The dynamics of consensus in a community: a genealogical approach
R. Blythe. Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Cultural traits, such as political opinions and linguistic usages, can propagate through a community by its members simply copying others. In its simplest form, this process is diffusion. As physicists know well, diffusion is a slow process. Is it possible, therefore, for a diffusive process to reproduce the very rapid process of consensus observed in the formation of the New Zealand English language dialect? By considering the ancestry of cultural traits (i.e., looking at who copied what from whom) in a manner familiar to population geneticists we will show that several different spreading processes are equivalent to the reaction-diffusion process $A+A\to A$ on a network. We will demonstrate that this approach allows consensus times to be precisely determined and furthermore give conditions under which consensus can be reached in an infinitely large community in a finite time.
Reference: R. A. Blythe (2007) ``The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population'' Theor. Popul. Biol. (in press, preprint: q.bio/0606037)