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Ann Bot. Apr 2011; 107(5): 793–803.
Published online Nov 22, 2010. doi:  10.1093/aob/mcq223
PMCID: PMC3077981
Simulation of fruit-set and trophic competition and optimization of yield advantages in six Capsicum cultivars using functional–structural plant modelling
Y. T. Ma,1,2,3* A. M. Wubs,2 A. Mathieu,4 E. Heuvelink,2 J. Y. Zhu,5* B. G. Hu,3 P. H. Cournède,4 and P. de Reffye6
1Key Laboratory of Plant–Soil Interactions, Ministry of Education, College of Resources and Environment, China Agricultural University, Beijing 100193, China
2Horticultural Supply Chains group, Wageningen University, PO Box 630, 6700 AP Wageningen, The Netherlands
3LIAMA, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
4Laboratory of Applied Mathematics, Ecole Centrale Paris, 92295 Antony Cedex, France
5The Institute of Vegetables and Flowers, Chinese Academy of Agricultural Sciences, Beijing 100081, China
6CIRAD, UMR AMAP, Montpellier, F-34000 France
*For correspondence. E-mail yuntao.ma/at/cau.edu.cn or ; ivf_2008/at/yahoo.com.cn
Received July 23, 2010; Revised August 18, 2010; Accepted October 14, 2010.
Background and aims
Many indeterminate plants can have wide fluctuations in the pattern of fruit-set and harvest. Fruit-set in these types of plants depends largely on the balance between source (assimilate supply) and sink strength (assimilate demand) within the plant. This study aims to evaluate the ability of functional–structural plant models to simulate different fruit-set patterns among Capsicum cultivars through source–sink relationships.
Methods
A greenhouse experiment of six Capsicum cultivars characterized with different fruit weight and fruit-set was conducted. Fruit-set patterns and potential fruit sink strength were determined through measurement. Source and sink strength of other organs were determined via the GREENLAB model, with a description of plant organ weight and dimensions according to plant topological structure established from the measured data as inputs. Parameter optimization was determined using a generalized least squares method for the entire growth cycle.
Key Results and Conclusions
Fruit sink strength differed among cultivars. Vegetative sink strength was generally lower for large-fruited cultivars than for small-fruited ones. The larger the size of the fruit, the larger variation there was in fruit-set and fruit yield. Large-fruited cultivars need a higher source–sink ratio for fruit-set, which means higher demand for assimilates. Temporal heterogeneity of fruit-set affected both number and yield of fruit. The simulation study showed that reducing heterogeneity of fruit-set was obtained by different approaches: for example, increasing source strength; decreasing vegetative sink strength, source–sink ratio for fruit-set and flower appearance rate; and harvesting individual fruits earlier before full ripeness. Simulation results showed that, when we increased source strength or decreased vegetative sink strength, fruit-set and fruit weight increased. However, no significant differences were found between large-fruited and small-fruited groups of cultivars regarding the effects of source and vegetative sink strength on fruit-set and fruit weight. When the source–sink ratio at fruit-set decreased, the number of fruit retained on the plant increased competition for assimilates with vegetative organs. Therefore, total plant and vegetative dry weights decreased, especially for large-fruited cultivars. Optimization study showed that temporal heterogeneity of fruit-set and ripening was predicted to be reduced when fruits were harvested earlier. Furthermore, there was a 20 % increase in the number of extra fruit set.
Keywords: Source–sink relationship, fruit-set pattern, functional–structural models, Capsicum annuum
Flower and fruit abortion is a yield-limiting factor in many crops (Pettigrew, 1994; Doré et al., 1998; Goldschmidt, 1999; Halbrecq et al., 2005; Bacci et al., 2006). Capsicum (pepper), like some other indeterminate glasshouse vegetable crops, shows strong fluctuations in the pattern of fruit harvest: periods of high yield alternate with periods of low yield (Heuvelink and Körner, 2001; Heuvelink et al., 2004). These fluctuations in pepper fruit-set and yield are a problem for the grower in the planning of activities throughout the production cycle as well as causing fluctuations in the price of peppers within a season.
