Our experimental results allowed us to validate the developmental scheme proposed in the Introduction for the Pollen genotype, and to quantify all the different processes involved in this developmental scheme.
The apparent complexity of the proposed scheme during the reproductive phase can be discussed under three headings. First, the rhythm of organ emergence (leaves, ramifications) or setting (pods) on a given axis is acropetal and controlled by temperature. Secondly, first-order ramifications appear synchronously with all their leaves being already present in the bud. Thirdly, flowering and pod setting starts from the main stem and sequentially propagates to ramifications in a basipetal order.
This developmental scheme, which is coherent with the literature (Leterme, 1985
; Tittonel, 1990
), was quantified. Leaf emergence dynamics were found to be bi-phasic with a 2·4-fold lower phyllochrone in the second phase than in the first phase, consistent with the results obtained by Morrison et al. (1989)
. The transition between the two phases was estimated to 610 °Cd cumulated from sowing, which corresponds to 16 January under the conditions of our experiments. However, the change might be progressive and sampling dates surrounding this date are remote in time (7 and 21 January), not sufficiently refined to get a precise estimation of the transition time. Thus, we can infer from these data merely that the change in phyllochron occurs in January, i.e. before plant bolting. Variations in phyllochron have been observed for other species (Cao and Moss, 1991
; Lemaire et al., 2008
) but with different patterns: for wheat, variation is similar to that for WOSR with a decrease of phyllochron whereas for sugar-beet the phyllochron increases. Several hypotheses are evoked in the literature to explain these bi-phasic dynamics. For instance, these variations were attributed to variations in the relationship between the air temperature used in the calculation of thermal time and the temperature of the apex during plant growth in height (Jamieson et al., 1995
). For WOSR, in our conditions, this explanation is not pertinent because change in the phyllochron occurs before plant bolting. Several studies (Tittonel, 1988
; Netzer et al., 1989
) demonstrate the role of plant ontogeny, and especially the correlation with flower initiation that occurs between November and January. This hypothesis is consistent with the phyllochron change observed in January in our conditions.
Pod setting on the main stem is six times faster than leaf emergence during the second phase. The thermal time between pod setting of two consecutive ramifications was 15 °Cd. The rhythm of pod setting for ramifications was found to be slower than for the main stem, with an increasing podochron gradient from apical to basal ramifications. Our interpretation is that pod setting on ramifications is subject to higher competition for assimilates than on the main stem because of the internode expansion and pod setting on all ramifications within a short period. Experimental results were used to compute reproductive development of rapeseed in the GreenLab model. A delay in ramification expansion and top-down propagation of flowering were implemented. This modification allowed us to correctly simulate the dynamics of reproductive development described for rapeseed. A delay function for ramification expansion has been already used in GreenLab to simulate structural development of Arabidopsis thaliana
(Christophe et al., 2008
). However, in their study delay was a function of the source–sink ratio. We did not consider this effect in our model for the sake of simplicity but this could be done in further versions of the model especially if we want to simulate the effect of variety, cultural techniques (density) or pests (for instance florivory) on plant structural development. In the same manner, a more generic function such as that proposed by Kang et al. (2006)
could be used.
Source–sink parameters were calculated by fitting model simulations to the experimental data. Positive results from the fitting are that we managed to reproduce the complete dynamics of organ development and growth of WOSR from sowing to harvest. Model adjustment to the experimental data was satisfying at the plant scale: total leaf, internode and seed biomasses were correctly simulated. The model accounted for the decrease in internode dry weight due to biomass demobilization and for the decrease in leaf dry weight due to falling off of leaves during the reproductive phase. Model adjustment at the organ scale presented some defaults showing that biomass repartition within the plant was not completely accounted for. In the example given, regarding internodes of the main stem, we observed that internode dry weight was underestimated for phytomers 19–22, i.e. during plant bolting. This can be explained either by an underestimation of internode sink strength during this period or to the fact that we did not calculate the secondary growth of the internodes in the model. In the same manner, seed dry weight were underestimated on the main stem. This has a weak influence on the total seed weight calculation because seeds of the main stem represent only 15 % of the total seed weight. The underestimation can be due either to an underestimation of seed sink strength or to an error in the model of pod development we used. Indeed, we had little information about pod development and its variation with pod position on the plant. In the same manner, the estimation of pod envelope photosynthesis remains incompletely resolved (Leterme, 1985
; Gammelvind et al., 1996
; Müller and Diepenbrock, 2006
). Further investigations should be done on these points to improve our description of pod development in the model. On the ramifications, error in organ dry weight estimation was more important for basal ramifications than for upper ramifications. This can be explained by the fact that the observed data are more variable for basal ramifications. Our interpretation is that at this position in the canopy, many factors other than source–sink relationships interact and generate crop heterogeneity. In the example given, abortion of a ramification on a neighbouring plant may induce a heterogeneity in light environment that will favour the development of basal ramifications on the studied plant. According to our observations, these events are more frequent at the base of the canopy.
