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Keywords:

  • Chrysanthemum morifolium Ramat.;
  • functional–structural plant model;
  • GreenLab;
  • model calibration;
  • secondary growth;
  • sink–source ratio;
  • validation;
  • virtual plant

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
  • Plants respond to environmental change through alterations in organ size, number and biomass. However, different phenotypes are rarely integrated in a single model, and the prediction of plant responses to environmental conditions is challenging. The aim of this study was to simulate and predict plant phenotypic plasticity in development and growth using an organ-level functional–structural plant model, GreenLab.
  • Chrysanthemum plants were grown in climate chambers in 16 different environmental regimes: four different temperatures (15, 18, 21 and 24°C) combined with four different light intensities (40%, 51%, 65% and 100%, where 100% is 340 μmol m−2 s−1). Measurements included plant height, flower number and major organ dry mass (main and side-shoot stems, main and side-shoot leaves and flowers). To describe the basipetal flowering sequence, a position-dependent growth delay function was introduced into the model.
  • The model was calibrated on eight treatments. It was capable of simulating multiple plant phenotypes (flower number, organ biomass, plant height) with visual output. Furthermore, it predicted well the phenotypes of the other eight treatments (validation) through parameter interpolation.
  • This model could potentially serve to bridge models of different scales, and to link energy input to crop output in glasshouses.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

The prediction of plant behavior under a range of environmental conditions has long been an aim of plant science. This aim is driven not just by scientific curiosity, but also by the practical needs of crop cultivation, especially for horticultural plants. To obtain an economic optimal control strategy, mathematical relationships between energy input in the glasshouse and crop production are needed (van Straten et al., 2000). Although, in many crops, the main interest is fruit yield itself, in ornamental plants, such as chrysanthemum, both the flower characteristics and other external quality aspects are important, including leaf morphology (number and size) and stem morphology (length, diameter and strength) (Carvalho & Heuvelink, 2001).

As for many crops, descriptive or empirical models for chrysanthemum have been developed for phenotypes, including plant height (Pearson et al., 1995), internode elongation (Jacobsen & Amsen, 1992; Karlsson & Heins, 1994; Schouten et al., 2002), total plant dry weight (Lee et al., 2003), leaf area (Lee & Heuvelink, 2003), time to flowering (Adams et al., 1998), flower development (Hidén & Larsen, 1994) and flower diameter (Nothnagl et al., 2004). However, several important quality aspects, such as individual flower biomass and stem biomass, are absent (Carvalho & Heuvelink, 2001), and the empirical models are hard to generalize to a wide range of environmental conditions. Above all, the mentioned characteristics are rarely integrated in a single model. Furthermore, the plant response often shows interaction between environmental factors.

As chrysanthemum is one of the most important horticultural plants, the reaction of chrysanthemum to temperature and light has been studied extensively. At higher light intensities, plants generally flower earlier (Karlsson et al., 1989); total flower dry mass increases, mainly by increasing the flower number rather than the mass of individual flowers (Carvalho & Heuvelink, 2003). At higher temperatures, a larger number of flowers and leaves on the main stem have been reported (Karlsson et al., 1989), but the diameters of individual flowers are generally smaller (Nothnagl et al., 2004; Carvalho et al., 2005). There is an interaction between light and temperature: in spring (better light conditions), a greater number of lateral shoots are observed with increasing temperature, whereas, in winter, no effect of temperature is observed (Schoellhorn et al., 1996). Both time to flowering and time to visible flower bud appearance show an optimum response to temperature between 17 and 22°C (Adams et al., 1998). Light use efficiency shows a rather flat temperature optimum, which is dependent on the light level (van der Ploeg & Heuvelink, 2006).

Both development and growth determine a plant’s phenotype. To simulate multiple phenotypes in a mechanistic way, functional–structural plant models (FSPMs) are likely to be the most suitable tools. According to Vos et al. (2009), an ideal FSPM software will inter alia allow modeling of the structural development of plants, the simulation of light distribution and absorption, the calculation of photosynthesis for each green element, the simulation of source–sink regulation and the generation of visual outputs. Organ phenotypes cannot be considered as isolated events, but are linked to each other and are dependent on the environmental conditions. This is the case in FSPM-based virtual plants, in which phenotypes are jointly regulated by variables representing source and sink. Several FSPMs have been published in the last decade (e.g. Yan et al., 2004; Allen et al., 2005; Evers et al., 2010), each with its own focus, time scale, target plant and implementation software. Generally speaking, because of model complexity, the calibration of an FSPM is a challenge. Most FSPMs provide insight into plant behavior by simulation experiments (e.g. Eschenbach, 2005; Evers et al., 2010). By contrast, the GreenLab model, described by a set of recurrent equations, has been calibrated for several crops (Guo et al., 2006; Christophe et al., 2008; Wang et al., 2010) grown at one environmental condition or at different planting densities (Dong et al., 2008; Ma et al., 2008; Kang et al., 2011).