Causes of fruit abortion can be environmental factors such as temperature stress (Guilioni et al., 1997), low light conditions (Aloni et al., 1996) and limited pollination (Berjano et al., 2006). However, even under non-limiting conditions, flower and young fruit abortion occurs in pepper plants possibly due to internal competition for assimilates (Heuvelink et al., 2004).
Simulations of fruit-set and partitioning in relation to the source–sink balance appear to be a powerful tool in several crops to study these phenomena (Bertin and Gary, 1993; Marcelis, 1994; Heuvelink, 1996). Dynamic variations in source–sink balance and different growth patterns among plants can be obtained through these modelling approaches. In Marcelis (1992), a cucumber model was developed to simulate accurately the weight of individual cucumber fruits based on a source–sink concept, in which a linear relationship was established between the number of aborted fruits and the source–sink ratio. The abortion of fruits has also been described as a function of assimilate supply and demand (source–sink ratio) for sweet pepper (Marcelis et al., 2004), tomato (Heuvelink, 1999) and cotton (Lieth et al., 1986).
However, only linking final fruit number to source–sink ratio neglects the dynamic nature of plant development and the temporal and spatial distribution of fruit-set (Marcelis et al., 2004; Wubs et al., 2009a). Functional–structural plant models (FSPMs) are successful for investigating source–sink dynamics and can simulate plant growth in three-dimensional space in response to environmental factors (de Reffye et al., 1988; Prusinkiewicz et al., 1988; Vos et al., 2009). The interaction (feedback) between assimilate production and assimilate partitioning of fruit-set and vegetative organs can then be analysed. Thus, increasing size of subsequently appearing organs can be simulated on the basis of sink–source dynamics resulting from the organogenetic process. Individual fruit size is an important aspect of fruit quality, earlier fruit harvest with similar size can be simulated and their effects on later fruit set and growth can be quantified with FSPMs.
The objective of this study was to investigate the temporal and spatial differences in fruit-set and yield patterns between pepper cultivars using experimental results with FSPMs. The research questions addressed were: (1) Does temporal heterogeneity of fruit load affect fruit and plant yield? (2) Are large-fruited cultivars more susceptible to the effects of source and vegetative sink strength on fruit-set and fruit weight than small-fruited cultivars? (3) Does earlier fruit harvest affect final fruit-set and yield among the different cultivars? If so, what is this effect for the different cultivars?
Greenhouse experiment and measurement on plants
A study of six Capsicum cultivars with different fruit weights was carried out in Wageningen, the Netherlands (52°N), from April to September in 2007. The six cultivars were: hot pepper ‘Medina’, ‘Fireflame’ and ‘Furila’, and sweet pepper ‘Gepetto’, ‘Nazar’ and ‘Funky’. Plants were pruned to two main stems, with the weak branch of each dichotomous split pruned above the first phytomer.
The experiment was set up as a randomized complete block design with three blocks and six plots per block. Each plot contained one cultivar with 20 plants in two rows. Additional plants contained in a fourth block were used for observations of fruit-set, fruit growth duration and fruit weight. Plants were grown in a Venlo-type greenhouse compartment on 600 cm3 of rockwool substrate per container. The population density was 3·8 plants m−2. Mean daily temperature over the total growth period was 21·6 ± 2·0 °C (± s.d.); mean humidity was 77 ± 10 %. There was no CO2 enrichment. The global radiation outside the greenhouse during the total growth period was 16·3 ± 5·6 MJ m−2 d−1 (mean ± s.d.).
