A Classification of Coalescent Processes for Haploid Exchangeable Population Models

We consider a class of haploid population models with nonoverlapping generations and fixed population size $N$ assuming that the family sizes within a generation are exchangeable random variables. A weak convergence criterion is established for a properly scaled ancestral process as $N \to \infty$. It results in a full classification of the coalescent generators in the case of exchangeable reproduction. In general the coalescent process allows for simultaneous multiple mergers of ancestral lines.