The aim of this study was to simulate multiple plant phenotypes under a range of environmental conditions using an FSPM, with comparisons being made with real data. Chrysanthemum plants were grown in a series of temperature and light combinations, as both are key factors for plant growth, especially in controlled-environment agriculture. We wanted to test whether the model, calibrated on half of the dataset, was able to predict the remaining half by interpolation of several model parameters (validation). Chrysanthemum was chosen because of its multiple phenotypes of interest. Moreover, chrysanthemum is a short-day plant having a basipetal flowering sequence, representing an important family of plants with the same feature (e.g. Arabidopsis). GreenLab is used to simulate plant development and growth processes, with a specific module dedicated to the basipetal flowering sequence. In addition to providing numerical output, the model also produces three-dimensional (3D) virtual plants, which is an appealing feature that allows direct visual comparisons between virtual and real plants.

Materials and Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Experimental set-up and data collection

The experiment was conducted at Wageningen University (the Netherlands) in four, large, artificially lit growth chambers of 4.50 × 3.25 × 2.20 m3 (l × w × h). A total of 16 treatments was imposed, resulting from all combinations of four temperatures (15, 18, 21 and 24°C) and four light intensities (obtained with shading screens; 40%, 51%, 65% and 100% light, with 100% being 340 μmol m−2 s−1) (Fig. 1a). Treatments are denoted TxLy for temperatures xoC and light intensities y%. Block-rooted cuttings of Chrysanthemum morifolium Ramat. ‘Splendid Reagan’ were obtained from a commercial propagator, planted in 12-cm pots and the pots were grouped at a density of 69 plants m−2. Plants were initially subjected to long-day (LD) conditions for 15 d, followed by a short-day (SD) period up to final harvest. Assimilation lamps (1 HPI-T plus 400 W : 1 HPS SON-T-Agro 400 W; Philips) were used as the light source. These were on continuously for 16 h daily during the LD period and for 11 h during the SD period. The CO2 concentration was maintained at ambient level. The terminal flower bud on the main stem was pinched at an early stage (< 5 mm) to reduce apical dominance and to promote the growth of branches.

image

Figure 1. Schematic representation of the experimental set-up and sampling strategy. (a) Sixteen combinations of temperature and light intensity: eight treatments (closed circles) were used for model calibration and the remaining eight treatments (open circles) for validation (100% light = 340 μmol m−2 s−1). (b) Nine destructive plant-level measurements for each treatment, from planting H0 to final harvest H4.

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Nine destructive harvests were conducted during the growth period (Fig. 1b). The first of these (H0) was made on 20 plants at planting. The second harvest (H1) was made 15 d later (at the beginning of the SD period) when five plants were harvested per treatment. The remaining seven harvests (H1.1, H2, H2.1 H3, H3.1, H3.2 and H4) of five plants per treatment were made every 7–10 d thereafter. The fourth harvest (H2) was made at the stage at which the terminal flower bud on the main stem was just visible, and the sixth harvest (H3) was made at the stage at which the lateral flower buds started to appear. The final harvest (H4) was made when the first row of disc florets reached anthesis in three or four flowers per plant. The timing of the transitions between these major stages (H2, H3 and H4) was dependent on treatment.

For all nine sampling dates and 16 treatments, measurements included the fresh and dry mass of the stems (main and side-shoot stems), leaves (main and side-shoot leaves) and flowers, main and side-shoot leaf areas, numbers of leaves on the main stems and numbers of flowers and flower buds (> 5 mm). Here, the term ‘side shoots’ is used to refer to branches of all orders.

The GreenLab model for basipetal inflorescence progression

The concept of the GreenLab model has been described in previous articles (Guo et al., 2006; Letort et al., 2008; Kang et al., 2011). Here, we summarize the relevant modeling concepts and detail the new features particularly associated with the current study.