Six plants were harvested in each destructive measurement. Measurements on two to four plants per harvest included each organ's fresh weight and organ geometry (internode length and diameter; leaf length, maximum width and leaf area; fruit length and diameter). Fresh weight of leaves, stems and fruits of each plant were measured on the remaining plants. Leaf area was measured with a LI-COR Model 3100 area meter (Lincoln, NB, USA). Leaves and stems were dried for 12 h in a ventilated oven at 105 °C, whereas fruits were dried for two cycles of 12 h at this temperature. Roots were not measured. Fruits that were completely red were harvested every Tuesday and Friday and their fresh and dry weights were measured. Then, for each harvested plant, the weight of any previously harvested fruits from that plant was added to obtain the total plant and fruit weights.
Observations on flowering and fruit-set were made six times a week on 12 plants per cultivar. Potential fruit growth rates were obtained by non-destructive measurements on potentially growing fruits as described by Marcelis and BaanHofman-Eijer (1995) and Wubs et al. (2009a). Conditions for potential fruit growth were created by tagging two flowers on a plant from which all other fruits were removed. New flowers were removed weekly. Length and diameter of the tagged fruits were measured to obtain fruit volume twice a week. On the basis of the lengths and diameters of the potentially growing fruits, their volume was calculated assuming a cylindrical fruit shape. This was subsequently converted into fresh weight, using a linear regression fitted between volume and fresh weight (R2 = 0·99). A relationship between fruit age and dry matter fraction of the fruits was then obtained to convert fruit volume into fruit dry weight (Wubs et al., 2009a). This was realized by labelling flowers at anthesis and measuring the fresh and dry weight of differently aged fruits. Detailed information of the experiment can be found in Wubs et al. (2009b).
Model description
Simulation of plant development was based on growth cycles (GCs) corresponding to the phyllochron (thermal time between the appearances of two successive leaves on the stem). Thermal time was computed as the sum of daily mean air temperatures minus a base temperature of 10 °C.
Photosynthesis for biomass production per plant was computed according to the following equation:
A mathematical equation, expression, or formula.
 Object name is mcq223eqn1.jpg
(1)
where LUE is light use efficiency (2·5 g MJ−1), k is the extinction coefficient (0·7), I is the global radiation outside the greenhouse, Y is the greenhouse transmission (0·5), f is the fraction of photosynthetically active radiation in the solar radiation (0·5). These parameter values are suggested by Heuvelink with personal discussion. LAI is leaf area index, computed from individual leaf area.
Organs receive an incremental allocation of biomass that is proportional to their sink strength. The sink strength for each type of organ is defined as a function of its age in terms of GCs:
A mathematical equation, expression, or formula.
 Object name is mcq223eqn2.jpg
(2)
Three physiological ages (pa) are used for the description of the topological structure of the plant (Barthélémy and Caraglio, 2007): PA1, PA2 and PA3 for lower stem, two main branches and secondary branches, as shown in Fig. 1. The indices for each organ type, designated by o in eqn (2) are leaf blade, b; petiole, p; internode, e; and fruit, f. Po is the sink strength associated with organ type o. The coefficient of sink strength for each organ type for different PAs was characterized by cpa,o. Therefore, the sink strength of organ type with physiological age pa is cpa,o Po. The coefficient of sink strength for all the organs of PA 1 was set to 1. fo(j) is an organ-specific beta function (Guo et al., 2006) which provides differences in sink strength between organ types. This function is characterized by two parameters ao and bo, which thus provides flexible shapes for the description of sink variation. Sink strength of each type of vegetative organ is assumed to be constant over time. Therefore, the corresponding parameter values of the beta function are set to 1 and the number of parameter values that need to be fitted decreased by six (two for each type of organ). This simplification of sink strength is consistent with Marcelis et al. (2004).
Fig. 1.
Fig. 1.
Description of the topological structure of Capsicum plants with three physiological ages. PA1, PA2 and PA3 are for lower stem, two main branches and secondary branches on the two main branches.
Simulated organ growth depends on its share in the total sink strength of the plant, D(i), and on source strength, Q(i – 1).
A mathematical equation, expression, or formula.
