A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that ...A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman’s coalescent is replaced byΞ-coalescent.We prove the existence of such a process by specifying its moments using the dual function-valuedΞ-coalescent process with geographical labels and migration,and then verifying a multidimensional Hausdorff moment problem.We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type.展开更多
基金NSF of Hebei Province(Grant No.A2019205299)Hebei Education Department(Grant No.QN2019073)+2 种基金NSFC(Grant No.11501164)and HNU(Grant No.L2019Z01)X.Zhou’s research is supported by Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2016-06704)National Science Foundation of China(Grant No.11771018)。
文摘A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman’s coalescent is replaced byΞ-coalescent.We prove the existence of such a process by specifying its moments using the dual function-valuedΞ-coalescent process with geographical labels and migration,and then verifying a multidimensional Hausdorff moment problem.We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type.
