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.	Schweinsberg (2000); Möhle and Sagitov (2001)
Λ-Coalescent	Yes	No	MMC events occur at rate λ (but ⩽1 event/time)	Donnelly and Kurtz (1999); Pitman (1999); Sagitov (1999)
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)	Kingman (1982)

Abbreviations: MM, multiple merger; MMC, multiple-merger coalescent.

Coalescent models listed in decreasing order with respect to generality.