh
weight and from 16 to 6 % for declination at C point. For the other traits
that did not show significant change with NI, for instance the number
of leaflets per leaf, simulations revealed less compliance to observations
(Fig. 5D). Results on leaflets dimensions (Fig. 5E and F) exhibited
higher variations in observations than in simulation, revealing the limits
of the model to simulate the observed variations at the leaflet scale. It is
however worth noting that observed coefficient of variation in leaflets
dimensions was very low (below 5 %), which could explain the incapac-
ity of the model to render such precision in predictions.

**3.4 Improvement of resources acquisition through
architectural plasticity is outdone by planting design**

The estimation of total plant leaf area is not straightforward for oil
palm since it integrates the area of thousands of leaflets. VPalm

<figure><img src="image_6.png" /><figcaption>Figure 5. Comparison of trait values observed in field and simulated in the VPalm model taking into account influence of the NI factor. Points indicate average value per leaf rank for each design (colours = NI value). Grey line represents the 1:1 line.</figcaption></figure>
simulations allowed the estimation of total plant leaf area and can
be used to compare leaf area between designs. Increase in rachis size
resulted in a global expansion in plant leaf area, but was only stressed
for the design B, C-p1 and D, with a gain varying from 4 to 10 % in
comparison to the conventional design A (Fig. 6). Combined to the
radiative balance model, 3D mock-ups enabled comparison of the
impact of architecture and design on light interception and the related
biophysical processes [see Supporting Information—Fig. S8].
The design A proved to be the most efficient to maximize resources
acquisition at the plant scale: the amount of light intercepted, car-
bon assimilated and water transpired being markedly higher for this
design than the four other designs. For instance, in high density rows
of design C (p1), plants presented 43 % less intercepted light and
54 % less carbon acquisition in comparison with design A. Only the
design D presented an equivalent level of transpiration, and reduc-
tion in light capture, carbon assimilation and WUE below 5 %. The
better resource acquisition in design A was mainly explained by the
lower mutual shading conferred by its lower planting density com-
pare to the four other design but also because the quincunx design
which allowed a homogeneous repartition and a better penetration
of light within the crown (Fig. 7). The design D also highlighted
a good penetration of light, with a global mutual shading of 23 %.
Design A presented the best penetration of light within the canopy
due to the lower total leaf area, but it is worthy to note that, at the
leaf area index (LAI) of design A (around 2.7 m²·m⁻²), design D pre-
sented inferior value of mutual shading than design A. As a result, it is
likely that competition for light in design D became lower that design
A when plants reach maturity.

Outputs at the stand scale highlighted the importance of planting
design on physiological processes (Fig. 8). Interestingly, we found a
trade-off between resource loss at the plant scale (Fig. 6) and perfor-
mance gain at stand scale due to higher planting density. Increased den-
sity globally improved light interception (from 9 to 44 %), but gain in
carbon assimilation was not correlated to the gain in light interception.
For instance, the gain in light interception due to the high density in
design E did not counterbalance the negative impact on photosynthe-
sis at the plant scale. Indeed, the total carbon assimilated per hectare in
design E remained close to design A. Only designs B and D highlighted
the benefits of higher density on carbon gain at the stand scale, with
13 % and 42 % more carbon assimilated than the conventional design,
respectively. Regarding WUE (Fig. 8D), design A demonstrated the
highest value but design D confirmed to be an interesting design with
only 3 % lower WUE compared to the design A.

When comparing simulations with and without architectural plas-
ticity, the increase in total leaf area only demonstrated little gain in light
capture and carbon assimilation (Fig. 8A and B). Even if the plasticity
effect resulted in more erected leaves, the spatial arrangement of leaves
did not prevent extra leaf area to increase mutual shading, except for
design E (Fig. 8C). Gain in carbon assimilation due to plasticity was
eventually negligible, with a maximum of 2 % for design C and D. As a
result, the potential gain at the plant scale in light capture and carbon
assimilation due to plastic response (leaf area expansion and leaf erect-
ness) under higher density did not overcome the biophysical draw-
backs of competition for light.