Modeling plant organogenesis

In GreenLab, all individual organs play the roles of sink and/or source. The numbers and ages of the organs are described precisely by a generic organogenesis model (Kang et al., 2008). A phyllochron, corresponding to the thermal time elapsing between the appearance of two successive leaves on the main stem, is used as a time step, called the ‘growth cycle’. From observations on chrysanthemum, the number of leaves (NoL) on the main stem increases linearly with the time since planting (H0) until the terminal bud becomes visible (H2), giving the relationship NoL = a ·t + b (R2 > 0.95), where t is the time in days after planting, a represents the leaf appearance rate (d−1) and b is the number of visible leaves in the original cutting (around five). This linear relationship gives the number of main-stem leaves until stabilization. The maximum number of main-stem leaves, T0, is directly observed from the plants (Supporting Information Table S1).

In chrysanthemum, a nonterminal phytomer consists of an internode, a leaf and a (dormant or active) axillary bud. A deterministic version of GreenLab was used to produce the branching structure as illustrated in Fig. 2. The maximal values of eight (T1max = 8) and three (T2max = 3) leaves were set for the first- and second-order branches, respectively, for all treatments (Fig. 2), according to observations. The numbers of leaves in a branch were set to increase from the top of the mother axis to the base until stabilization, based on the hypothesis that a hormonal signal is transported basipetally to the side shoots to stop their development (Lindenmayer, 1984) once the main stem differentiates into a flower.

image

Figure 2. Illustration of the aboveground topological structure of a second-order chrysanthemum plant. Phytomers are represented by rectangles and apical flowers by circles. The final numbers of leaves are indicated at the top of each axis: T0 for the main stem; T1(x) for a first-order branch of coordinate (x); T2(x, y) for a second-order branch of coordinate (x, y); x and y are the phytomer ranks from the bottom of the mother axis.

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Modeling the basipetal flowering sequence

In chrysanthemum, stacked leaves appear in the side shoots and start to expand in the vegetative stage, whereas the associated internodes remain dormant until the flowering stage. Branches of higher phytomeric ranks elongate earlier than those of lower ranks (earlier appearance), which leads to the basipetal flowering sequence. The time lag between the appearance and elongation of a branch, called the ‘growth delay’, needs to be quantified in order to determine when the side-shoot internodes and flowers become significant sinks.

As higher ranking branches show less growth delay, a position-dependent growth delay function is defined in which the coordinate (phytomeric rank) of each phytomer and branch is specified. The coordinate (x) of a first-order branch is the phytomer rank of this branch on the main stem, and the maximum number of leaves in this branch is T1(x). The coordinate of a second-order branch is (x, y), y being the phytomeric rank of this branch on its mother branch and x being the coordinate of its mother branch (Fig. 2); the maximum number of leaves in this branch is T2(x, y). The growth delays (in cycles) of a first-order branch, dO(x), and a second-order branch, dO(x, y), are defined in a recursive manner (Eqn 1):

  • image(Eqn 1)

(g1 and g2, initial delay intensities for the first- and second-order branches, respectively; c1 and c2, two coefficients describing the nonlinear increase in delay intensity along the mother axis). In Eqn 1, lower phytomeric ranks (x and y) give greater delays; second-order branches (x, y) have longer growth delays than their mother branch (x). When c1 and c2 are ones, the growth delay becomes a linear function of coordinate (x, y), as in Kang et al. (2006). Under this condition, if = 2, branches start growth one by one, as proposed in de Visser et al. (2006).

A dormant axillary bud begins to extend when its age exceeds the delay, and the delay function can be organ specific. For chrysanthemum, the main organ types include leaves (L), internodes (I) and flowers (F). As leaves start to expand early in the vegetative stage, their delays are set to zero, that is, dL = 0. For internodes and flowers, it is supposed that both organs share the same growth delay, that is, dI = dF. Then, the notation dO can be simplified to d, and there are only four parameters (g1, g2, c1, c2) controlling the basipetal flowering sequences of first- and second-order branches (Table 1).

Table 1.   Description of model parameters
g1, g2, c1, c2Delay parameters (Eqn 1)
Q0Initial plant biomass
rLight use efficiency (g mol−1; Eqn 2)
PI1Sink strength of main-stem internode (Eqn 3)
PL2Sink strength of side-shoot leaf (Eqn 3)
PF2Sink strength of flower (Eqn 3)
PI2Sink strength of side-shoot internode (Eqn 3)
SCSecondary growth coefficient (g−1; Eqn 5)
aI, bIAllometric parameters of internodes (Eqn 9)

Modeling biomass production

In the current GreenLab model, the leaf is the only source organ and the biomass produced at each growth cycle is a function of the plant leaf area. At a growth cycle n, the biomass increment of a plant, Q(n), is computed as in Eqn 2:

  • image(Eqn 2)

