A particular subclass of compound Poisson population models is analyzed. The models in the domain of attraction of the Kingman coalescent are characterized and it is shown that these models are never in the domain of attraction of any other continuous-time coalescent process. Results are obtained characterizing which of these models are in the domain of attraction of a discrete-time coalescent with simultaneous multiple mergers of ancestral lineages. The results extend those obtained by Huillet and the author in `Population genetics models with skewed fertilities: a forward and backward analysis', Stochastic Models 27 (2011), 521-554.
"Coalescent processes derived from some compound Poisson population models." Electron. Commun. Probab. 16 567 - 582, 2011. https://doi.org/10.1214/ECP.v16-1654