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.
"A Classification of Coalescent Processes for Haploid Exchangeable Population Models." Ann. Probab. 29 (4) 1547 - 1562, October 2001. https://doi.org/10.1214/aop/1015345761