Fast fixation without fast networks
arXiv:1208.0530 · doi:10.1103/PhysRevE.86.031142
Abstract
We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance selection model) and opinion dynamics (the voter model) as special cases. These models all have absorbing states of fixation where all the nodes are in the same state. Earlier studies of these models showed that the mean time when this occurs can be made to grow as different powers of the network size by varying the the degree distribution of the network. Here we demonstrate that this effect can also arise if one varies the asymmetry of the copying dynamics whilst holding the degree distribution constant. In particular, we show that the mean time to fixation can be accelerated even on homogeneous networks when certain nodes are very much more likely to be copied from than copied to. We further show that there is a complex interplay between degree distribution and asymmetry when they may co-vary; and that the results are robust to correlations in the network or the initial condition.
11 pages, 5 figures
References in corpus (11)
- Statistical physics of social dynamics
- Voter Models on Heterogeneous Networks
- Generic Absorbing Transition in Coevolution Dynamics
- Stochastic Models of Evolution in Genetics, Ecology and Linguistics
- Conservation laws for the voter model in complex networks
- Who's talking first? Consensus or lack thereof in coevolving opinion formation models
- Heterogeneous Voter Models
- Fixation and consensus times on a network: a unified approach
- Ordering in voter models on networks: Exact reduction to a single-coordinate diffusion
- Heterogenous mean-field analysis of a generalized voter-like model on networks
- Voter Model with Time dependent Flip-rates