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1.  Computing Competition for Light in the GREENLAB Model of Plant Growth: A Contribution to the Study of the Effects of Density on Resource Acquisition and Architectural Development 
Annals of Botany  2007;101(8):1207-1219.
Background and Aims
The dynamical system of plant growth GREENLAB was originally developed for individual plants, without explicitly taking into account interplant competition for light. Inspired by the competition models developed in the context of forest science for mono-specific stands, we propose to adapt the method of crown projection onto the x–y plane to GREENLAB, in order to study the effects of density on resource acquisition and on architectural development.
The empirical production equation of GREENLAB is extrapolated to stands by computing the exposed photosynthetic foliage area of each plant. The computation is based on the combination of Poisson models of leaf distribution for all the neighbouring plants whose crown projection surfaces overlap. To study the effects of density on architectural development, we link the proposed competition model to the model of interaction between functional growth and structural development introduced by Mathieu (2006, PhD Thesis, Ecole Centrale de Paris, France).
Key Results and Conclusions
The model is applied to mono-specific field crops and forest stands. For high-density crops at full cover, the model is shown to be equivalent to the classical equation of field crop production ( Howell and Musick, 1985, in Les besoins en eau des cultures; Paris: INRA Editions). However, our method is more accurate at the early stages of growth (before cover) or in the case of intermediate densities. It may potentially account for local effects, such as uneven spacing, variation in the time of plant emergence or variation in seed biomass. The application of the model to trees illustrates the expression of plant plasticity in response to competition for light. Density strongly impacts on tree architectural development through interactions with the source–sink balances during growth. The effects of density on tree height and radial growth that are commonly observed in real stands appear as emerging properties of the model.
PMCID: PMC2710279  PMID: 18037666
Functional–structural plant models; GREENLAB; competition for light; Beer–Lambert Law; plant plasticity; dynamical system
2.  AmapSim: A Structural Whole-plant Simulator Based on Botanical Knowledge and Designed to Host External Functional Models 
Annals of Botany  2007;101(8):1125-1138.
Background and Aims
AmapSim is a tool that implements a structural plant growth model based on a botanical theory and simulates plant morphogenesis to produce accurate, complex and detailed plant architectures. This software is the result of more than a decade of research and development devoted to plant architecture. New advances in the software development have yielded plug-in external functions that open up the simulator to functional processes.
The simulation of plant topology is based on the growth of a set of virtual buds whose activity is modelled using stochastic processes. The geometry of the resulting axes is modelled by simple descriptive functions. The potential growth of each bud is represented by means of a numerical value called physiological age, which controls the value for each parameter in the model. The set of possible values for physiological ages is called the reference axis. In order to mimic morphological and architectural metamorphosis, the value allocated for the physiological age of buds evolves along this reference axis according to an oriented finite state automaton whose occupation and transition law follows a semi-Markovian function.
Key Results
Simulations were performed on tomato plants to demostrate how the AmapSim simulator can interface external modules, e.g. a GREENLAB growth model and a radiosity model.
The algorithmic ability provided by AmapSim, e.g. the reference axis, enables unified control to be exercised over plant development parameter values, depending on the biological process target: how to affect the local pertinent process, i.e. the pertinent parameter(s), while keeping the rest unchanged. This opening up to external functions also offers a broadened field of applications and thus allows feedback between plant growth and the physical environment.
PMCID: PMC2710271  PMID: 17766310
Simulation software; physiological age; reference axis; FSPM; plant growth modelling; plant architecture
3.  Rhythms and Alternating Patterns in Plants as Emergent Properties of a Model of Interaction between Development and Functioning 
Annals of Botany  2007;101(8):1233-1242.
Background and Aims
To model plasticity of plants in their environment, a new version of the functional–structural model GREENLAB has been developed with full interactions between architecture and functioning. Emergent properties of this model were revealed by simulations, in particular the automatic generation of rhythms in plant development. Such behaviour can be observed in natural phenomena such as the appearance of fruit (cucumber or capsicum plants, for example) or branch formation in trees.
In the model, a single variable, the source–sink ratio controls different events in plant architecture. In particular, the number of fruits and branch formation are determined as increasing functions of this ratio. For some sets of well-chosen parameters of the model, the dynamical evolution of the ratio during plant growth generates rhythms.
Key Results and Conclusions
Cyclic patterns in branch formation or fruit appearance emerge without being forced by the model. The model is based on the theory of discrete dynamical systems. The mathematical formalism helps us to explain rhythm generation and to control the behaviour of the system. Rhythms can appear during both the exponential and stabilized phases of growth, but the causes are different as shown by an analytical study of the system. Simulated plant behaviours are very close to those observed on real plants. With a small number of parameters, the model gives very interesting results from a qualitative point of view. It will soon be subjected to experimental data to estimate the model parameters.
PMCID: PMC2710268  PMID: 17715304
Rhythms; plasticity; plant growth model; GREENLAB; interactions; branching system; fructification; emergent properties
4.  Plant Architecture: A Dynamic, Multilevel and Comprehensive Approach to Plant Form, Structure and Ontogeny 
Annals of Botany  2007;99(3):375-407.
Background and Aims
The architecture of a plant depends on the nature and relative arrangement of each of its parts; it is, at any given time, the expression of an equilibrium between endogenous growth processes and exogenous constraints exerted by the environment. The aim of architectural analysis is, by means of observation and sometimes experimentation, to identify and understand these endogenous processes and to separate them from the plasticity of their expression resulting from external influences.
Using the identification of several morphological criteria and considering the plant as a whole, from germination to death, architectural analysis is essentially a detailed, multilevel, comprehensive and dynamic approach to plant development. Despite their recent origin, architectural concepts and analysis methods provide a powerful tool for studying plant form and ontogeny. Completed by precise morphological observations and appropriated quantitative methods of analysis, recent researches in this field have greatly increased our understanding of plant structure and development and have led to the establishment of a real conceptual and methodological framework for plant form and structure analysis and representation. This paper is a summarized update of current knowledge on plant architecture and morphology; its implication and possible role in various aspects of modern plant biology is also discussed.
PMCID: PMC2802949  PMID: 17218346
Plant morphology; plant architecture; level of organization; growth; branching; differentiation; morphogenetic gradients; physiological age; meristem; annual shoot; phenotypic plasticity; ontogeny; phase change

Results 1-4 (4)