Читать книгу Numerical Simulation, An Art of Prediction, Volume 2 - Jean-François Sigrist - Страница 19

Vegetation is one of the crucial resources for humanity, providing it with food and energy – and in some cases a place to live. Satellite observations help to consolidate plant occupancy data on the planet’s surface (Figure 1.19). They enable scientists to understand the influence of natural cycles on vegetation (such as droughts or epidemics) or that of human activities (such as deforestation or CO₂ emissions).

Figure 1.19. Vegetation map obtained from satellite observations (source: NASA/www.nasa.gouv). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 1.19.– The shades of green on the map correspond to values ranging from 0.0 to 1.0, in arbitrary units. Values close to 1.0 (dark green) indicate the presence of abundant vegetation, as in the Amazon rainforest. Values close to 0.0 (beige) indicate areas with little vegetation, such as the oceans or the Arctic continent. Forests cover 30% of the world’s land area, equivalent to just under 40 million km2, while treeless vegetation (tundra, savannah, temperate grasslands) occupies about the same area.

In 1985, English filmmaker John Boorman recounted in The Esmerald Forest how a world disappears, the world of the Amazon rainforest tribes [BOO 85]. The son of an engineer who oversees the construction of a gigantic dam is taken from his parents by a tribe of Forest Men. As the dam’s construction was completed, the father and son found themselves in circumstances that led them both to confront progress and humanity. The dam will eventually give way under the waters of a river doped by torrential rain, engulfed by the songs of frogs calling on the forces of nature. The engineer who wanted to destroy his work to protect the future of his son and that of a tribe wishing to live in peace will not have this power.

The Amazon rainforest is still one of the largest plant communities on the planet today. According to FAO² estimates, it is now disappearing at an average rate of 25,000 km² per year (equivalent to half the size of Austria) to make way for new crops. At this rate, it will have completely disappeared by the first half of the next century. It pays the highest price for the consequences of human activities: more than half of the world’s deforestation. The evolution of vegetation as a whole is of particular concern because of its dual importance: it supports a large part of biodiversity and contributes to the absorption of atmospheric CO₂. Analyzing satellite observation data, NASA researchers show that in just under 20 years, the planet has re-vegetated with an area equivalent to that of the Amazon, with India and China being among the main contributors to this trend. The observed vegetation corresponds, on the one hand, to the growth of new forests, contributing to the sequestration of carbon from the atmosphere, and, on the other hand, to an extension of agricultural areas, whose natural carbon storage balance is generally neutral [CHE 19].

Understanding the growth mechanisms of species continues to occupy scientists. In the first half of the 20th Century, the British biologist d’Arcy Thompson (1881–1946) became interested in the shape and growth of living organisms, publishing his thoughts in an exciting collection [THO 61]. He looks for invariants and universal principles that govern the evolution of life – for example, fractal structures or particular sequences (Figure 1.20).

Figure 1.20. The Fibonacci spiral: a model (too simple?) to explain plant growth

(source: www.123rf)

COMMENT ON FIGURE 1.20.– Leonardo Fibonacci (1170–1250) was a 13th Century Italian mathematician. The Italy of his time was a region formed by scatterings of merchant cities in strong competition (Venice, Pisa, Genoa). Trade activities needed numbers and calculation to support their economic development. The mathematician developed algebraic methods to contribute to this. In particular, he drew inspiration from Indian and Arab mathematics, while Roman numerals, still widely used in Europe, forced calculation in a rigid numbering system that the invention of zero helped to loosen. The sequence that bears his name is defined from two values, then each term is calculated as the sum of the two previous ones. Thus, starting from 1 and 1, the terms are 2, 3, 5, 8, 13, 21, etc. This sequence, which has properties of interest to mathematicians, is found in some natural growth mechanisms. The Fibonacci sequence hides the famous golden number Discovered in the 3rd Century BC by Greek mathematicians, Φ seems to be present behind the architectural choices made in antiquity, for example in the construction of the Parthenon in Greece. “Let no one ignorant of geometry enter” is the motto of the Academy, founded in Athens by Plato in the 4th Century BC. The Platonic school makes mathematics one of the instruments of the search for truth. To this is added that of harmony, whose golden number is the hyphen. Φ is the Greek letter traditionally used to designate it and it also refers to philosophy. For very different reasons, the golden number fascinates human beings who sometimes tend to find it everywhere even where it is not [LIV 02].

Created at the initiative of the Royal Botanical Garden of Edinburgh, the website The Plant List3 aims to provide an exhaustive list of the various plant species: there are currently more than 1 million. Nature is characterized by a great variability of shapes (Figure 1.21): how can we accurately model the development of such diverse plants?

Figure 1.21. Variety of leaf shapes

(source: www.123rf/Liliia Khuzhakhmetova)

Since the late 1960s, scientists have been using a formalism that is particularly well suited to modeling plant growth. It finds its roots not in the field of mathematics but in that of grammar! Frédéric Boudon, a researcher at CIRAD*, is an expert in these tools, the so-called “L-systems”:

“The L-systems were 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/.