F S P M 0 4 Modelling the relationships between growth and assimilates partitioning from the organ to the whole plant Jean-Louis Drouet 1, Loïc Pagès 2, Valérie Serra 2 1 UMR INRA-INAPG Environnement et Grandes Cultures, BP 01, 78850 Thiverval-Grignon, France 2Unité INRA, Plantes et Systèmes de Culture Horticoles, Domaine Saint-Paul, Site Agroparc, 84914 Avignon cedex 9, France Introduction Plant architecture determines its ability to capture resources and transport assimilates to its organs. The architecture results from developmental processes linked to assimilates partitioning among shoot and root organs, and depends on organ sink strength. Although there is considerable information on individual processes in plants at the organ level (such as photosynthesis, sugar metabolism and cell expansion), the controls which actually regulate the partitioning of assimilates at the whole plant level are still poorly understood. In this context, models are helpful for synthesising knowledge, describing and understanding complex systems such as plants, and testing hypotheses on interactive mechanisms between plant organs. Herein, we present a modelling tool, called GRAAL (GRowth Architecture and ALlocation), to test various hypotheses of plant functioning by integrating ecophysiological processes of plant development from the organ level to the plant level. This implies taking into account competition between plants for resource acquisition (carbon and nitrogen) and competition between organs for assimilates partitioning within the plant. We emphasise the benefit of object-oriented modelling methods to describe plants from several organisation levels and to study plant structure and function in relation to the environment. An example was developed for maize to simulate the interactions between the dynamics of shoot and root architecture and assimilates availability. Principle and hypotheses of the model GRAAL associates two aspects of plant functioning: (i) morphogenetic processes which determine the initiation of new organs and plant topology and are considered to be functions of growing temperature (see for the shoot system Fournier and Andrieu, 1998; see for the root system Pagès et al., 1989; Mollier, 1999) and (ii) resource acquisition and assimilates exchange between organs which modulate their extension and increase in dry mass (see Lemaire and Millard, 1999). Based on a source-sink approach (Warren-Wilson, 1972, see Lacointe et al., 2002), the model uses only one simple rule for assimilates partitioning: the general hypothesis is that the effective growth of a given organ is proportional to its potential growth rate and depends on assimilates availability, without predetermined coefficients of partitioning between organs. The time period of the model is one day. The model was developed for maize plants during the vegetative phase (until silking). Hypotheses for initiation and growth of each organ were described in an earlier paper (Drouet and Pagès, 2003). They deal with i) processes of morphogenesis (organ initiation, organ ramification, leaf growth in length and width, stem growth in length and diameter, root growth in length and diameter) which depends on environmental conditions (e.g. temperature) and carbon availability and ii) processes of assimilates partitioning (increase in dry mass for each individual organ) which depends on organ demand in carbon and overall carbon availability. For each organ, an increase in dry mass per unit area (for leaves) or per unit volume (for stems and roots) results from an increase in dry mass and growth in dimension. The model was formalised using object-oriented methods (UML approach, Unified Modelling Language; Muller, 2000) useful for integrating complex processes. It was implemented in the C programming language. The general principle (Fig. 1) is to divide the system studied (the plant) into entities (or objects) that are characterised by an identifier (e.g. lamina 10), attributes (e.g. surface) and methods allowing the system to develop (e.g. increase in dry mass). Objects are linked by specific relationships: composition (e.g. a stem consists of phytomers), generalisation (e.g. a lamina is a particular case of an organ) or simple association (e.g. a lamina is associated with air temperature). 4th International Workshop on Functional-Structural Plant Models, 7-11 june 2004 Montpellier, France Edited by C. Godin et al., pp. 115-119
116 J.-L. Drouet et al. Figure 1. Class-object diagram of GRAAL (GRowth Architectural and ALlocation) which integrates processes from the organ level to the whole plant level, example of an object of the model. Outputs of the model and evaluation of the model The model was parameterised essentially from bibliographic data (see Drouet and Pagès, 2003). It makes it possible to simulate organ and plant morphogenesis and, in association with two geometrical models (i.e. for the shoot system; Drouet, 2003; for the root system; Pagès et al., 1989), the threedimensional (3D) plant structure. The resulting function-structure model may be associated with a light model (Chelle and Andrieu, 1998) processing the exchanges between plant and environment at the organ level. The model also simulates dynamics of dry mass partitioning between individual organs within the plant and accounts for changes in dry mass partitioning according to light quantity (Fig. 2b). The hypotheses introduced into the model were evaluated from experiments done in growth chambers using an experimental set up called rhizotron (Fig. 3a) which makes it possible to monitor root growth over time (Fig. 3b). The growth of each shoot organ and a sample of root organs were recorded daily during the vegetative phase of maize for well-lit and shaded plants. Dry matter weights as well as biochemical analyses of total carbon, soluble sugars, starch, total nitrogen and nitrates were carried out to evaluate the results of simulation for assimilates partitioning. First results indicate that simulated root:shoot ratio are consistent with data reported by several authors as well as simulations using the CERES model (Fig. 4a). A detailed analysis of the intermediate variables (organ length, width, diameter, organ dry mass or dry mass per unit area or volume) is in progress (Fig. 4b,c,d) to evaluate the ability of GRAAL to simulate carbon partitioning for various environmental conditions. SESSION 3 ORAL PRESENTATIONS
Modelling the relationships between growth and assimilates partitioning from the organ to the whole plant 117 60 DAS 40 DAS 20 DAS Figure 2. Simulation of organ and plant morphogenesis (at 20, 40, 60 days after sowing, DAS) coupled with a 3D geometrical model for shoot and roots, simulation of dynamics of dry mass partitioning between organs at low (resp. high) PAR: daily average PAR within the canopy decreased exponentially as a function of time from of 800 (resp. 500) µmol m-2 s-1 at sowing to 200 (resp. 100) µmol m-2 s-1 at silking. Figure 3. Experimental set up using rhizotron, growth analysis of the root system (37 days after sowing), each colour represents root elongation during one day.