(E, incident radiance integral per cycle (mol m−2 phyllochron−1); L, light intensity (mol m−2 s−1); LoD, day length (h); NoD, duration of a phyllochron (day); r, light use efficiency (g mol−1), estimated through parameter identification (Tables 1, 2); Sp, projection area of a plant (m2), set as the inverse of the population density (0.0145 m2) because of rapid canopy closure; k, light extinction coefficient, set to an empirical value of 0.6; A(n), total leaf area of a plant (m2) at cycle n, computed as the ratio between the leaf dry mass and specific leaf weight (SLW), the latter observed directly from the data (Tables S2, S3)). Leaf, internode and flower biomasses were individually computed using the sink functions as below.

Table 2.   Values of sink and source parameters (see Table 1) for the eight calibration treatments (Fig. 1) of temperature (T) and light intensity (L) (where 100% = 340 μmol m−2 s−1)
T (oC)L (%)PL2PF2PI2SCr
  1. Q 0 = 0.103 ± 0.01, PI1 = 0.55 ± 0.03 for all treatments.

  2. *Coefficient of variation.

15400.01318.0*1.3024.60.1225.43.847.30.0772.0
15510.01619.01.8920.40.2016.93.986.00.0772.2
15650.01717.02.9723.50.2018.05.206.90.0641.9
151000.02113.14.4920.00.3512.36.345.80.0661.7
18400.01225.51.4925.10.0925.74.707.50.0842.0
21400.01034.91.7023.10.1219.14.606.90.0961.9
24400.01032.01.6629.80.1616.44.149.00.0831.9
241000.0426.81.3015.40.256.75.194.70.0660.8

Modeling biomass partitioning among individual organs

In GreenLab, each growing organ competes for biomass according to its relative sink strength (the competitive ability of an organ to accumulate biomass) based on the common biomass pool assumption (Marcelis, 1994). Sink functions deal with the allocation of available biomass among individual organs. For an organ of age i since its appearance, its sink strength (fOp) is computed as in Eqn 3:

  • image(Eqn 3)

(POp, relative sink strength of organ O of branching order p, a dimensionless constant to be obtained by parameter identification (Tables 1, 2)). The main-stem leaf is set as the reference organ, that is, PL1 = 1. ϕo is a Beta function describing the sink variation of organ O with age (Yan et al., 2004). Its parameters were estimated by fitting with organ biomass values measured destructively in a separate experiment. The growth delay of this organ, dO(pos), is computed from Eqn 1, ‘pos’ being the coordinate of the branch to which this organ belongs. An organ competes for biomass only if it starts to expand, that is, if its age is greater than the delay; otherwise, its sink strength is negligible. The sum of the individual organ sink strengths quantifies a plant’s primary demand for biomass, D1(n), as in Eqn 4:

  • image(Eqn 4)

(M(n), total number of phytomers at age n; id, index of each phytomer, from which the information can be retrieved, including coordinate (pos), branching order (p) and age (i) of the phytomer (organ); f, sink function (Eqn 3)).

In chrysanthemum, although the main-stem length usually stabilizes by H2.1 (the fifth sampling date, Fig. 6a), secondary (thickening) growth continues so that biomass increases thereafter (Fig. 3). On the basis of the hypothesis that the secondary growth is dependent on the vigor of the plant, quantified as the ratio between biomass supply and demand (i.e. the sink–source ratio), the secondary demand, D2(n), is computed as in Eqn 5:

image

Figure 3. Simultaneous fitting of the dry mass of chrysanthemum leaves (main-stem and side-shoot leaves), stem (main stem and side shoots) and flowers on nine sampling dates (H0–H4) for eight calibration treatments. MS, main stem; SS, side shoot; TxLy, x°C, y% light. Vertical bars denote standard errors of the mean.

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  • image(Eqn 5)

(SC, secondary growth coefficient (g−1), an unknown parameter to be inversely estimated (Tables 1, 2)). The total plant demand, D(n), is the sum of both primary and secondary demand, given by Eqn 6:

  • image(Eqn 6)

Resolving the quadratic equation gives Eqn 7:

  • image(Eqn 7)

Multiple factors have an influence on plant demand, including the plant growth rate Q(n), the secondary growth coefficient SC, the organ sink function fOp and the delay function d (Eqns 3, 4). The secondary demand term, D2(n), introduces a feedback of biomass availability on plant demand; therefore, a greater available biomass introduces a greater plant demand.

Computing organ size and biomass

At plant age n, the biomass increment from the primary growth of an organ of age iqO,np,i) is proportional to its sink strength fOp(i) and sink–source ratio (Eqn 8). Summing up the biomass increment since appearance gives its biomass (qO,np,i; Eqn 8):

  • image(Eqn 8)

The individual leaf area is computed as the ratio between the leaf biomass and SLW. For a flower, its diameter is computed from the biomass using an empirical function (Kang et al., 2006). As a result of primary growth, the internode length (l ) is computed as a function of the pith biomass (qI,np,i) (Eqn 9), instead of from the total internode biomass, as in de Visser et al. (2006), which mixes both primary and secondary growth.

  • image(Eqn 9)

Equation 9 is obtained on the basis of an allometric relationship between the internode length and cross-sectional area (Yan et al., 2004). Two empirical parameters (aI and bI) controlling the relationship need to be identified (Table 1). The pith biomass (qI,np,i) is hard to measure, but it can be computed by the model once the sink–source parameters are estimated.

Similar to Eqn 8, the biomass for secondary growth is proportional to the secondary demand D2(n) (Eqn 5) and the sink–source ratio. This portion of biomass is allocated uniformly along the main stem, giving the biomass increment from secondary growth (Δsni) and the total biomass (Ini) of an i-aged individual main stem internode (Eqn 10):

  • image(Eqn 10)

The total biomass of an internode results from both primary and secondary growth throughout its life period. Modeling the secondary growth of chrysanthemum stems is based on a simplified version of the cambial growth model for trees (Letort et al., 2008). Summing up the individual organ biomasses of the same type gives the corresponding data from the measurement.

Unifying the time scale for different treatments

It has been observed that the leaf appearance rate is influenced by both temperature and light treatments (Table S4). To obtain comparable parameter values, the time scales must be unified for all treatments. The shortest phyllochron was that of the plants at the highest temperature and light level (T24L100), which was chosen as the common time step for the simulation of organogenesis and growth. To simulate the number of organs for other treatments using this time step, the ‘rhythm ratio’ between the leaf appearance rate of a particular treatment and that of T24L100 was computed. A sequence of zeros or ones can be generated from the rhythm ratio to imitate the leaf appearance events of a treatment (Kang et al., 2011). For instance, a rhythm ratio of 0.5 represents the production of a phytomer every other cycle.

Model calibration and validation

Unknown source and sink parameters (Table 1) were estimated by the inverse method, typically used in engineering to identify hidden model parameters from observed data (Palmer & Barnett, 2001). One calibration was conducted on the delay function (Eqn 1; parameters g1, c1, g2, c2) in order to decide when the side-shoot internodes and flowers become sinks. One way of quantifying these parameters is to record the time durations between branch appearance and elongation, and to fit these to the growth delay function (Eqn 1). However, this procedure demands careful observation and extensive tagging of each branch, and is highly susceptible to error. The inverse approach is to count the number of visible flower buds and to fit them with the corresponding model output. In the model, a flower bud is considered to be visible when it begins to expand, that is, when its age is greater than the growth delay. An evolutionary algorithm ‘particle swarm optimization (PSO)’ (He et al., 2004) was used to avoid the rounding-off effects of flower number data.

When the fitting target data are the measured biomasses of the different organ types from nine sampling dates, the parameters identified are the sink and source parameters (Table 1). Organ sink parameters for first- and second-order branches were set to be the same (PO2). The dry mass of the organs was used instead of the fresh mass as the fitting target, because of its greater physiological meaning and also greater accuracy of measurement (Louarn et al., 2007). As organs in the main stem and side shoots have different sink strengths and growth delays, they are distinguished in the fitting target. When the sink–source parameters are known, the model can compute the internode biomasses from the primary growth (qI,np,i), from which the plant height is computed. By fitting the plant height on the nine sampling dates with the corresponding model output, the two allometric parameters (aI and bI, Eqn 9) are estimated.

For model validation, a bivariate quadratic function (a1 × T2 + a2 × L2 + a3 × T + a4 × L + a5 × T × L + a6) was used to fit the relationship between a parameter y and the two environmental factors, temperature (T, °C) and light level (L, %), for the eight calibration treatments (Fig. 1a). Through interpolation, the sink–source parameters were obtained for the eight validation treatments (Fig. 1a). Using the interpolated parameters, the organ biomasses for main stem and side shoots were computed for each validation treatment to test whether GreenLab can predict well the independent dataset. A dedicated version of the open-source software GreenScilab (http://liama.ia.ac.cn/greenscilab) has been developed for simulation, model calibration and plant 3D output.

