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We investigate a set of stochastic models of biodiversity, populationgenetics, language evolution and opinion dynamics on a network within a commonframework. Each node has a state, 0 < x_i < 1, with interactions specified bystrengths m_{ij}. For any set of m_{ij} we derive an approximate expression forthe mean time to reach fixation or consensus (all x_i=0 or 1). Remarkably in acase relevant to language change this time is independent of the networkstructure.

Fixation and consensus times on a network: a unified approach