## Introduction

This article attempts to describe the state of the art in building efficient dynamical plant growth and architecture models that contain the basic knowledge coming from botany, ecophysiology, agronomy, applied mathematics, and computer science.

The world of flowering plants is incredibly diverse with over 250 000-300 000 species on Earth. Even inside a family (e.g., Dilleniaceae) one can find trees, shrubs, creepers, and herbs. Despite this diversity, plant architecture is always made of the same kind of basic botanical elements, namely leaves, stems, fruits, roots, etc., whose functions are always the same as sources and sinks for biomass production and partitioning. Important studies to model and simulate the underlying complex mechanisms of plant morphology and physiology have been carried out at the end of the twentieth century in two opposite directions. One tries to simulate with high precision the knowledge of plant physiology taking into consideration plant structure and even gene action; meanwhile, others try to simplify the upper level of the scale (i.e., the level of plant architecture) and find the emergent properties of the system that allows building mathematical plant growth models. To understand such a complex system as plant growth and development, knowledge about botany (plant structure organization) and physiology (action of environmental parameters, water transport, respiration, and photosynthesis) is not sufficient. Statistical correlations or empirical functions between variables such as temperature, light, or measurements such as plant height or plant weight are also not sufficient mathematically speaking, because these measures are themselves the result of a complex functioning that involves the hidden parameters of an underlying mathematical model that is to be built.

Identifying the relevant parameters that bridge together the various disciplines results in 'translating the reality into a mathematical model' that will allow plant behavior study. Mathematical modeling needs to simplify a lot of the complexity of the real world and this is achieved by a dialog between biologists, who have the qualitative knowledge, and mathematicians, who handle quantitative relationships through equations. Results will be more or less accurate according to the validity of the model, and the minimum number of parameters that fulfill the research work should give the best model, since the powerful tools of applied mathematics cannot run properly with too many (overparametrized models).

Computing the numerical values of the hidden parameters from measurements on real plant architecture is what is called an inverse problem. Enginery applications for agriculture can be worked out only if this problem is solved. Otherwise the model remains at a speculative stage. Plant architecture results from both meristem functioning (organogenesis) and photosynthesis (biomass production and partitioning) and it may be assumed that plant architectural development concerns the growth process trajectory keeping at any time in its memory the underlying structure. Thus the hope is to trace back the growth process from measurements on plant architecture in given environmental conditions, and furthermore to control the plant behavior from acting on the environmental parameters. The research work may be considered as fulfilled if it is possible to simulate the growth process with a minimum number of parameters and to build step by step the plant architecture with all the organs in the right place inside the plant structure and with the correct biomass content. Such important problems as optimizing the use of resources (water, fertilizers in fields, temperature and light in glasshouses) and cultivation systems (planting density, pruning) can then be successfully solved.

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