The voter model, with mutations occurring at a positive rate a, has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in d ≥ 2. We show that, as α → 0, the limiting distribution is right triangular in d = 2 and uniform in d > 3. We also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions.
- Coalescing random walk
- Multitype voter model
- Species abundance distributions
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty