  We study a class of Cannings models with population size $N$ having a mixed
multinomial offspring distribution with random success probabilities
$W_1,\ldots,W_N$ induced by independent and identically distributed positive
random 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 a
sampling with replacement strategy from a random partition of the unit interval
into $N$ subintervals of lengths $W_1,\ldots,W_N$. Convergence results for the
genealogy of these Cannings models are provided under regularly varying
assumptions on the tail distribution of $X_1$. In the limit several coalescent
processes with multiple and simultaneous multiple collisions occur. The results
extend those obtained by Huillet (2014) for the case when $X_1$ is Pareto
distributed and complement those obtained by Schweinsberg (2003) for models
where one samples without replacement from a supercritical branching process.
