Winter oilseed rape (Brassica napus L.) is an important oilseed and fodder crop worldwide (Zhang and Wu, 2007), not only because of its high oil yield (between 40 and 50% of dry mass of seeds), but also because the oil has a high nutritious value, due to the presence of different kinds of aliphatic acids and vitamins (Yang and Tu, 2003). This makes rapeseed oil a very important and healthy ingredient for human nutrition, with a long history as edible oil in Asia and Europe. In addition, if the content of erucic acid is higher than 50%, the seeds can be used as raw ingredient for the production of lubricating oil and suspending agents (Yang and Tu, 2003). Sowing of rapeseed crop mostly starts in September or October at latitudes of 30° in Eastern China. Undergoing vernalization throughout winter, rapeseed blooms in April and harvest in May next year.

A number of climatic and nutritional factors are known to influence both rates and daily integrals of photosynthesis and respiration. Temperature is known to be of utmost importance for photosynthesis and respiration rate (Marcelis, 1996). High temperature leads to a decrease in carboxylation rate as it decreases the specificity of Rubisco for CO₂ (Lambers et al., 2008), whereas low temperature affects the sucrose metabolism, which leads to accumulation of phosphorylated intermediates and ultimately reduces inorganic phosphates. Finally, inhibition occurs in ATP and photosynthetic accumulation (Chawade, 2011). Besides those effects on photosynthesis, temperature induces some modifications in the morphology of rapeseed. The stems become thinner and the leaves turn thicker under high temperature (Qaderi et al., 2006, 2010). These effects on rapeseed growth (as the decrease of total leaf area) will lead to differences in photosynthesis. Fresh and dry masses have been considered as being positively correlated with temperature during the seedling stage (Rapacz, 1998). Temperature is thus an important factor for photosynthesis rate and consequently growth of rapeseed plants. In order to avoid a potentially considerable reduction in production, it is therefore, important to be able to predict accurately the phenological stage and the topological and geometrical structure of the plant during this period, in order to better assess recovery and survival rates of the crop, which are pivotal for ultimate yield.

To accelerate breeding and optimize the production of rapeseed, the use of crop models as a tool in rapeseed research has been proposed by a number of researchers (Diepenbrock, 2000; Fourcaud et al., 2008; Xu et al., 2011; Robertson and Lilley, 2016). Models for oilseed rape production have been diversified in objectives and methodology. In some classic crop models, the plant canopy was divided into different layers, where the main processes of biomass production were computed for each layer separately and then integrated for the whole crop (Tang et al., 2007, 2009; da Luz et al., 2012). Some models considered the 3D structure and selected functions of the whole plant (Groer et al., 2007). Other models mainly focused on the accurate description of the rates of photosynthesis, respiration, and biomass production at the leaf and whole-plant scale, with local climate parameters as input (Paul and Driscoll, 1997; Müller and Diepenbrock, 2006; Deligios et al., 2013).

In the present study, we investigated the growth and development of young winter oilseed rape plants under different temperature treatments, with a special consideration of the morphology of leaves of different ranks. On the basis of the data established in this study a functional–structural plant model (FSPM) for young rapeseed plants was devised, representing leaf extension kinetics; data about leaf photosynthesis, respiration, biomass production and allocation at the organ and whole-plant scale were obtained from the literature. FSPM being a modeling paradigm that allows not only an instructive visualization of growth and development, but also the integration of heterogeneous datasets in a common scheme, the model we created already helped us to better interpret the correlated datasets of our experiments, apart from the conclusions drawn based on the statistical analyses. However, in this model, we were only able to explore leaf development of young plants. In a further extension of the model, we will eventually use it as a visual decision-support tool for rapeseed breeding and production utilization.

The present model is based on a previous rapeseed model by Groer et al. (2007) and the general sink-source-based FSPM-prototype (FSPM-P; prototype model) by Henke et al. (2016). The FSPM-P is a general model based on the 3D structure of the plant including the physiological characteristics (photosynthesis, maintenance respiration, growth respiration, and plant organ biomass accumulation). The FSPM-P being not designed for a specific crop, it can be adapted in principle to any crop plant with C3 photosynthesis. Its main advantage is that it is easy to parameterize, use, and extend (Henke et al., 2016). In the present study, we discuss how this model could be used to predict the kinetics of storage of carbon reserves (starch) during autumn and winter that might be the key to successful reestablishment of the crop in spring.

