Cannings models, population size changes and multiple-merger coalescents

Source abstract

Abstract Multiple-merger coalescents, e.g. $$\varLambda$$ Λ - n -coalescents, have been proposed as models of the genealogy of n sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman’s n -coalescent. $$\varLambda$$ Λ - n -coalescents can be seen as the limit process of the discrete genealogies of Cannings models with fixed population size, when time is rescaled and population size $$N\rightarrow \infty$$ N → ∞ . As established for Kingman’s n -coalescent, moderate population size fluctuations in the discrete population model should be reflected by a time-change of the limit coalescent. For $$\varLambda$$ Λ - n -coalescents, this has been explicitly shown for only a limited subclass of $$\varLambda$$ Λ - n -coalescents and exponentially growing populations. This article gives a more general construction of time-changed $$\varLambda$$ Λ - n -coalescents as limits of specific Cannings models with rather arbitrary time changes.