The values obtained for the source–sink parameters after adjustment must be interpreted with care because they correspond to a specific experimental data set, and because they are highly sensitive to the values of measured parameters entered, for which there can be an important uncertainty. For example, regarding phenology, the transition time between the two values of the phyllochron will have an impact on the phenology and source–sink relationships. This is also the case for the duration of life and the expansion duration of leaves, pod envelopes and internodes as well as the leaf mass per area, which are all involved in calculation of the offer and of the demand, and to which the model is applicable. This is especially the case for the ramifications, for which we have very little data to estimate life duration and expansion duration of leaves and internodes. In the same manner, the rate of biomass remobilization from the internodes and the time of beginning of remobilization may influence the source–sink relationships. Internode dry weight decreased by 20 %, within the range of 15–25 % described in the literature as a function of genotypes and growing conditions (Allen and Morgan, 1975
; Mendham and Scott, 1975
; Tayo and Morgan, 1975
). However, in the model average values of these parameters were set for all internodes even if they could also vary with the number of the phytomer and the ramification.
In addition to uncertainty in parameter values, estimation errors may also be due to processes that the model does not account for. This is the case for the secondary growth mentioned above, and also for the root growth. It is possible to introduce a root compartment in the model. However, we chose not to do so for two reasons. First, we measured only the pivot-roots of sampled plants in the experiment, which form only a part of the total root system. Secondly, measurements showed a decrease in pivot-root dry weight during spring and summer of approx. 1 g (data not shown), suggesting that biomass remobilization from root compartment to aerial parts was negligible in our experiment. Thus, we consider that not taking the root compartment into account may have an influence on photosynthetic resistance but would not affect the estimation of offer in biomass and its repartition within aerial parts during the reproductive phase.
All these limits could be improved in a further version of the model. However, before modifying the model with new processes or before refining the estimation of the measured parameters, the first step will be to analyse the sensitivity of the model to identify parameters that should be precisely defined as well as their variations with organ position in the plant, and those that can be estimated by using an average value.
Values of source–sink parameters obtained after model adjustments and source–sink dynamics calculated are consistent with what we know about WOSR ecophysiology. The increase in internode sink during bolting and ramification leads to a dramatic decrease in the source–sink ratio; falling off of leaves of the main stem is compensated for by pod envelope photosynthesis until a certain point, and seed filling takes place at very low Q
. However, photosynthetic surfaces correspond to a GPS calculated by the model of approx. 3·3. This variable, equivalent to an LAI at the plant scale, can be used to estimate the efficiency of light interception during seed filling. Measurements carried out at the crop scale show that 80 % of the light is intercepted with an LAI of 2, and 90 % with an LAI of 3 (J.-M. Allirand, pers. observ.). This indicates that under the conditions of our experiment, GPS would be sufficient to intercept 80–90 % of the incident light during seed filling. However, this needs to be confirmed by further results because GPS calculated is highly dependent on variations in leaf specific area that we specified in the model, and we know that this parameter is in fact very variable (Jullien et al., 2009a
This work is a first step towards building and calibrating a structure–function model of WOSR that accounts for variations in dry weight at the organ scale. Improvements are needed concerning the secondary growth of stems, variations of pod development with position in the plant and estimation of growth parameters of the ramifications. Nevertheless, it seems to be a satisfying tool to analyse source/sink relationships within the plant. First results shed light on the important cost of the ramification and its impact on the source–sink ratio; they also confirmed the significant role of pod envelopes in biomass production during seed filling. This should be validated on other data sets recorded under different environments and/or genotypes.
Once validated for other situations, the model could be used to reproduce plant plasticity. Indeed, this model will allow us to simulate ramification or organ pruning due to damage from parasites and that induces modifications in plant architecture and biomass allocation. This is a recent challenge that functional structural plant models deal with (Robert et al., 2008
) and we intend to apply it to the interactions between insects and plants based on experimental data (Pinet et al., 2009