Table 1 Hierarchy of coalescent models in decreasing order of generality
Coalescent model | Allows MMs? | Allows simultaneous MMs? | Distribution and parameters | References |
|---|---|---|---|---|
Ξ-Coalescent | Yes | Yes | MMC events occur at rate λ, with a specific measure ξ on the infinite simplex and which allows an arbitrary number of simultaneous mergers. | |
Λ-Coalescent | Yes | No | MMC events occur at rate λ (but ⩽1 event/time) | |
Ψ-Coalescent | Yes | No | λ follows a distribution that depends on Ψ, that is,, the fraction of the population replaced by the offspring of a single individual | Eldon and Wakeley (2006); Eldon and Wakeley (2008); Eldon and Wakeley (2009); Eldon and Degnan (2012) |
Beta-coalescent | Yes | No | λ follows β-distribution: β(α, 2-α) with 1⩽α<2 | Schweinsberg (2003); Berestycki et al. (2007); Berestycki et al. (2008); Birkner and Blath (2008); Birkner et al. (2013); Steinrücken et al. (2013) |
Bolthausen–Sznitman | Yes | No | λ follows β-distribution with α=1: β(1,1)=uniform on [0,1] | Bolthausen and Snznitman (1998); Basdevant and Goldschmidt (2008); Neher and Hallatschek (2013) |
Kingman coalescent | No | No | λ follows β-distribution with α=2; Λ has unit mass at 0 (Λ(dx)=δ0(x)dx) |
