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We study a class of Cannings models with population size $N$ having a mixedmultinomial offspring distribution with random success probabilities$W_1,\ldots,W_N$ induced by independent and identically distributed positiverandom variables $X_1,X_2,\ldots$ via $W_i:=X_i/S_N$, $i\in\{1,\ldots,N\}$,where $S_N:=X_1+\cdots+X_N$. The ancestral lineages are hence based on asampling with replacement strategy from a random partition of the unit intervalinto $N$ subintervals of lengths $W_1,\ldots,W_N$. Convergence results for thegenealogy of these Cannings models are provided under regularly varyingassumptions on the tail distribution of $X_1$. In the limit several coalescentprocesses with multiple and simultaneous multiple collisions occur. The resultsextend those obtained by Huillet (2014) for the case when $X_1$ is Paretodistributed and complement those obtained by Schweinsberg (2003) for modelswhere one samples without replacement from a supercritical branching process.

Asymptotic genealogies for a class of generalized Wright-Fisher models