  Multiple-merger coalescents, e.g. $\Lambda$-$n$-coalescents, have been
proposed as models of the genealogy of $n$ sampled individuals for a range of
populations whose genealogical structures are not captured well by Kingman's
$n$-coalescent. $\Lambda$-$n$-coalescents can be seen as the limit process of
the discrete genealogies of Cannings models with fixed population size, when
time is rescaled and population size $N\to\infty$. As established for Kingman's
$n$-coalescent, moderate population size fluctuations in the discrete
population model should be reflected by a time-change of the limit coalescent.
For $\Lambda$-$n$-coalescents, this has been explicitly shown for only a
limited subclass of $\Lambda$-$n$-coalescents and exponentially growing
populations. This article gives a general construction of time-changed
$\Lambda$-$n$-coalescents as limits of specific Cannings models with rather
arbitrary time changes.
