The dynamical systems theory of natural selection

Darwin's (1859) theory of evolution by natural selection accounts for the adaptations of organisms, but, as Fisher (1930) famously said, 'natural selection is not evolution.' Evolutionary theory has two major components: i) natural selection, which involves the underlying dynamics of populations; and ii) adaptive evolutionary change, which involves the optimisation of phenotypes for ï¬tness maximisation. Many of the traditional theoretical frameworks in evolutionary theory have focussed on studying optimisation processes that generate biological adaptations. In recent years, however, a number of evolutionary theorists have turned to using frameworks such as the 'replicator dynamics' or 'eco-evolutionary dynamics', to explore the dynamics of natural selection. There has, however, been little attempt to explore how these dynamical systems frameworks relate to more traditional frameworks in evolutionary theory or how they incorporate the principles that embody the process of evolution by natural selection, namely, phenotypic variation, diï¬erential reproductive success, and heritability. In this thesis, I use these principles to provide the formal foundations of a general frameworkâa mathematical synthesisâin which the future state of an evolutionary system can be predicted from its present state; what I will call a 'dynamical systems theory of natural selection.' Given the state of an existing biological system, and a set of assumptions about how individuals within the system interact, the job of the dynamical systems theory of natural selection is no less than to predict the future in its entirety.