4. DISCUSSION

4.1 Phenotyping oil palm architecture with LiDAR

Phenotyping plants in the field usually requires techniques that are
laborious, time-consuming and destructive. This is particularly true for
3D data, which can be very sensitive to manipulators or equipment,
involving bias with consequences hardly predictable. LiDAR-based
phenotyping is a promising technology to overcome these drawbacks
(Lin 2015; Furbank et al. 2019). Here we found close match between
LiDAR and manual measurements, for both dimensions and 3D coor-
dinates of oil palm leaves, suggesting that both methods can be used
for accurately phenotyping these traits. The added value of LiDAR
measurements remains in the possibility to screen 3D architecture
without manipulating leaves, contrarily to handmade measurements
that often requires deforming or even cutting the leaves. In addition,
LiDAR offers the capacity to phenotype tall palms, which are difficult
to access manually, and makes architectural measurements on old
stands possible. Scanning plants with TLS can simultaneously and rap-
idly collect data on several organ or plants, but often requires multiple
views to avoid occlusion problem (Thapa et al. 2018). When field con-
ditions are windy, the subsequent co-registration of scans introduces
noise in the point clouds, decreasing data quality for post-processing.
Nowadays, post-processing is the main bottleneck in LiDAR-based
measurement, since manual work on point clouds is still needed to
extract trait value. As a result, the time saved in collecting scan in field,
in comparison to traditional measurements, can be lose afterwards in
computational processes. In the present study, post-processing was
supported by the software PlantScan3D (Boudon et al. 2014), which
provided a semi-automatic methodology to rapidly extract 3D coordi-
nates along rachis nerve. Enhancement of the current method could
be achieved to render the process fully automatic, for instance using
deep learning method allowing automated segmentation of leaves and
extraction of phenotypic properties (Ziamtsov and Navlakha 2019).
It is worth to precise that such improvements could be achieved rap-
idly on few traits like rachis length, shape and angles. Nevertheless,
regarding other traits like biomass components or leaflets counts for
instance, further technical improvements and dedicated data set would
be required.

## 4.2 Towards a model of oil palm that accounts for architectural plasticity over plant development

The present study indicated the main changes in oil palm architecture
in response to plant proximity. The increase in rachis length confirmed
the results obtained by Bonneau *et al.* (2014), which showed signifi-
cant frond length difference among planting density starting from
72 months after planting (same stage than the present study). Bonneau
*et al.* (2014) observed significant increase in frond length for densities
below a distance of 8 m between plants, whereas in our study we found
plastic response below 6.14 m (Table 2). The plant proximity thresh-
old was not fully in accordance between the two studies, which could
be explained by the asymmetrical designs changing incoming light at
equivalent density. The increase in rachis length in response to increas-
ing competition for light confirmed the role of leaf expansion to cap-
ture more light, as demonstrated in the sensitivity analysis previously
performed on VPalm (Perez *et al.* 2018).
<figure><img src="image_7.png" /><figcaption>Figure 6. Simulation outputs at the plant scale for each design using plastic responses in the model (blue boxes) or not (red boxes). Bars indicate mean values and error bars standard deviation of the seven virtual individuals. Values in blue labels on top of bars represent inter-design comparison, i.e. gain or loss relatively to the design control (design A). Values in white labels on bars represent the gain or loss when architectural plasticity is considered in simulations. Design C presents two groups of plants due to the irregular spacing between plants in the plot.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 7. Mutual shading with cumulated leaf area index with canopy deepness for the five studied designs (indicated by colours and labels). Mutual shading is calculated from the difference in light intercepted within the canopy of an isolated plant and the same plant in stand. Points represent average mutual shading depending on canopy deepness; vertical lines the standard deviation between individuals. Design C presents the two groups of plants due to the irregular spacing between plants in the plot.</figcaption></figure>

In many crops, plants with more erected habit are less competitive for light and thus can be planted at higher density (Reynolds et al. 2000; Truong et al. 2015; Perez et al. 2019). Here we observed that to avoid competition for light, oil palm modulate leaf erectness and confirmed the SAS observed on other crops (Gommers et al. 2013). To our knowledge, this work is a first attempt to evaluate the plasticity of biomechanical properties of leaves. We found that oil palm erectness was likely modulated through a decrease in rachis fresh weight rather than a significant change in biomechanical properties of leaves. However, further dedicated studies are needed since the ratio between rachis length and biomass was not constant depending on design, pointing out the potential existence of differences in water content and/or structural composition. Moreover, the biomechanical model presented in this study considered a unique value of elasticity and shear modulus along the leaf and with leaf age, but it is likely that properties change with space and time.

