On spatial coalescents with multiple mergers in two dimensions

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 Λ-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.