%0 Journal Article %1 heuer2013spatial %A Heuer, Benjamin %A Sturm, Anja %D 2013 %J Theoretical Population Biology %K coalescent_theory coupling_time lambda_coalescent random_walks_on_graphs spatial_coalescent %N 0 %P 90 - 104 %R http://dx.doi.org/10.1016/j.tpb.2012.11.006 %T On spatial coalescents with multiple mergers in two dimensions %U http://www.sciencedirect.com/science/article/pii/S0040580912001220 %V 87 %X 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 Λ -coalescents, for which ancestral lines migrate in space and coalesce according to some Λ -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 2 L + 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.

@article{heuer2013spatial, abstract = {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 Λ -coalescents, for which ancestral lines migrate in space and coalesce according to some Λ -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 2 L + 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. }, added-at = {2015-06-15T03:09:08.000+0200}, author = {Heuer, Benjamin and Sturm, Anja}, biburl = {https://www.bibsonomy.org/bibtex/2defa63734548a2a2038e595b95be48b1/peter.ralph}, doi = {http://dx.doi.org/10.1016/j.tpb.2012.11.006}, interhash = {42a394ff90da172c9423e6b89627d03b}, intrahash = {defa63734548a2a2038e595b95be48b1}, issn = {0040-5809}, journal = {Theoretical Population Biology }, keywords = {coalescent_theory coupling_time lambda_coalescent random_walks_on_graphs spatial_coalescent}, number = 0, pages = {90 - 104}, timestamp = {2015-06-15T03:09:08.000+0200}, title = {On spatial coalescents with multiple mergers in two dimensions }, url = {http://www.sciencedirect.com/science/article/pii/S0040580912001220}, volume = 87, year = 2013 }