NI-based allometries allowed to correctly render the architectural plasticity observed in field, and enabled generating 3D mock-ups reproducing the main geometrical changes in response to planting design. The major limitation of the proposed approach is that the allometries are specific to the developmental stage of oil palm (72 months after planting), and therefore requires additional experiments and analysis to be generalize for younger or older stages. Indeed, it is clear that competition for light will depend on plant age: no competition in the early stages

to high competition in the mature stage. One limitation of using only the nearest distance as an explanatory variable for architectural plasticity is that it does not account for other distances in anisotropic patterns (e.g. inter-row distances). The limited subset of planting patterns studied prevented us for measuring the effect of inter-row distances beyond a certain threshold, and thus from inferring architectural plasticity to broader designs. The NI proposed is biased because it only accounts for distance between plants, without considering crowns proximity (distance between leaf tips) which affects light change over time and plant development. A way to account for the dynamic changes in competition for light in relation with plasticity would be to simulate a signal which evolves with plant growth and that can trigger plastic responses beyond a given threshold. This could be achieved by directly simulating R:FR ratio (Evers et al. 2007; Kahlen and Stützel 2011; Bongers et al. 2018) in virtual scenes, but would raise questions about how to integrate the signal in time and space while adopting a parsimonious model and with reasonable computational time. As proposed by Lecarpentier et al. (2019), GAI can be used as a simple environmental cue of light competition. Another option could be to use directly the mutual shading as the triggering signal. It is likely to be the variable that represents the best the competition for light, but the computational cost to estimate it is still a bottleneck. One could suggest to perform simulations with a simpler approach using voxel-based (Munier-Jolain et al. 2013) or envelope-based (Duursma et al. 2012; Louarn et al. 2012) models, enabling fast calculation of light interception and mutual shading. In any case, the development of a dynamic approach of architectural plasticity would need phenotypic data over a period from early to mature stages. The data available for this study only concerned a relatively short period compared to oil palm development. Besides, the development of the palms has most certainly not reached a stable level, which is often observed at a later age of the plants. The ongoing collection of data in this trial would enable the development of a more integrated and generic modelling approach.

## 4.3 A limited architectural plasticity compensated by plasticity in carbon allocation

Our study allowed estimating the contribution of architectural plasticity in light interception, carbon allocation and WUE. Interestingly, we demonstrated that the expansion in leaf area in response to shade enabled to enhance light harvesting and increased assimilate supply at the plant scale, but also decreased WUE. Our results emphasized the trade-off between plant performance and stand performance, since higher plant density did not increase carbon assimilation at the plot scale (Fig. 8B). In this agronomic context, the similar and simultaneous plastic behaviour of plants has generated an environmental neighbourhood highly competitive for light. The monocaulous habit of oil palm architecture did not allow limiting mutual shading while expanding leaf, rendering the competition for light ineluctable. We conclude from this simulation study that, under the light stress imposed by planting design, oil palm presented a maladaptive plasticity (futile elongation of leaves) which negatively impacted community performance (Valladares et al. 2007). One can suggest that the limited architectural plasticity of oil palm can be compensated by the high plasticity of oil palm in term of biomass allocation (Legros et al. 2009).
<figure><img src="image_9.png" /><figcaption>Figure 8. Simulation outputs at the stand scale for each design using plastic responses in the model (blue boxes) or not (red boxes). Bars indicate the mean value and error bars the standard deviation of the seven simulations. Values in blue labels on top of bars represent inter-design comparison, i.e. gain or loss relatively to the design control (design A). Values in white labels on bars represent the gain or loss when architectural plasticity is considered in simulations.</figcaption></figure>

Pallas *et al.* (2013a) demonstrated how source-sink imbalance could modulate yield components. As a result, it is likely that the cost of allocating additional biomass in leaf expansion will be at the expense of bunch production. Comparison of the designs in term of oil production would be very interesting to investigate whether the estimated improvement in total carbon assimilation at the plot scale for some designs involved increasing yield or not.

