title: Fixation and consensus times on a network: a unified approach.
abstract: We investigate a set of stochastic models of biodiversity, population genetics, language evolution, and opinion dynamics on a network within a common framework. Each node has a state 0<x(i)<1 with interactions specified by strengths m(ij). For any set of m(ij), we derive an approximate expression for the mean time to reach fixation or consensus (all x(i)=0 or 1). Remarkably, in a case relevant to language change, this time is independent of the network structure.
authors.affiliation: School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand.
authors.forename: G J
authors.initials: GJ
authors.lastname: Baxter
authors.forename: R A
authors.initials: RA
authors.lastname: Blythe
authors.forename: A J
authors.initials: AJ
authors.lastname: McKane
mesh_terms: D044822:Biodiversity; D017753:Ecosystem; D008954:Models, Biological; D015233:Models, Statistical; D013269:Stochastic Processes