Genealogical constructions of population models
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(2014)arxiv:1402.6724.

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.
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