Article ID Journal Published Year Pages File Type
1155502 Stochastic Processes and their Applications 2015 29 Pages PDF
Abstract

We apply our general method of duality, introduced in Giardinà et al. (2007), to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions dual to coalescents of Kingman’s type, as well as for models with finite population size.Next, using SU(1,1)SU(1,1) raising and lowering operators, we find new dualities between the Wright–Fisher diffusion with dd types and the Moran model, both in presence and absence of mutations. These new dualities relates two forward evolutions. From our general scheme we also identify self-duality of the Moran model.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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