| Life is that which evolves. Evolutionary dynamics shape the living world around us. At the center of every evolutionary process is a population of reproducing individuals. These individuals can be molecules, cells, viruses, multi-cellular organisms or humans with language, hopes and some rationality. The laws of evolution are formulated in terms of mathematical equations. Whenever the fitness of individuals depends on the relative abundance of various strategies or phenotypes in the population, then we are in the realm of evolutionary game theory. Evolutionary game theory is a fairly general approach that helps to understand the interaction of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviors in the human population. Here we present recent results on stochastic dynamics in finite sized and structured populations. We derive fundamental laws that determine how natural selection chooses between competing strategies. Two of the results are concerned with the study of multiple strategies and continuous strategies in a well-mixed population. Next we introduce a new way to think of population structure: set-structured populations. Unlike previous structures, the sets are dynamical: the population structure itself is a consequence of evolutionary dynamics. I will present a general mathematical approach for studying any evolutionary game in this structure. Finally, I give a general result which characterizes two-strategy games in any structured population. |
