Stationary distributions for the β-process (solid lines) and Wright-Fisher process (dashed lines). (A and B) Stationary densities. (C and D) Stationary cumulative distribution functions. (A and C) Beta process (solid lines) with Beta density parameters α = 0.7, β = 1. (B and D) Beta process (solid lines) with parameters α = 1.3, β = 1. Mutation values are θ = 0.1, 0.3, 0.6, 1.2. Population size N = 8000. Note that for a given mutation rate, the Wright–Fisher process concentrates more mass at the boundaries than the β-process.
Diversity sn = Sn/Θ vs. jump-size λ in the pure Λ-processes, for n = 4, 7, 10, 13 (bottom to top). These functions attain their extrema at the endpoints 0 and 1, implying that the Wright–Fisher and star processes minimize and maximize diversity for these sample sizes.