On the extended Moran model and its relation to coalescents with multiple collisions

We study the asymptotics of the extended Moran model as the total population size NN tends to infinity. Two convergence results are provided, the first result leading to discrete-time limiting coalescent processes and the second result leading to continuous-time limiting coalescent processes. The limiting coalescent processes allow for multiple mergers of ancestral lineages (ΛΛ-coalescent). It is furthermore verified that any continuous time ΛΛ-coalescent (with ΛΛ any probability distribution) can arise in the limit. Typical examples of extended Moran models are discussed, with an emphasis on models being in the domain of attraction of beta coalescents or ΛΛ-coalescents with ΛΛ being log infinitely divisible.