%0 Journal Article %1 MR1681126 %A Donnelly, Peter %A Kurtz, Thomas G. %D 1999 %J Ann. Probab. %K Fleming_Viot coalescent_theory particle_systems popgen superprocesses %N 1 %P 166--205 %T Particle representations for measure-valued population models %U http://dx.doi.org/10.1214/aop/1022677258 %V 27 %X Models of populations in which a type or location, represented by a point in a metric spaceE, is associated with each individual in the population are considered. A population process is neutral if the chances of an individual replicating or dying do not depend on its type. Measure-valued processes are obtained as infinite population limits for a large class of neutral population models, and it is shown that these measure-valued processes can be represented in terms of the total mass of the population and the de Finetti measures associated with an E∞ -valued particle modelX=(X1,X2…) such that, for each t≥0,(X1(t),X2(t),…) is exchangeable. The construction gives an explicit connection between genealogical and diffusion models in population genetics. The class of measure-valued models covered includes both neutral Fleming-Viot and Dawson-Watanabe processes. The particle model gives a simple representation of the Dawson-Perkins historical process and Perkins’s historical stochastic integral can be obtained in terms of classical semimartingale integration. A number of applications to new and known results on conditioning, uniqueness and limiting behavior are described. MR: The authors consider several models of neutral populations in which a type or location is associated with each individual in the population, and the chances of an individual replicating or dying do not depend on its type. Measure-valued processes are obtained as infinite population limits for a large class of neutral population models. It is shown that these measure-valued processes can be represented in terms of the total mass of the population and the de Finetti measures associated with an $E^ınfty$-valued particle model $X=(X_1,X_2,\cdots)$ such that, for each $t0, (X_1(t), X_2(t),\cdots)$ is exchangeable. The class of measure-valued models covers both neutral Fleming-Viot and Dawson-Watanabe processes. The particle model gives a simple representation of the Dawson-Perkins historical process. Perkins' historical stochastic integral can be obtained in terms of classical semimartingale integration. A number of applications to new and known results on conditioning, uniqueness and limiting behavior are described. It is worth mentioning that the construction gives an explicit connection between genealogical and diffusion models in population genetics.

@article{MR1681126, abstract = {Models of populations in which a type or location, represented by a point in a metric spaceE, is associated with each individual in the population are considered. A population process is neutral if the chances of an individual replicating or dying do not depend on its type. Measure-valued processes are obtained as infinite population limits for a large class of neutral population models, and it is shown that these measure-valued processes can be represented in terms of the total mass of the population and the de Finetti measures associated with an E∞ -valued particle modelX=(X1,X2…) such that, for each t≥0,(X1(t),X2(t),…) is exchangeable. The construction gives an explicit connection between genealogical and diffusion models in population genetics. The class of measure-valued models covered includes both neutral Fleming-Viot and Dawson-Watanabe processes. The particle model gives a simple representation of the Dawson-Perkins historical process and Perkins’s historical stochastic integral can be obtained in terms of classical semimartingale integration. A number of applications to new and known results on conditioning, uniqueness and limiting behavior are described. MR: The authors consider several models of neutral populations in which a type or location is associated with each individual in the population, and the chances of an individual replicating or dying do not depend on its type. Measure-valued processes are obtained as infinite population limits for a large class of neutral population models. It is shown that these measure-valued processes can be represented in terms of the total mass of the population and the de Finetti measures associated with an $E^\infty$-valued particle model $X=(X_1,X_2,\cdots)$ such that, for each $t\ge 0, (X_1(t), X_2(t),\cdots)$ is exchangeable. The class of measure-valued models covers both neutral Fleming-Viot and Dawson-Watanabe processes. The particle model gives a simple representation of the Dawson-Perkins historical process. Perkins' historical stochastic integral can be obtained in terms of classical semimartingale integration. A number of applications to new and known results on conditioning, uniqueness and limiting behavior are described. It is worth mentioning that the construction gives an explicit connection between genealogical and diffusion models in population genetics.}, added-at = {2009-01-20T20:54:53.000+0100}, author = {Donnelly, Peter and Kurtz, Thomas G.}, biburl = {https://www.bibsonomy.org/bibtex/2b168f639e8f48786de29334508d018a7/peter.ralph}, coden = {APBYAE}, fjournal = {The Annals of Probability}, interhash = {e4b628d813fd3156cc691bcf5fbaff78}, intrahash = {b168f639e8f48786de29334508d018a7}, issn = {0091-1798}, journal = {Ann. Probab.}, keywords = {Fleming_Viot coalescent_theory particle_systems popgen superprocesses}, mrclass = {60J25 (60G57 60J70 60J80 60K35 92D25)}, mrnumber = {MR1681126 (2000f:60108)}, mrreviewer = {Xue Lei Zhao}, number = 1, pages = {166--205}, timestamp = {2014-05-19T21:46:23.000+0200}, title = {Particle representations for measure-valued population models}, url = {http://dx.doi.org/10.1214/aop/1022677258}, volume = 27, year = 1999 }