introduced in the late 1960s by Hungarian biologist Aristid Lindenmayer to describe some of the processes encountered in biology. They are particularly effective in modeling plant development and are based on the rules of ‘formal grammar’. These can provide a realistic account of the influence of the plant’s architecture, vitality and environment on its growth”.
In an L-system, a plant is represented by a sentence whose elements, or modules, themselves symbolize the components of the plant (stem, branch, flower, leaf, etc.). A set of rules governs the dynamics of these modules: they formalize biological processes and model plant transformations. The production of a new element (leaf, flower, fruit), growth or division of an existing element (stem, branch) are therefore represented by sentence equivalents of our language, which itself has its own syntactic rules (the order of words in a sentence) and is based on a given semantics (a set of words).
Figure 1.22. Weeds generated by a three-dimensional L-system program
(source: www.commons.wikimedia.org)
COMMENT ON FIGURE 1.22.– The rules implemented in the L-systems seek to represent the living: the probability of regrowth of a cut part, the amount of biomass produced, the birth and hatching of a flower, the production and ripening of a fruit. They can take into account environmental factors: amount of light received, level of sugar reserves, concentration of a hormone, etc. They make it possible to arrive at a very realistic modeling, a genuine digital plant!
“The validation of models is done by comparing them with the dynamics and patterns observed in the field. There are no specific restrictions on the use of L-systems and researchers can therefore treat any type of plant: grasses, plants, trees! Their architectures can be reproduced in a very realistic way, including at fine detail levels. By using so-called ‘stochastic approaches’, it is possible to reproduce by simulation the heterogeneity observed in nature. Different biophysical phenomena such as branch mechanics or their reorientation towards the sun or as a function of gravity can be included in these simulations”.
While they formalize the understanding of plant growth through simple mathematical rules, L-system-based models allow different types of applications such as yield prediction. The challenge in this case is to have models interact at different scales in order to obtain an overview: from plants or planting groups, to the plot and the entire farm. This is a vast field of research in digital agriculture. Modeling by L-systems already contributes to the evaluation of certain techniques, such as agro-ecology, which are receiving increasing interest due to the growing awareness of ecological issues and the need to preserve the emerald forest?
NOTE.– Growing plants “in-silico” with L-systems.
The typology of a plant, the phenotype, results from the expression of its genetic heritage (its genotype), and its interactions with the characteristics of the environment in which it develops (its environment). These interactions largely determine biomass production: reconstituting the phenotype of plants is therefore a key-factor in calculating the yield of a production.
Artificial intelligence techniques based on deep learning from imaging data can contribute to this objective by automatically and quickly performing repetitive tasks such as counting sheets. In the learning phase, it is necessary to have a database large enough to make the algorithms efficient, which is not always the case in agronomy! The databases that can be used are generally limited and campaigns to enrich them are very expensive. One solution proposed by some researchers is to generate digital plants by simulation: the variety of forms produced thus enriches existing databases at low cost (Figure 1.23).
Figure 1.23. The virtual plants (left), obtained in silico by means of L-systems, have similar characteristics to the real plants (right), obtained in vitro
COMMENT ON FIGURE 1.23.– The efficiency of the L-systems is such that researchers show that the simulations are able to produce a variability in the characteristics of synthetic plants close to that of real plants – otherwise the data used by the learning algorithms would not be of good quality. The researchers even demonstrate that the latter learn, with similar effectiveness, either from real data or from data produced by synthetic models [UBB 18].
Let us conclude this chapter with the understanding that, in general, agricultural modeling addresses three scientific issues:
– understand and predict plant growth processes;
– assess the impact of agricultural practices in ecological and economic terms;
– informing the policies of decision makers and farmers’ choices.
They are thus becoming an essential tool for agricultural research, meeting the vital needs of humanity in the 21st Century: feeding populations and preserving their environment.
1 1 Available at: https://www6.inra.fr/record.
2 2 Data available at: http://www.fao.org/forestry.
3 3 Available at: http://www.theplantlist.org/.
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