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 N 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 (Λ-coalescent). It is furthermore verified that any continuous time Λ-coalescent (with Λ 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 Λ-coalescents with Λ being log infinitely divisible.