Statistical analysis

The experimental set-up was a split-plot design with temperature as the main factor and light intensity as the split factor. Analysis of variance (ANOVA) was conducted using the package Genstat 7 (VSN International Ltd., Hemel Hempstead, Hertfordshire, UK). Effects of light and temperature were dissected in a linear component, a quadratic component and deviations. Significance was tested at the 5% probability level.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Observations on phenotypic data

The plant phenotype was strongly influenced by temperature and light intensity, mainly in line with previous studies (Fig. S1). The final plant height (at H4) showed a linear decrease (< 0.001) with increasing light intensity and an optimum response to temperature (= 0.018). Total dry weight at final harvest showed a linear increase (< 0.001) with increasing light intensity, and was not influenced significantly by temperature (= 0.198). The final number of flowers and flower buds showed a linear increase with both increasing light intensity (< 0.001) and increasing temperature (< 0.001). For the final leaf area, a significant interaction (= 0.021) between light intensity and temperature was observed. At 18 or 24°C, the light intensity did not influence significantly the leaf area, whereas, at 15°C, the leaf area decreased with increasing light intensity and, at 21°C, the leaf area increased with increasing light intensity.

Regardless of the different quantitative changes in the phenotypic data, qualitatively speaking, a common pattern exists in both development and growth among the different treatments. Typically, the leaf biomass, on both the main stem and side shoots, increased from planting and stabilized soon after the emergence of the terminal flower bud (H2.1) (Fig. 3). The main-stem biomass continued to increase, although its length stabilized (Fig. 5). Side shoots and flowers increased in biomass after H2.1 (Fig. 3). This led to the question of whether it is possible to use a single model to describe the phenotypic data (mainly organ biomass), simply by taking different parameter values.

Before identifying the sink–source parameters for each treatment, values for several parameters were calculated from the data. A parameter indicating plant development is the leaf appearance rate (Table S4), which increased with light and temperature (< 0.01). The final number of leaves on the main stem (T0) generally decreased with light intensity (< 0.01) (Table S1): this was because flower evocation took place more rapidly at higher light intensity, preventing the formation of further leaves. SLW, an important parameter for the evaluation of the leaf area, was rather constant during the chrysanthemum’s life cycle (not shown). Nevertheless, it increased with light intensity (< 0.01) and decreased with temperature. The SLW of side-shoot leaves was lower than that of leaves on the main stem (< 0.01) (Tables S2, S3).

Fitting the model

By optimizing the parameters controlling the flowering sequence (c1, c2, g1, g2; Eqn 1), for each treatment, the model was fitted to the number of flowers from H3 to H4 (Fig. S2, Table S5). The global performance for all treatments is shown in Fig. 4.

image

Figure 4. Comparison between the average numbers of flowers (flower buds) per chrysanthemum plant from model and measurement, counted at H3, H3.1, H3.2 and H4, for each treatment. Linear regression gives y = 0.92x (R2 = 0.63; RMSE = 2.03). Light intensity (%): 40 (triangles); 51 (diamonds); 65 (circles); 100 (squares). Temperature (°C): 15 (open symbols); 18 (light grey symbols); 21 (dark grey symbols); 24 (black symbols).

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The dynamics of organ biomass were fitted by GreenLab for eight calibration treatments (Fig. 3). Values of seven sink–source parameters, as well as their coefficients of variation (CVs), were obtained for each treatment (Table 2). The initial biomasses were the same for all treatments (Q0 = 0.103 ± 0.01). The sink strength of the main-stem internodes was also stable across treatments (PI1 = 0.55 ± 0.03), which means that biomass allocation to the primary growth of the internode was not influenced by light or temperature. The remaining parameter values, except for the light use efficiency, increased with light intensity (Table 2). The parameter values showed no monotonic response to temperature, as was the case for the organ biomass (Fig. 3).

Using the bivariate quadratic function, the parameter values for the eight validation treatments were estimated through interpolation (one result in Fig. 5a). Using the interpolated parameter values (Table S6), GreenLab predicted the organ biomass for the eight validation treatments quite well (on average, 9% underestimation; R2 = 0.95) (Fig. 5b). Leaf biomass was best predicted. As SLW was derived from real data (Tables S2, S3), the plant leaf area was also well predicted (Fig. S3).

image

Figure 5. Parameter interpolation and prediction. (a) Parameter interpolation for secondary growth coefficient (SC) (see Table 1) using a bivariate quadratic function, y = a1 × T2 + a2 × L2 + a3 × a4 × a5 × T × a6, describing the relationship between a parameter y and temperature (T, °C) and light level (L, %). The bars represent the parameters identified from the eight calibration treatments (Fig. 1), and the grid shows the results of interpolation. (b) The measured and simulated plant-level organ dry mass at nine sampling dates for the eight validation treatments, including chrysanthemum stem (main and side-shoot stems), leaves (main-stem and side-shoot leaves) and flowers, shown with a regression line = 0.91x (R2 = 0.95). MS, main stem; SS, side shoots. 100% light = 340 μmol m−2 s−1.

