Reviews results on spatial population models, genealogies, and extensions including Fleming-Viot processes, Cannings models with block resampling, seedbanks, selection, and mutation.
Stochastic evolution of genealogies of spatial populations: state description, characterization of dynamics and properties
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abstract
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In particular we explain the choice of state spaces and their topologies, describe the dynamics of genealogical Fleming-Viot and branching models by well-posed martingale problems, and formulate the typical results on the longtime behavior. Furthermore we discuss the basic techniques of proofs and sketch as two key tools of analysis the different forms of duality and the Girsanov transformation.
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math.PR 1years
2019 1verdicts
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Stochastic Evolution of spatial populations: From configurations to genealogies and back
Reviews results on spatial population models, genealogies, and extensions including Fleming-Viot processes, Cannings models with block resampling, seedbanks, selection, and mutation.