  We consider the genealogy of a sample of individuals taken from a spatially
structured population when the variance of the offspring distribution is
relatively large. The space is structured into discrete sites of a graph G. If
the population size at each site is large, spatial coalescents with multiple
mergers, so called spatial Lambda-coalescents, for which ancestral lines
migrate in space and coalesce according to some Lambda-coalescent mechanism,
are shown to be appropriate approximations to the genealogy of a sample of
individuals.
  We then consider as the graph G the two dimensional torus with side length
2L+1 and show that as L tends to infinity, and time is rescaled appropriately,
the partition structure of spatial Lambda-coalescents of individuals sampled
far enough apart converges to the partition structure of a non-spatial Kingman
coalescent. From a biological point of view this means that in certain
circumstances both the spatial structure as well as larger variances of the
underlying offspring distribution are harder to detect from the sample.
However, supplemental simulations show that for moderately large L the
different structure is still evident.
