ABSTRACT
Unlike physics, which has been inextricably linked to mathematics since its foundations, the relationship between biology and mathematics has not been strong, and until relatively recently the application of mathematics in the life sciences in general has been very limited. Mathematical biology, however, has been rapidly advancing on a number of fronts with both the rise of powerful computing methods and the understanding of complex low level biological structures, in particular the sequencing of the human genome, allowing the modelling of complex molecular systems and the development of early stage multiscale models. Important early mathematical developments in the modelling of organisms include the predator-prey modelling of Lotka (1925) and Volterra (1926), and the development of population genetics (e.g. Hardy, 1908; Weinberg, 1908, Wright, 1930 and Fisher, 1930), but arguably the most influential modelling in this area concerns the development of the theory of evolutionary games, which is the subject of this book. Both the type of dynamics used in predator-prey models and the core concepts of population genetics have had important influences on evolutionary games, but the origins of evolutionary games go back a long way with ideas developed for a very different type of scenario, and we begin by discussing games and game theory more generally.
