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 $0,$, 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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