Preface -- What changes has mathematics made to the Darwinian theory? by Warren J. Ewens -- The mathematics of Darwin’s theory of evolution: 1859 and 150 years later by Peter Schuster -- Some Mathematical Models in Evolutionary Genetics by Reinhard Bürger -- Extinction, Persistence, and Evolution by Peter Jagers -- Group Theory in Homogeneous Populations (Rescuing Darwin from the mud) by Peter Taylor -- Evolutionary dynamics of collective action by Jorge M. Pacheco, Francisco C. Santos, Max O. Souza and Brian Skyrms -- On kin and group selection, and the haystack model by Vincent A. A. Jansen -- Population formulation of adaptative meso-evolution: theory and numerics by Sepideh Mirrahimi, Benoît Perthame, Emeric Bouin and Pierre Millien -- Random Modeling of Adaptive Dynamics and Evolutionary Branching by Sylvie Méléard -- Thoughts on the geometry of meso-evolution: collecting mathematical elements for a postmodern synthesis by J.A.J. (Hans) Metz -- When do optimisation arguments make evolutionary sense? by Mats Gyllenberg, J.A.J. (Hans) Metz and Robert Service -- Bibliography -- Index.

The book presents a general overview of mathematical models in the context of evolution. It covers a wide range of topics such as population genetics, population dynamics, speciation, adaptive dynamics, game theory, kin selection, and stochastic processes. Written by leading scientists working at the interface between evolutionary biology and mathematics the book is the outcome of a conference commemorating Charles Darwin's 200th birthday, and the 150th anniversary of the first publication of his book "On the origin of species". Its chapters vary in format between general introductory and state-of-the-art research texts in biomathematics, in this way addressing both students and researchers in mathematics, biology and related fields. Mathematicians looking for new problems as well as biologists looking for rigorous description of population dynamics will find this book fundamental.