DARWINS LOG - A TOY MODEL OF SPECIATION AND EXTINCTION

Stochastic models for the origin and extinction of species have been rather neglected in applied probability. As an alternative to modelling speciation and extinction as intrinsically random, I shall describe and show simulations of a rule-based model. This involves mathematical representations of notions such as genetic type of species, environmental niche, fitness of a species in a niche, and adaptation. There are underlying random mechanisms for changes of niche sizes and for disconnection and reconnection of geographical regions, and these ultimately drive the evolution of species. Other approaches to mathematical modelling of evolution are briefly mentioned.