118 J.-L. Drouet et al. (c) (d) Figure 4. Evaluation of the model globally for root:shoot ratio. Use of experimental data for evaluation of processes of growth in dimension (e.g. root growth in length), (c, d) processes of increase in dry mass per unit leaf area or per unit root volume. Conclusion The specificity of GRAAL is to integrate, at the whole plant level (i.e. shoot and root systems), organ production and carbon partitioning processes described at the organ level. It associates two separate approaches: growth as an increase in surface or volume (i.e. architectural approach) and growth as an increase in dry mass. GRAAL is a useful tool for improving our understanding of processes involved in plant functioning and their regulation by environmental factors. It has produced the original following results. Global plant properties (e.g. root:shoot ratio, leaf:stem ratio) are the result of integration from the local organ properties and organ growth processes to the whole plant level, which makes it possible to analyse empirical coefficients used in classical crop models (e.g. CERES). Successive priorities between organs result from proportionality of assimilates partitioning to organ demand over time (without predetermined priorities between organs) and organ development stage. Organ dry mass per unit area or volume are output variables of the model (and not input parameters like in classical approaches). They result from processes of growth in dimension and processes of increase in dry mass. Finally, each organ is considered as a potential storage compartment (without global pool of reserves within the plant). It makes it possible to simulate growth heterogeneity (e.g. changes in the kinetics of root ramification owing to the ability of the root system to adapt the size of its meristems to carbon supply, changes in the kinetics of organ dry mass per unit area or volume, changes in the kinetics of reserves). It also makes it possible to reproduce the kinetics of carbon partitioning between organs, to point out periods of plant sensitivity to carbon availability (e.g. stem elongation) and to determine local parameters particularly sensitive from a whole plant perspective. It is likewise useful to establish hierarchy between the elementary functions which are involved in plant and stand architectural SESSION 3 ORAL PRESENTATIONS
Modelling the relationships between growth and assimilates partitioning from the organ to the whole plant 119 construction, and to quantify their variability (depending on the genotype) in relation to environmental conditions. As it is possible from the model to ask questions concerning plant functioning, architecture plasticity and assimilates partitioning, the model is also a useful guide for experiments. First simulation results are consistent with the literature and our experimental data. The latter makes it possible to evaluate each component of the model, which is in progress. This is an ascending modelling process and the analysis of a system from its objects makes a direct parallel between the structure and function of the real plant and the organisation of the model. GRAAL has been developed to be generic with concepts and structure transposable to other crops. It is therefore a good framework for discussions about processes of plant functioning between multidisciplinary partners. References Chelle M., Andrieu B., 1998. The nested radiosity model for the distribution of light within plant canopies. Ecological Modelling, 111: 75-91. Drouet J.-L., 2003. MODICA and MODANCA: modelling the three-dimensional shoot structure of graminaceous crops from two methods of plant description. Field Crops Research, 83: 215-222. Drouet J.-L., Pagès L., 2003. GRAAL: a model of GRowth, Architecture and carbon ALlocation during the vegetative phase of the whole maize plant. Model description and parameterisation. Ecological Modelling, 165: 147-173 Fournier C., Andrieu B., 1998. A 3D architectural and process-based model of maize development. Annals of Botany, 81: 233-250. Lacointe A., Isebrands J.G., Host G.E., 2002. A new way to account for the effect of source-sink spatial relationships in whole plant carbon allocation models. Canadian Journal of Forest Research, 32: 1838-1848. Lemaire G., Millard P., 1999. An ecophysiological approach to modelling resource fluxes in competing plants. Journal of Experimental Botany, 50: 15-28. allocation in greenhouse crops. A review. Acta Horticulturae, 328: 49-67. Mollier A., 1999. Croissance racinaire du maïs (Zea mays L.) sous deficience en phosphore. Étude expérimentale et modélisation. PhD. Thesis, Université Paris-Sud, Orsay. Muller P.A., 2000. Modélisation Objet avec UML. Eyrolles, Paris, 630 pp.. Pagès L., Jordan M.O., Picard, D., 1989. A simulation model of the three-dimensional architecture of the maize root system. Plant and Soil, 119: 147-154. Thornley J.H.M., 1972. A balanced quantitative model for root:shoot ratios in vegetative plants. Annals of Botany, 36: 431-441. Warren-Wilson J., 1972. Control of crop processes. In: A.R. Rees, K.E. Cockshull, D.W. Hand, R.G. Hurd (Eds.), Crop processes in controlled environment. Academic Press, New York, 7-30.