The fitted model parameters for the first five leaf blade ranks and temperature treatments are given in Table 1. The first two true leaves (except cotyledons) of oilseed rape were usually small, and preformed in the seed. As the first leaf was already present or fully extended by the time of the start of the experiment, the fit of timing (x₀) and slope (b) parameter of the logistic equation was not very good. A true sigmoid curve was only fitted for leaf ranks of three and above (Figure 1). Furthermore, at low temperature leaves were smaller and grew more slowly, also leaf appearance rate was slower, leading to fewer observed leaves within the observation period (Figure 1).

Temperature is a major factor for plant growth rate and daily photosynthesis (Rapacz et al., 2001, 2003; Qaderi et al., 2006, 2010, 2012; Kromdijk and Long, 2016; Zhang et al., 2016). Furthermore, it has also an influence on oil quality (Baux et al., 2008, 2013). In the present study, the effect of temperature on leaf expansion was investigated in oilseed rape. Width-length ratio (WLR) at different temperatures exhibited significant differences only at high temperature (WLR = 0.849). In the M and L treatments PBR of the upper leaves was small, which means that the petiole was shorter relative to the blade. Overall, the decrease of PBR with rank will result in a conical leaf arrangement (with upper leaf blades being less distant from the main stem), which could be a plant-level strategy to increase light penetration to the lower leaves. More experimental work will be required to determine the exact reasons for the observed patterns. The PBR is one factor, besides WLR, determining leaf shape. Its change along the main stem can be interpreted in terms of developmental progress from the vegetative to the reproductive stage, with lower-ranked leaves being, in principle, more “vegetative”. The increase in total leaf area and dry mass was lowest under the low temperature treatment. In a study similar to the present one leaf area decreased while leaf blade thickness increased when rapeseed plants were exposed to cold temperatures (Stefanowska et al., 1999). Furthermore, there were no significant differences in leaf area between medium and high temperature at the beginning of juvenile stage. However, when treatment duration was long enough (>6 or >10 days, Table 6), leaf area and dry mass at medium temperature were increasing faster than at high temperature. Thus, it can be concluded tentatively that an accumulated temperature increment of 75°Cd is necessary as a phyllochron for the formation of a leaf on the main stem.

Leaf mass per area (LMA) was correlated with environmental and topological factors, such as temperature and leaf rank. LMA was positively correlated with temperature; similar research was also found in other studies (Gausman et al., 1971; Qaderi et al., 2006; Jullien et al., 2009). In the present study, the average LMA under the H, M, and L treatments were 0.01328 kg m^-2, 0.01766 kg m^-2, and 0.01639 kg m^-2, respectively. There was a significant difference between the H treatment and the other two treatments. However, M and L did not differ significantly from each other. A more specific experimental study would be required to obtain a better idea concerning this phenomenon. LMA of upper leaves was higher than that of lower leaves, confirming the findings of Gausman et al. (1971). This effect was not significant for the three or four adjacent ranks in each treatment (Figure 4). The absence of a significant difference at the L treatment could be explained by the fact that only four leaves per main stem were formed in total.