 Object name is mcq223eqn3.jpg
(3)
In previous versions of this model, the term ‘sink strength’ for different organ classes was relative because it was calculated relative to that of one specific organ class (the leaves), which is set to 1. However, these relative sink strengths have no units and cannot represent the organ's real ability to compete for assimilates. In this current study, measured potential fruit sink strength was used as a reference to estimate the parameters of the other type of organs. In this way, the sink strength has units (g GC−1) and represents the organ's ability to compete for assimilates in each growth cycle.
The model was parameterized by optimization procedures using botanical and morphological observations measured on sampled plants. Parameter optimization of the model uses the generalized least squares method implemented in DigiPlant software (Mathieu et al., 2008). The source–sink ratio at fruit-set is quantified by computing this ratio when each fruit appeared. On the branches (PA higher than 1), a flower will possibly appear at each node. Only a small number of potential fruiting sites are able to set a fruit at any one time, and therefore when the site sets a fruit, the ratio goes back under the threshold. Therefore, some later-produced fruiting sites never have the opportunity to set a fruit (i.e. they undergo flower abortion), as their age moves beyond the state of ‘readiness’ while the ratio remains below the threshold. In this way, spatial fruit position can be determined by source–sink ratio.
Simulations were carried out and the number of fruit-set, the variation of fruit-set (c.v.), the average fruit and plant total weight were calculated. Variation in fruit-set was based on ‘weekly’ numbers of fruits set, where ‘weekly’ fruit-set was obtained by counting the numbers of fruits set every 7 d. Sensitivity analysis of the effect of a given parameter on the simulation output (dry weight of total plant, individual fruit and vegetative organ; fruit-set etc.) was investigated by changing the model parameters one by one while keeping the default value for the remaining parameters. The effect of early fruit harvest on fruit-set and final weight was then simulated. Early fruit harvest was represented by the percentage decrease of fruit dry weight relative to the original fruit dry weight. Statistical analyses were performed in Matlab 7·0.
Experimental results
The six cultivars differed in individual fruit weight (18·5–199·2 g f. wt and 2·3–13·6 g d. wt) except for ‘Medina’ and ‘Fireflame’, which were similar for fresh and dry weight. A fruit was considered to be set if it reached the harvestable stage or if it survived for more than 10 d in small-fruited cultivars or more than 20 d in large-fruited cultivars according to the survival analysis given in Wubs et al. (2009a). The number of fruit set was smaller for large-fruited cultivars (1·1 per plant week−1) than for small-fruited ones (4·6 per plant week−1). Although the fruit-set per plant per week differed between the cultivars, the harvested fruit dry weight per plant per week was much more similar (Table 1).
Table 1.
Table 1.
Harvested fresh and dry weight of individual fruit, total harvested fruit dry weight, number of set and harvested fruits of the six Capsicum cultivars
The large-fruited cultivars (‘Gepetto’, ‘Nazar’ and ‘Funky’) showed a wave-like pattern with simultaneously timed peaks of fruit-set number in intervals of 3–6 weeks, while 2- to 3-week intervals were noted for the small-fruited cultivars (‘Medina’, ‘Fireflame’ and ‘Furila’, Fig. 2A). Fruit-set started 1 week later for the large-fruited cultivars than for the small-fruited ones (Fig. 2A). The timing and the number of harvested fruits differed between the cultivars. Fruit harvest for the large-fruited cultivars started 2 weeks later and number of harvested fruits per plant was lower in these cultivars than those of small-fruited cultivars (Fig. 2B).
Fig. 2.
Fig. 2.
Weekly number of fruit set (A) and weekly number of fruit harvest (B) for the six Capsicum cultivars. Error bars indicate s.e. (n = 12).
Fruit-set percentage was calculated as the number of fruits set divided by the number of flowers times 100. Fruit-set percentage differed between the cultivars (P < 0·001, Table 1). The higher the individual fruit weight of a cultivar, the lower the average fruit-set percentage (Table 1). Fraction of dry weight partitioned into the fruits was also significantly different among the cultivars. For small-fruited cultivars, dry matter partitioning to the fruits was about 50 %, whereas a lower percentage of dry matter was partitioned to the large fruited cultivars (35–47 %).
