Cannings models, population size changes and multiple-merger coalescents

摘要

Multiple-merger coalescents, e.g. Lambda-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. Lambda-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.8. 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 Lambda-n-coalescents, this has been explicitly shown for only a limited subclass of Lambda-n-coalescents and exponentially growing populations. This article gives a more general construction of time-changed Lambda-n-coalescents as limits of specific Cannings models with rather arbitrary time changes.