Plant architecture is of major agronomic importance for the adaptability of a plant for cultivation, and to predict how the plant grows under different environments (Reinhardt and Kuhlemeier, 2002). The impact of plant architecture and morphology on the light climate within the plant canopy and the resulting amount of light locally incident, absorbed by a given assimilating surface, and finally used for photosynthesis plays a major role in plant development as it determines local assimilate availability and thus source strength (Evers et al., 2006). To investigate this complex context and the underlying relationships, we implemented a FSPM as an extension of the FSPM-P model devised by Henke et al. (2016). This model, apart from having a generic description of the sink behavior of young leaves and internodes, also contains provisions to simulate generically photosynthesis on a per-leaf basis, using local light and temperature as an input. Employing a prototype as a departure point permitted us to obtain a usable model relatively rapidly, as the only major steps to be done were parameterization and, eventually, the writing of simple extensions of rules to accommodate crop-specific processes that were not covered by the general model. The FSPM-P is written in the language XL which is included in the GroIMP platform (Kniemeyer et al., 2007; Kniemeyer, 2008), with specialized tools for plant modeling. GroIMP provides an adequate radiation model that can compute the amount of light absorbed by each plant organ (more generally, objects in a simulated scene; Hemmerling et al., 2008). For more advanced studies of the impact of light quality (e.g., red to far-red ratio) on growth processes, spectral light can be simulated (Henke et al., 2016). The new light model makes use of parallel processing on a graphical processing unit of the computer, thereby accelerating computation enormously (van Antwerpen et al., 2011).

In recent years, models of the main agricultural crops (de Carvalho Lopes and Steidle Neto, 2011) have been developed and their usefulness and importance has been increasingly recognized by the agronomical community (Vos et al., 2010). The most striking advantage of a modeling approach is the time that can be saved when employing a model to predict yield or quality features of a new crop, compared with traditional methods of experimentation and breeding in the field. At the same time, the vivid and realistic visualization of plant development in the case of a 3D model renders teaching much easier and more attractive (Fourcaud et al., 2008). Apart from that, virtual plants or FSPMs, usually integrate a lot of information about the morphology of the crop in question as well as about the nature and spatiotemporal dynamics of physical and biological processes (Buck-Sorlin, 2013). Thus, such models that are capable of integrating the dynamics of architectural development with the rate of photosynthesis and respiration are an excellent means to estimate the production of future biomass of a plant (Godin and Sinoquet, 2005).

In the field, a rapeseed plant stops growth below 5°C; whereas photosynthesis usually continues well below this threshold temperature for growth (Tang et al., 2007, 2009). This leads to products of photosynthesis accumulating in the plant (as starch), where the extent of accumulation will be a function of photosynthetically active leaf area as well as of the accumulated temperature favorable for photosynthesis (below the threshold for growth yet above the threshold for photosynthesis and above that leading to frost damage). Consequently, regrowth of the plant in spring, as temperatures rise again to favorable values for growth, will be the more rapid the more reserves the plant has been able to accumulate during winter. In a future version of the model, we will link the rate of regrowth of rapeseed in spring with the amount of stored starch during the winter (Martre et al., 2011). In doing so, an existing photosynthesis module [based on the LEAFC3 model by Nikolov et al. (1995)] will be reparameterized from the literature (Leng et al., 2002; Liu et al., 2003; Ma et al., 2009) in order to obtain more accurate values for parameters influencing the rates of photosynthesis and respiration of the young rapeseed. It is possible to compute the total dry mass from an estimate of the amount of carbon fixed by photosynthesis and the amount of carbon lost through maintenance and growth respiration.

The primary aim of the present study was to build a model of the young stages of rapeseed in the leading commercial cultivar (Brassica napus L. cv. ZS 758). In order to build a robust and representative model in the future we will need to consider an experimental setup consisting of more plants and several, contrasting rapeseed cultivars. In addition, as a further step, the current model will be extended to also represent further development from regrowth in spring to maturity (early summer). If successfully parameterized and calibrated such a model could be used to predict harvestable yield, as a function of architectural development at the seedling and juvenile stages. This could in consequence allow the use of such a model as a tool to optimize yield by proposing leaf architecture ideotypes optimized for a given temperature regime in autumn and winter, respectively, an optimal climate dynamics for a given cultivar.

The present study yielded new knowledge about the influence of temperature on leaf expansion in the early development of oilseed rape by combination of observed and literature-derived data. This combination is feasible and useful, as a complete measured dataset is almost never available. Furthermore, embedding of the datasets into an FSPM delivered interesting insights into the interactions of organogenetic and morphogenetic processes with temperature and into source–sink interactions in particular.

GB-S and WZ conceived the study. TT, LW, MH, and BA conducted experiments and analyzed data. MH and GB-S adapted the model. TT, MH, GB-S, and WZ wrote and revised the manuscript. All authors read and approved the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.