%0 Generic %1 etheridge2014genealogical %A Etheridge, Alison M. %A Kurtz, Thomas G. %D 2014 %K Moran_model SLFV duality lookdown_process stepping_stone_models voter_model %T Genealogical constructions of population models %U http://arxiv.org/abs/1402.6724 %X Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on $0,$, whereas in the infinite intensity limit, at each time $t$, the joint distribution of types and levels is conditionally Poisson, with mean measure $\Xi (t)l$ where $l$ denotes Lebesgue measure and $\Xi (t)$ is a measure-valued population process. Key forces of ecology and genetics can be captured within this common framework. Models covered incorporate both individual and event based births and deaths, one-for-one replacement, immigration, independent `thinning' and independent or exchangeable spatial motion and mutation of individuals. Since birth and death probabilities can depend on type, they also include natural selection.

@misc{etheridge2014genealogical, abstract = {Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on $[0,\lambda ]$, whereas in the infinite intensity limit, at each time $t$, the joint distribution of types and levels is conditionally Poisson, with mean measure $\Xi (t)\times l$ where $l$ denotes Lebesgue measure and $\Xi (t)$ is a measure-valued population process. Key forces of ecology and genetics can be captured within this common framework. Models covered incorporate both individual and event based births and deaths, one-for-one replacement, immigration, independent `thinning' and independent or exchangeable spatial motion and mutation of individuals. Since birth and death probabilities can depend on type, they also include natural selection.}, added-at = {2016-03-25T19:25:02.000+0100}, author = {Etheridge, Alison M. and Kurtz, Thomas G.}, biburl = {https://www.bibsonomy.org/bibtex/26c933f94901e8f613a7df680dccd63a3/peter.ralph}, interhash = {9c82514128e9e4b7634d133f2da7f8ee}, intrahash = {6c933f94901e8f613a7df680dccd63a3}, keywords = {Moran_model SLFV duality lookdown_process stepping_stone_models voter_model}, note = {arxiv:1402.6724}, timestamp = {2016-09-17T11:33:50.000+0200}, title = {Genealogical constructions of population models}, url = {http://arxiv.org/abs/1402.6724}, year = 2014 }