Alain Pavé

Monod's bacterial growth model revisited

An attempt to justify Monods bacterial growth model is presented. The justification is based on a mechanistic approach to growth which leads to a differential equation with delay and then to Monods model. An unexpected increase of parameter K s with μ m is predicted by the theory. A survey of literature shows that this effect is present in a large majority of published data.

Environnement : modélisation et modèles pour comprendre, agir ou décider dans un contexte interdisciplinaire

Abstract If the physical sciences were the cradle of modelling approaches, now almost all disciplines are concerned by this methodology. First based on mathematical language, the modelling formalisms become more and more diverse. Computer sciences contribute widely to the extension of the methodology at two levels : the first to make easier the use of mathematical models, the second to develop new formalisms, such as cellular automata or neural networks. The fields of basic and applied research on the environment and related technological developments give good examples of applications of this methodology, from global modelling at the planet level, for example for the study of climate changes, to local and specialised models, for example in population dynamics or water transfers in soils. Models are also developed to reach various goals : in basic research, to understand how environmental systems work, in technological development, to design adapted techniques, and in decision making process, as an argument, among others, to elaborate a decision. The recent expansion of modelling, to almost all disciplines implied in environmental research, makes it also a tool in interdisciplinary dialog. The model becomes a link between disciplines, for example between natural and social sciences, by combining dynamics of ecological and social systems. But the use of models is not exempt of hazards. Used in bad conditions, off its limits of validity, or running with a deficient simulator, it may lead to incorrect results. It may also be a screen to hide an insufficient knowledge. It such cases, it can be a wrong decisive argument in decision process or to lead to a bad technical device or protocol. Anyway, built and used carefully it is a precious and efficient tool. So, the state of the art and actual methodological problems and applications in environmental basic and technical research are presented. The foreseeable advances and endeavours are also envisaged. The text is essentially illustrated by examples developed by scientists and engineers of the Cemagref. Finally, the environment is an example of a complex system. Modelling is a good tool for complexity analysis and methodological advances in environmental research would be useful for other systems which are qualified “complex”, and then have a larger range of application than studies on environment.

Dynamics of macromolecular populations: a mathematical model of the quantitative changes of RNA in the silkgland during the last larval instar

The quantitative changes of RNA in the silkgland of Bombyx mori have been studied during the last larval instar by using a mathematical model (Volterra-Kostitzin model). This model can be associated with a global mechanism including synthesis and degradative processes. The numerical and statistical methods used for model analysis are described in an appendix. Thus we have compared the accumulation of total RNA (essentially ribosomal) after a treatment (juvenile hormone) and between several strains. The importance of the degradative factor is denoted to explain the observed differences, whereas the synthesis rates remain relatively stable. The last observation may lead us to an interpretation of the molecular effect of a selection to increase silk production : rather than an increase of the productivity of cellular machinery, the degradative process has been limited.

An approach to computer-aided design: a tool for mathematical modelling in biology and ecology.

Abstract A matricial formulation of like chemical systems is proposed. This representation permits us to draw up easily a generation algorithm of rate equation, and reversively an algorithm which gives, if it is possible, a descriptive chemical system from a set of differential equations. The problem of numerical simulation is also studied. All these levels have been integrated in a general computer program which can be considered as a tool for modelling. A biological example illustrates the use of this program in the study of a model: the evolution of RNA in the silkgland of the silkworm.

Chance and Evolution

Several explicit references are made throughout the French edition of this book to the Darwinian theory of evolution. Indeed, the attempt that was made to summarise it is completely in line with this point of view. It is also an illustration of Theodosius Dobzhansky’s famous citation (above).

Biodiversity and Ecological Theories

Recent publications have pitted, on the one hand, the neutral theory of biodiversity – that leaves ample room for demographic processes such as reproduction, mortality, migrations, extinctions and speciation that have major random components – and, on the other hand, the ecological niche theory, more deterministic, that favours relationships with the environment and mechanisms between populations, especially competition. These two ecological theories, the foundations of which we review in Sections 5.1 and 5.2 of this chapter, do not truly include the other levels of biological organisation where, as we have seen, processes of diversification play a role. They are, in fact, complementary if we assume that the same niche can be shared by different species, phylogenetically close or not, and that, simultaneously, demographic processes – the keys to the neutral theory – play a major role. In fact and as is customary in demographic approaches, we introduce environmental constraints by varying the demographic parameters or by observing variations that we can attribute to environmental factors. First, here are some obvious facts.

Chance in Living Systems

Randomness is an integral part of certain biological and ecological processes, and has been for nearly all of the 4 billion years that living systems have been evolving. Indeed, as we will see, the processes that, from the gene to the ecosystem, bring about randomness produce biological diversity. This is “chance as creator” (Lestienne, 1993) and it is also, perhaps, thanks to this diversification that Life has been able to continue on Earth, despite the risks it runs, as proven by the catastrophes that have been sprinkled throughout the history of our planet. We must return here to Monod’s brilliant discussion on Chance and Necessity in the living world. The fundamental question is to know whether chance is necessary. And, if so, then the question arises: how is the process that brings it about selected to produce the diversity that, quite simply, permits Life to go on in an environment that is itself uncertain?

Lessons for Managing Living Systems

Making hypotheses and conjectures is an integral part of the scientific approach, and perhaps the principal one. Providing proof is essential, but it is at least as important to examine the practical consequences. If we highlight the importance of the spontaneous, random processes in living systems resulting from endogenous mechanisms, it is because they must be taken into account. So, and in these cases, managing them could be made simpler and more effective. It is even possible that, in certain cases, it is in our interest to improve the efficaciousness of the processes that create randomness; for example, to increase the pace of diversification or to improve the conditions that preserve biodiversity.

The Contribution of Models and Modelling: Some Examples

In this chapter are several illustrations and/or results that were made possible thanks to models. The first part of this chapter, devoted to genetics, shows a typical probabilistic model, which we know and have demonstrated to be effective, but which says nothing about the mechanisms bringing about the random phenomena observed. With this in mind and as a basis for reflection, we can consider the transition chaos-randomness as we sketch it out in the second part of this chapter. Lastly, the major trends in the evolution of biodiversity can be modelled through simple mathematical expressions; for example, the logistic model. We can see that despite its simplicity, it can teach us something about the possible global mechanisms explaining these dynamics. In the last section, we propose a general plan for modelling living systems that includes the average “deterministic” trends and the random and chaotic components.

Evaluating Biodiversity: The Example of French Guiana

French Guiana, “the French Amazon”, is situated close to the equator (between 3° and 5.5° latitude north). This region enjoys a warm and humid climate, with rather calm meteorological conditions (i.e., neither cyclones nor tropical storms). It is positioned on an extremely old gneiss and granite block (Proterozoic, about 2 billion years old, with a trace of Archeozoic more than 3 billion years old). Moreover, it is not subject to major telluric upheavals. So its ecological systems are not very often disturbed by extremely violent and widespread natural events. Nevertheless, we must remember that droughts have left a mark on its history and that, sporadically, these droughts have had consequences. We find in particular traces of paleo-fires in the forest, and the savannah is often burned.