This book defines and develops probabilistic tools for modeling populations, describing the dynamics of biological quantities such as population size, allele proportions, and individual locations. Beginning with discrete Markovian models (random walks, GaltonWatson processes), it gradually introduces stochastic calculus, stochastic differential equations, and jump Markov processes, including continuous-time branching processes and birth-and-death processes. It also explores discrete and continuous models of genetic evolution, genealogies, and the WrightFisher process and coalescent theory. Throughout, the book emphasizes the computation of biologically relevant quantities and includes numerous exercises. The final chapter demonstrates the application of probabilistic tools to real-world biological problems and discusses recent research in detail.

Written and course-tested by a leading expert, this book offers a solid foundation in the mathematical modeling of biological systems, population dynamics, genetic evolution, and ecological impact.

Presents essential mathematical tools for applications to ecology and evolution Discusses questions of current interest in mathematical biology Tackles real-world problems with mathematical rigor

Autorentext

Sylvie Méléard holds the Chair in Mathematical Modeling for Biodiversity in the Applied Mathematics Department of the École Polytechnique (France). She is a distinguished mathematician specializing in probability theory and its applications to mathematical biology, including population dynamics, evolutionary ecology, bacterial biology and haematology. She is the recipient of numerous awards, including the Irène Joliot-Curie Scientific Woman of the Year 2024 award of the French Academy of Sciences.

Inhalt

1 Introduction.- 2 Spatial Populations and Discrete Time.- 3 Population Dynamics in Discrete Time.- 4 Brownian Motion and Diffusion Processes.- 5 Continuous Time Population Processes.- 6 Genetic Evolutionary Processes.- 7 Some Modern Developments in Ecology-Evolution.- Appendix A: Measures, Integration and Probability Measures.- Appendix B: Poisson Point Measures.