Model calibration
The dry weight of each organ at the last harvest stage (about 210 d after sowing) and the accumulated dry weight of each type of organ from the previous stages were taken as inputs to estimate the parameter values (Mathieu et al., 2008). A single set of parameters are shown in Table 2. The sink strength of the blade (Pb), internode (Pe) and petiole (Ps) differed between the cultivars and was in general lower for large-fruited cultivars than for small-fruited cultivars. The source–sink ratio required for fruit-set was higher (almost double) for large-fruited cultivars than for small-fruited cultivars.
Table 2.
Table 2.
Parameter values of source and sink strength for the six Capsicum cultivars
Figure 3 shows the observed and simulated accumulated vegetative, fruit and shoot (vegetative + fruit) dry weights. As each point represents a single destructive measurement, the results using phytomer information were reasonably good. Sink strength of each type of vegetative organ is simplified to be constant over time in this study and assumed to vary with time in our previous analysis (Ma et al., 2010). The corresponding relative errors in reference to the measurements are less than 7 % in this study and 6 % in our previous analysis (Ma et al., 2010). Therefore, the simplification in the current analysis did not introduce any significant weaknesses into our model.
Fig. 3.
Fig. 3.
Biomass of shoot (vegetative + fruit), vegetative organs and fruits for measured (symbols) and simulated (lines) plants for the six Capsicum cultivars.
The parameter values fitted from the destructive measurement in Table 2 were then used to simulate fruit production over the lifetime of 12 plants and compared with the observed data for each cultivar. The number of simulated fruits ranged from 74 to 142 for sweet pepper (‘Funky’, ‘Nazar’ and ‘Gepetto’) and from 311 to 439 for hot pepper (‘Furila’, ‘Medina’ and ‘Fireflame’). The comparisons between measured and simulated data of harvested individual fruit weight are shown in Fig. 4. Although the data points are scattered around the 1 : 1 line, generally the fitted parameter values were able to reproduce individual fruit growth well and the corresponding relative errors in reference to the measurements are less than 10 % for all the cultivars. Measured and simulated individual fruit weights and their corresponding position on one sampled plant for three cultivars are shown in Fig. 5.
Fig. 4.
Fig. 4.
A comparison between measured and simulated harvested individual fruit dry weight from 12 observed plants for each Capsicum cultivar. The number of simulated fruits ranged from 74 to 142 for sweet pepper and 311 to 439 for hot pepper.
Fig. 5.
Fig. 5.
Measured and simulated individual fruit weights and their corresponding position on one sampled plant for ‘Funky’, ‘Nazar’ and ‘Medina’. The named fruit rank refers to Fig. Fig.11.
Growth rates of four individual fully grown fruits for ‘Funky’, ‘Nazar’ and ‘Medina’ were shown in Fig. 6 and also their corresponding potential growth curves. Although the same potential sink strength was used for all the fruits of the same cultivars, the simulated individual fruit growth rates were different among fruits and their final dry weights were also different.
Fig. 6.
Fig. 6.
Individual fruit growth rates for ‘Funky’, ‘Nazar’ and ‘Medina’ and their corresponding potential growth curves. The named fruit rank refers to Fig. Fig.11.
Sensitivity analysis
If we reduced flower appearance rate, simulated total fruit dry weight, number of fruit-set, c.v. of fruit-set and fruit weight decreased and simulated total dry weight of vegetative organs increased significantly. However, simulated total plant dry weight was hardly affected (Table 3).
Table 3.
Table 3.
