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Evolution du Principe d'Exclusion Compétitive : Le rôle des mathématiques

Claude Lobry

TL;DR

The paper traces the mathematical evolution of the Competitive Exclusion Principle (PEC) from its early observational roots to modern population dynamics, emphasizing how a progressive shift from descriptive ecology to rigorous mathematical modeling redefined coherence between theory and data. It documents key milestones—logistic growth, Lotka-Volterra dynamics, Gause experiments, chemostat and functional-response frameworks, and the bootstrap into dynamical systems—culminating in ratio-dependent approaches that challenge classic mass-action views. The central argument is that mathematics functions as a 'roman mathématique': a narrative that translates ecological phenomena into precise formal structures, enabling predictions about coexistence, persistence, and complex dynamics beyond simple equilibrium outcomes. This perspective highlights the deep, ongoing interplay between theory, experiment, and computation in shaping theoretical ecology and its interpretation of competitive interactions.

Abstract

Everyone can see that over the last 150 years, theoretical ecology has become considerably more mathematical. But what is the nature of this phenomenon? Are mathematics applied, as in the use of statistical tests, for example, or are they involved, as in physics, where laws cannot be expressed without them? Through the history of the {\em Competitive Exclusion Principle} formulated at the very beginning of the 20th century by the naturalist Grinnell concerning the distribution of brown-backed chickadees, up to its modern integration into what is known in mathematics as population dynamics, I highlight the effectiveness of what could be called the mathematical novel in clarifying certain concepts in theoretical ecology.

Evolution du Principe d'Exclusion Compétitive : Le rôle des mathématiques

TL;DR

The paper traces the mathematical evolution of the Competitive Exclusion Principle (PEC) from its early observational roots to modern population dynamics, emphasizing how a progressive shift from descriptive ecology to rigorous mathematical modeling redefined coherence between theory and data. It documents key milestones—logistic growth, Lotka-Volterra dynamics, Gause experiments, chemostat and functional-response frameworks, and the bootstrap into dynamical systems—culminating in ratio-dependent approaches that challenge classic mass-action views. The central argument is that mathematics functions as a 'roman mathématique': a narrative that translates ecological phenomena into precise formal structures, enabling predictions about coexistence, persistence, and complex dynamics beyond simple equilibrium outcomes. This perspective highlights the deep, ongoing interplay between theory, experiment, and computation in shaping theoretical ecology and its interpretation of competitive interactions.

Abstract

Everyone can see that over the last 150 years, theoretical ecology has become considerably more mathematical. But what is the nature of this phenomenon? Are mathematics applied, as in the use of statistical tests, for example, or are they involved, as in physics, where laws cannot be expressed without them? Through the history of the {\em Competitive Exclusion Principle} formulated at the very beginning of the 20th century by the naturalist Grinnell concerning the distribution of brown-backed chickadees, up to its modern integration into what is known in mathematics as population dynamics, I highlight the effectiveness of what could be called the mathematical novel in clarifying certain concepts in theoretical ecology.

Paper Structure

This paper contains 29 sections, 59 equations, 23 figures.

Table of Contents

  1. Introduction : Qu'est-ce que le Principe d'Exclusion Compétitive ?
  2. 1840-1920 : Modèle ou courbe d'ajustement ? La logistique.
  3. Modèle et fonction logistique : le point de vue actuel
  4. Verhulst le démographe.
  5. Pearl et les croissances de microorganismes
  6. Premiers enseignements.
  7. 1920-1940 : L'âge d'or de l'écologie théorique
  8. Lotka et Volterra
  9. La compétition : vision moderne
  10. La compétition chez Volterra
  11. La compétition chez Lotka
  12. Gause : mathématiques et expériences.
  13. 1936 Un O.V.N.I. piloté par un extraterrestre.
  14. Derrière l'O.V.N.I. des mathématiques en devenir.
  15. 1940-1970 : Un peu plus de biologie
  16. ...and 14 more sections

Figures (23)

  • Figure 1: Quelques références de The origin and distribution of the chestnut-backed chickadee
  • Figure 2: Une page typique de la revue Theoretical Population Biology avec de nombreuses formules mathématiques..
  • Figure 3: Graphe de la fonction "logistique" \ref{['flogistic']}, $K = 4, r =1, x_0 = 0.1$
  • Figure 4: Ajustement à une logistique de données de croissance d'une population de levures par Pearl PEA27. Les chiffres des colonnes (a) (observations) et (b) (ajustement logistique) sont représentés graphiquement à droite.
  • Figure 5: La réaction chimique hypothétique de Lotka. Extrait de LOT20
  • ...and 18 more figures