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.

• 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.

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.

• 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.

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.

• 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.