UBC Mathematics Department
The voter model, closely related to the stepping stone model of mathematical genetics, was introduced independently by Clifford and Sudbury in 1973 and Holley and Liggett in 1975. It is a stochastic process designed to model the evolution of a spatially distributed population whose individuals hold various "opinions" and try, at random times, to influence the opinions of nearby individuals. (Alternatively, one can think of individuals of various species who try to "colonize" nearby sites.) The voter model is one of the most mathematically tractable of a class of stochastic processes called interacting particle systems. In this talk, I will describe some of the basic features of the model, and present some recent work motivated by questions on "species abundance" distributions. Technology willing, the talk will include some computer simulations.