Rhythms and alternating patterns in plants as emergent properties of a model of interaction between development and functioning.
OBJECTIVE
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.


METHODS
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.


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.
Mathieu
Amélie
A
Ecole Centrale Paris, Laboratoire de Mathématiques Appliquées aux Systèmes, Grande Voie des Vignes, 92295 Chatenay Malabry, France. mathieu@mas.ecp.fr
Cournède
Paul-Henry
PH
Barthélémy
Daniel
D
de Reffye
Philippe
P
D003198:Computer Simulation; D005638:Fruit / Q000254:growth & development / Q000502:physiology; D008962:Models, Theoretical; D009024:Morphogenesis; D063245:Plant Development; D013997:Time Factors
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