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The main-stem pith biomass (from simulation) showed the same pattern over time as the main-stem leaves (Fig. S4). Two allometric parameters (Eqn 9) were estimated for each treatment (Table S5); calibration results for four combinations of lowest and highest temperatures and light levels are shown in Fig. 6(a). The effects of light and temperature on the main-stem pith biomass and length are not the same (Figs 6a, S4), which results in different allometric relationships between the pith length and biomass. Using the allometric parameters (Table S5), it can be seen that, with the same amount of biomass, the pith tends to be longer at lower light intensity and higher temperature (Fig. 6b).

image

Figure 6. Illustration of the primary growth of the chrysanthemum main stem. (a) The main-stem length at nine sampling dates (symbols) and the corresponding simulations (lines) for four treatments. (b) Simulated internode shapes from primary growth, the pith dry mass being 0.05 g: 15°C, 40% light; 15°C, 100% light; 24°C, 40% light; 24°C, 100% light; TxLy = x°C, y% light (100% light = 340 μmol m−2 s−1). Vertical bars denote standard errors of the mean.

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Using the calibrated model, the growth and development processes of the plants could be simulated for each treatment. Three-dimensional plant shapes are shown for four treatments (Fig. 7). The age, size and biomass of each individual organ are known from the model. The realistic virtual plants gave an integrated view of plant behavior in response to different light and temperature conditions (see animation in Video S1). As in real plants, a larger number of branches were initiated at higher light intensities, whereas individual flower sizes were similar to those at low light; larger flowers were produced at lower temperature and the plants were shorter.

image

Figure 7. Virtual chrysanthemum architectures at H4, under conditions (from left to right) of 15°C, 40% light; 15°C, 100% light; 24°C, 40% light; and 24°C, 100% light. Photographs of real plants are shown on the right side for reference, T15L40 and T24L100 at H3.1, T24L40 and T15L100 at H4. TxLy = x°C, y% light (100% light = 340 μmol m−2 s−1).

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The model also shows the dynamics of the source–sink ratio of the plant, Q/D (Eqns 2, 6; Fig. 8). During the LD period (before day 15), Q/D values were indifferent to temperature, but were higher at L100 than at L40. In fact, Q increased slightly with temperature, but was balanced by higher plant demand (Fig. S5). Interestingly, soon after the start of the SD period (shown by a drop in Q/D; Fig. 8), higher temperatures resulted in lower Q/D values. This was probably because of a rapid increase in organ number and corresponding plant demand (Fig. S5). Later, Q/D patterns fluctuated, because of the growth of individual flowers at irregular intervals.

image

Figure 8. Simulated kinetics of the sink–source ratio (Q/D) under four treatments: 15°C, 40% light; 15°C, 100% light; 24°C, 40% light; 24°C, 100% light (100% light = 340 μmol m−2 s−1).

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

The development of living organisms has been simulated for > 50 yr since the appearance of the digital computer. Although for animals and humans, much effort has been given to aspects of intellectual development, such as listening, speaking and understanding, for plants, most work has focused on biomass production (van Ittersum et al., 2003) and form (Prusinkiewicz & Runions, 2012). Thanks to computer graphics and simulation algorithms, visually realistic virtual plants have been obtained (Smith, 1984; Prusinkiewicz et al., 1988; de Reffye et al., 1988). They have been shown to be able to change their shapes in response to environmental variables (Měch & Prusinkiewicz, 1996; Paubicki et al., 2009), but with little physiological meaning. To develop virtual plants that can react to environmental conditions in the same way as real ones, the underlying processes of both plant development and growth must be simulated. In the present work, steps towards this goal have been made using a functional–structural model in which organ size is dependent on biomass production and partitioning, which, in turn, are dependent on environmental conditions.