Eventually, the coupling between the structural model VPalm and the carbon assimilation model XPalm developed by Pallas (Pallas *et al.*

2013b) would enable to predict oil palm yield performance depending on planting designs. Such development would also enable to take into account the root system in the model and would consider competition for water, which was neglected in the present work.

## 5. CONCLUSION

The present study supports the value of using FSPMs in an agro-nomic context. *In silico* experiments estimated the importance of architectural plasticity in physiological processes, and drew attention
to the physiological consequences of the limited architectural plasticity of oil palm when planting designs are inappropriate. Indeed, the leaf expansion in response to shade together with the inability of oil palm to modulate mutual shading decreased carbon assimilation at the stand scale. The modelling tool presented here paves the way to design innovative patterns of plantation based on *in silico* estimations of plant performance. Architectural screening of an enlarged diversity of oil palm architecture, involving *E. oleifera* × *E. guineensis* hybrids which present shorter leaves (Barcelos et al. 2015), could extend the possibility of defining planting designs specific to genetic material. Furthermore, in the context of rising interest for ‘ecologically intensified’ oil palm systems (Bhagwat and Willis 2008; Khasanah et al. 2020), the modelling approach proposed in this paper will help providing insights in the comprehension of the ecophysiological processes driving performance of oil palm agroforestry and intercropping systems.

## SUPPORTING INFORMATION

The following additional information is available in the online version of this article—

**Figure S1.** Description of planting patterns and neighbourhood.

**Table S1.** Analysis of covariance table of rachis length to assess the effect of plots.

**Figure S2.** Rachis length depending on leaf rank for the five studied designs and the two plots.

**Figure S3.** Description of the leaf and the remarkable points.

**Appendix S1.** Estimation of the shear modulus.

**Figure S4.** Mechanical device used to estimate the shear modulus (G) of the rachis.

**Figure S5.** Optimization process to adjust the modulus of elasticity (E).

**Figure S6.** Correlations between the selected NI (minimal distance between plants) and the others neighbourhood indices tested to design allometries.

**Figure S7.** Leaf bending depending on manual versus LiDAR-based measurements.

**Figure S8.** Mock-ups generated with the VPalm model for each design.

**Table S2.** Coefficient of variation of variable outputs estimated from the seven simulations on each design.

## ACKNOWLEDGEMENTS

The authors make special thanks to the SMARTRI staff for the logistic and technical assistance for their much valued help in the field data acquisition. The authors are also grateful for the comments of the three anonymous reviewers, and particularly reviewer 1 for his inputs on statistical revisions.

## SOURCES OF FUNDING

This work was financially supported by the SMART Research Institute (SMARTRI, Smart Tbk.).

## CONFLICT OF INTEREST

None declared.

## CONTRIBUTIONS BY THE AUTHORS

Conceptualization: R.P.A.P., R.V., J.-P.C. and J.D.; software and methodology: R.P.A.P., R.V., J.D., L.B., F.G. and F.B.; data analysis: R.P.A.P., R.V., L.B. and D.A.R.; investigation: R.P.A.P., R.V., J.D. and J.-P.C.; resources: D.A.R. and J.-P.C.; data curation: R.P.A.P., R.V., M.R. and D.A.R.; writing—original draft preparation: R.P.A.P.; writing—review and editing: R.P.A.P., R.V., L.B., F.B., D.A.R. and J.-P.C.; visualization: R.P.A.P., R.V., M.R., and F.B.; supervision: R.P.A.P. and R.V.; project administration: R.P.A.P., R.V., D.A.R. and J.-P.C.

## DATA AVAILABILITY

Processed data, as well as models code, are available from the authors upon request. Archimed-phi model is available online (https://archimed-platform.github.io/archimed-phys-user-doc/). An example configuration of simulation is available in Zenodo repository (doi:10.5281/zenodo.6246090).

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