Modeling of Living Systems

Modeling is now one of the most efficient methodologies in life
sciences. From practice to theory, this book develops this approach
illustrated by many examples; general concepts and the current
state of the art are also presented and discussed.

An historical and general introduction informs the reader how
mathematics and formal tools are used to solve biological problems
at all levels of the organization of life. The core of this book
explains how this is done, based on practical examples coming, for
the most part, from the author's personal experience. In most
cases, data are included so that the reader can follow the
reasoning process and even reproduce calculus. The final chapter is
devoted to essential concepts and current developments. The main
mathematical tools are presented in an appendix to the book and are
written in an adapted language readable by scientists,
professionals or students, with a basic knowledge of
mathematics.

Auteur

Alain Pavé is Emeritus Professor of University, Member of the French National Academy of Technologies and Associate Member of the French Academy of Agriculture, Lyon, France.

Résumé
Modeling is now one of the most efficient methodologies in life sciences. From practice to theory, this book develops this approach illustrated by many examples; general concepts and the current state of the art are also presented and discussed.
An historical and general introduction informs the reader how mathematics and formal tools are used to solve biological problems at all levels of the organization of life. The core of this book explains how this is done, based on practical examples coming, for the most part, from the author's personal experience. In most cases, data are included so that the reader can follow the reasoning process and even reproduce calculus. The final chapter is devoted to essential concepts and current developments. The main mathematical tools are presented in an appendix to the book and are written in an adapted language readable by scientists, professionals or students, with a basic knowledge of mathematics.

Contenu

Preface xi

Introduction xv

Chapter 1. Methodology of Modeling in Biology and Ecology 1

1.1. Models and modeling 1

1.1.1. Models 2

1.1.2. Modeling 4

1.2. Mathematical modeling 6

1.2.1. Analysis of the biological situation and problem 7

1.2.2. Characterization and analysis of the system 11

1.2.3. Choice or construction of a model 14

1.2.4. Study of the properties of the model 18

1.2.5. Identification 25

1.2.6. Validation 26

1.2.7. Use 31

1.2.8. Conclusion 32

1.3. Supplements 33

1.3.1. Differences between a mathematical object and a mathematical model 33

1.3.2. Different types of objects and formalizations used in mathematical modeling 34

1.3.3. Elements for choosing a mathematical formalism 36

1.3.4. Stochastic and deterministic approaches 37

1.3.5. Discrete and continuous time 39

1.3.6. Biological and physical variables 39

1.3.7. The quantitative qualitative debate 40

1.4. Models and modeling in life sciences 41

1.4.1. Historical overview 42

1.4.2. Modeling in biological disciplines 46

1.4.3. Modeling in population biology and ecology 47

1.4.4. Actors 48

1.4.5. Modeling and informatics 49

1.4.6. Definition of bioinformatics 49

1.5. A brief history of ecology and the importance of models in this discipline 51

1.6. Systems: a unifying concept 56

Chapter 2. Functional Representations: Construction and Interpretation of Mathematical Models 59

2.1. Introduction 60

2.2. Box and arrow diagrams: compartmental models 62

2.3. Representations based on Forrester diagrams 65

2.4. Chemical-type representation and multilinear differential models 66

2.4.1. General overview of the translation algorithm 67

2.4.2. Example of the logistic model 71

2.4.3. Saturation phenomena 73

2.5. Functional representations of models in population dynamics 76

2.5.1. Single population model 76

2.5.2. Models with two interacting populations 79

2.6. General points on functional representations and the interpretation of differential models 84

2.6.1. General hypotheses 84

2.6.2. Interpretation: phenomenological and mechanistic aspects, superficial knowledge and deep knowledge 85

2.6.3. Towards a classification of differential and integro-differential models of population dynamics 86

2.7. Conclusion 87

Chapter 3. Growth Models Population Dynamics and Genetics 89

3.1. The biological processes of growth 90

3.2. Experimental data 93

3.2.1. Organism growth data 93

3.2.2. Data relating to population growth 96

3.3. Models 98

3.3.1. Questions and uses of models 99

3.3.2. Some examples of classic growth models 100

3.4. Growth modeling and functional representations 104

3.4.1. Quantitative aspects 106

3.4.2. Qualitative aspects: choice and construction of models 107

3.4.3. Functional representations and growth models 107

3.4.4. Examples of the construction of new models 110

3.4.5. Typology of growth models 115

3.5. Growth of organisms: some examples 117

3.5.1. Individual growth of the European herring gull, Larus argentatus 117

3.5.2. Individual growth of young muskrats, Ondatra zibethica 118

3.5.3. Growth of a tree in a forest: examples of the application of individual growth models 124

3.5.4. Human growth 132

3.6. Models of population dynamics 133

3.6.1. Examples of growth models for bacterial populations: the exponential model, the logistic model, the Monod model and the Contois model 133

3.6.2. Dynamics of biodiversity at a geological level 146

3.7. Discrete time elementary demographic models 153

3.7.1. A discrete time demographic model of microbial populations 153

3.7.2. The Fibonacci model 155 3.7.3. Lindenmayer syst...