Functional–structural models are usually complex, and the resulting virtual plant can produce interesting emergent properties (Eschenbach, 2005; Mathieu et al., 2009). The question to address is how to minimize the gap between the behavior of real and virtual plants in their responses to the environment. In this study, the phenotypic data included most of the commercial ‘quality’ aspects of chrysanthemums, such as the number of flowers, plant height and biomass of different organs. Moreover, the identified source–sink parameters displayed coherent trends in response to the environmental conditions. This is important in testing the predictive ability of the model, through a comparison of model output for validation treatments. The underlying hypothesis is that the validation treatments can be described by the same model, but with different parameter values. This aim was achieved by interpolation of the parameters from the calibration dataset. This approach is an important step towards the prediction of multiple phenotypes with an FSPM.

The calibration of a functional–structural model provides a deeper understanding of plant behavior in response to temperature and light. For example, the sink strength of the main-stem internode (PI1) was the same for all treatments, which suggests that the biomass allocation between internodes and leaves was not sensitive to the environment during the vegetative stage. However, the allometric growth of internodes changes with the environmental conditions (Fig. 6), which explains the conflicting responses of main-stem biomass and length. These computational speculations need to be tested by cell-level studies. Furthermore, the model helps to identify certain internal variables that are difficult to measure, such as the source to sink ratio (Q/D).

The organ–plant-level model presented here potentially builds a bridge between finer and coarser scale models. For example, the method of computing biomass production (Eqn 2) can be replaced by the classical photosynthesis model (Yin & Van Laar, 2005) which takes into account stomatal conductance, organ microclimate, global environment and their relationships to leaf nitrogen content and temperature. Similarly, internode elongation (Fig. 6) may be linked to cell-level modeling work. The final number of leaves (T0 in Fig. 2) is controlled by temperature, light and photoperiod (Adams et al., 1998); therefore, a submodel on organogenesis can be built, which links this variable with the external conditions prevailing during the sensitive period. A color model can also be built, as color is an important quality characteristic in many horticultural plants. The extension of the current organ-level research leads naturally to concepts of systems biology (Yin & Van Laar, 2005), building links from the cell level to the plant population (crop) level. Ongoing work in this laboratory includes the linking of GreenLab to a light distribution model and a biomechanics computation of the stem.

Although, in the present work, the plant plasticity shown in response to each treatment was simulated by parameter interpolation, the prediction of plant behavior under different environments (extrapolation) is still a challenging task. With so many different plant aspects changing simultaneously, an interesting question is which mechanism governs and coordinates these responses. This may lead to a controversial topic of plant intelligence (Trewavas, 2003). Nevertheless, before being trapped by this scientific question, a practical usage of current modeling work is to build the link between the energy input, linked directly to the temperature and light level, and the glasshouse output, being the quality and quantity of crop phenotypes. Such a link is of great importance for the optimal control of glasshouse climate (van Straten et al., 2000).

In conclusion, a functional–structural plant model, GreenLab, was used to describe multiple phenotypes of chrysanthemum in response to temperature and light treatments. A growth delay function was introduced to describe the basipetal flowering sequence. The model was capable of simulating different plant phenotypes through model calibration, and could predict phenotypes in other environmental conditions by parameter interpolation (validation). This model could potentially serve to bridge models of different scales, and to link greenhouse energy input to crop growth, development and architecture.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

This work was supported by the Chinese 863 plan (grant number 2012AA101906-2), the Natural Science Foundation of China (grant number 31170670) and the C. T. de Wit Graduate School for Production Ecology and Resource Conservation. Eshetu Janka is acknowledged for help with experimental implementation and data collection. The authors thank the anonymous reviewers for their constructive comments.

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  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Fig. S1 Phenotypic data of organ dry mass, main stem length, flower number and flower size; vertical bars denote standard errors of the mean.

Fig. S2 Fitting on the number of flowers (flower buds) for four treatments (T15L40, T15L100, T24L40, T24L100); vertical bars denote standard errors of the mean.

Fig. S3 Comparison of leaf area from model and measurement for four treatments (T15L40, T15L100, T24L40, T24L100).

Fig. S4 Kinetics of pith biomass for four treatments (T15L40, T15L100, T24L40, T24L100).

Fig. S5 Kinetics of biomass production and plant demand for four treatments (T15L40, T15L100, T24L40, T24L100).

Table S1 Final number of leaves (T0) on the main stem

Table S2 Specific leaf weight (g cm−2) of the main stem

Table S3 Specific leaf weight (g cm−2) of the side shoots

Table S4 Leaf appearance rate (d−1) on the main stem

Table S5 Delay parameter and allometric parameter values for four treatments

Table S6 Sink and source parameter values from interpolation

Video S1 Growth animation of virtual chrysanthemum for four treatments (T15L40, T15L100, T24L40, T24L100).

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