Simulated total plant dry weight, vegetative dry weight, total fruit dry weight, number of fruit-set with changes in parameter values for large-fruited cultivar ‘Funky’ and, in brackets, small-fruited cultivar ‘Medina’
If we increased the source strength or decreased the vegetative sink strength, the simulated fruit-set and fruit dry weight increased and the variation in fruit-set and fruit weight decreased. Fruits became larger as well (Table 3). Simulated total plant dry weight, vegetative dry weight and total fruit dry weight increased with increasing source strength. Decreasing vegetative sink strength reduced simulated vegetative dry weight significantly. However, no significant differences were found between ‘Funky’ and ‘Medina’ with respect to the effects of source and vegetative sink strength on fruit-set and fruit weight in our simulation study.
When we decreased the value of the source–sink ratio at fruit-set, the number of fruits retained on the plant increased and simulated total plant and vegetative dry weight decreased. The decreasing trend was more obvious for large-fruited cultivars (‘Funky’) than for small-fruited ones (‘Medina’).
The effect of early fruit harvest on later organ growth was simulated for three cultivars and is shown in Table 4. For plants with earlier harvested fruit, the number of fruit set and the dry weight of the total harvested fruit increased (P < 0·05). More than 20 % extra fruits were set, suggesting that more fruits could potentially be harvested in real plants. However, total plant dry weight was hardly affected (P = 0·86), although vegetative dry weight increased significantly (P < 0·05), due to the canopy closure. Generally the c.v. of fruit-set and fruit harvest also decreased, which means that temporal fluctuations in fruit-set and harvest decreased.
Table 4.
Table 4.
Effect of early fruit harvest on total plant dry weight, vegetative dry weight, total harvest fruit dry weight, dry matter in fruit, number of fruit set and the c.v. of fruit set per plant per week (about 210 d after sowing)
Spatial distribution of fruit
Three-dimensional representations of different periodic fruit-sets were simulated for small-fruited cultivar ‘Medina’ and large-fruited cultivar ‘Funky’ (Fig. 7). In this simulation, it was assumed that only one fruit can be set per node. Where every node bore a fruit, the plant was small. This trend was more obvious in ‘Funky’ than ‘Medina’ (plant height 1·6 m in Fig. 7A vs. 2·2 m in Fig. 7D). Where the fruit was only retained on every fifth node, the plant was taller (2·8 m for the large-fruited cultivar in Fig. 7C vs. 3·1 m for the small-fruited cultivar in Fig. 7F). The plant with fruit-set at every third node was in between, with 2·3 m for the former (Fig. 7B) and 2·9 m for the latter (Fig. 7E).
Fig. 7.
Fig. 7.
Simulation of three-dimensional architecture for small-fruited cultivar ‘Medina’ and large-fruited cultivar ‘Funky’ 210 d after sowing. Ripped fruit, growing fruit and dead leaves are characterized with red, green and yellow, (more ...)
In previous research, either one cultivar was studied to investigate the effect of source and sink strength on fruit-set (Pettigrew, 1994; Marcelis et al., 2004) or fruit-set on different cultivars was studied without any explanation of the possible causes of the observed differences (Egli and Bruening, 2006). In the present study, cultivar differences were compared with experimental and modelling approaches for the analyses of fruit-set, fruit harvest and plant yield. Temporal heterogeneity of fruit-set occurred for pepper plants with wave-like patterns over the fruiting period of the plant: the larger the fruit, the larger the c.v. of fruit-set and fruit yield for different weeks (Table 1), thus affecting fruit yield between the cultivars (Table 1, Fig. 2). Simulation showed that large-fruited cultivars need a higher source–sink ratio for fruit-set (threshold), which means higher demand for assimilates per fruit (Table 2).
The GREENLAB model was used to study the source–sink dynamics of individual organ growth and link it to fruit-set and fruit yield for different cultivars with variations of fruit size. The advantage of this model over our previous model (Wubs et al., 2009a) is that the temporal and spatial positions of fruit-set (Fig. 5) were considered and their effects on plant growth and yield were quantified. One of the results of this study compared with earlier GREENLAB models (Yan et al., 2004; Guo et al., 2006) was to introduce the measured potential fruit growth rate (Marcelis and BaanHofman-Eijer, 1995) into the GREENLAB model to represent the fruit sink strength. The sink strength of each organ then has units of (g GC−1) and represents the ability to compete for assimilates instead of a relative value compared with the leaf blade. An individual organ's absolute share of the currently available assimilates depends on the number, type and expansion status of other organs competing for the same resources.
Reduced heterogeneity of fruit-set was achieved through different ways in our simulation with changing model parameter values (Tables 3 and and4):4): increasing source strength; decreasing vegetative sink strength and source–sink ratio for fruit-set and flower appearance rate; and harvesting fruit earlier. Generally, reducing this heterogeneity, by increasing source strength and decreasing vegetative sink strength, increased fruit-set and weight for all cultivars. This result agreed well with the experimental study of Marcelis et al. (2004). When we decreased the required source–sink ratio for fruit-set, the number of fruits retained on the plant increased, and fruit competition for assimilates significantly increased. However, individual fruit dry weight decreased significantly (Table 3). The changes to source and vegetative sink strength could be achieved by plant breeding, which may be able to develop a plant with high yield and low variation of fruit-set and harvest.
In commercial production, growers benefit from less variation in fruit production leading to relatively constant prices and labour requirements for harvest. Several methods have been used to reduce or even avoid cyclical fluctuations in fruit-set and yield: different planting dates and fruit pruning (Heuvelink et al., 2004); plant growth regulators (Wien and Zhang, 1991); temperature regulators (Van Henten et al., 2006); or parthenocarpic fruit growth (Heuvelink and Körner, 2001). From our sensitivity analysis, we propose that a decrease in fruit size at harvest results in more fruit-set, and thus more potential harvest fruits and less variation of fruit production are obtained. Similar results were obtained on cucumber by Marcelis (1994). The reason for this is that when fruit was harvested earlier, a sink was removed. The total sink strength of fruits decreases and fruit-set can increase. If fruit-set increased, the variation in fruit-set decreased. This is one strategy for reducing yield fluctuation for pepper plants. However, more experiments to validate the response to these harvest criteria are needed in future studies.
In our simulation, constant specific leaf area (SLA) and leaf functioning time were used. However, studies have shown that SLA is affected by light intensity (Shipley, 2002), temperature (Nilwik, 1981) and source–sink ratio (Marcelis et al., 2004). Leaf senescence is also determined at the whole-plant level by source–sink relationships in the plant (Rajcan and Tollenaar, 1999). Therefore, quantitative relationships of SLA and leaf senescence with plant carbon balance should be established and introduced into our model in a future version.
FSPMs can simulate plant growth based on interactions among structural dynamics, external resources and the physiological processes that govern inter-organ competition with the source–sink concept, the key concept in competition theory representing the supply and demand for assimilates, respectively (Marcelis, 1994). When the total sink strength is high, due to the presence of many growing fruits, flowers and young fruits are not able to compete for assimilates with the fast-growing fruits and hence abort. The results found in the current experiment are also likely to explain differences in fruit-set between cultivars with different fruit sizes in other crops such as pumpkin, melon, tomato and cucumber. Furthermore, the effect of dynamic fruit-set pattern on plant architecture can be simulated with a three-dimensional crop architecture model. Such a model can be output for each simulation time step and used to calculate precise light interception and energy balances for a single plant and stand in a greenhouse (Buck-Sorlin et al., 2010).
ACKNOWLEDGEMENTS
The present experiments were funded by the Wellensiek fund; the graduate school PE&RC of Wageningen University financially supported A.M.W. and Y.T.M.; MOST of China (No. 2007DFC10740) and China Agricultural University Started Foundation for Research (No. 2009019) partly supported Y.T.M. We thank Dr Albert Weiss and two anonymous reviewers for their helpful comments on the manuscript. AMAP (Botany and Computational Plant Architecture) is a joint research unit that links CIRAD (UMR51), CNRS (UMR5120), INRA (UMR931), IRD (2M123) and Montpellier 2 University (UM27); see http://amap.cirad.fr/
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