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Formulation of the Main Results in the General Case

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Spatial Fleming-Viot Models with Selection and Mutation

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2092))

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Abstract

Our goal is to identify the combined effect of mutation, selection and migration on the evolution of the system introduced in Section 3 as time proceeds.

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References

  1. S.R. Athreya, J.M. Swart, Branching-coalescing systems. Probab. Theory Relat. Fields 131(3), 376–414. Electronic, 39 p. (2005). doi:10.1007/s00440-004- 0377-4

    Google Scholar 

  2. R. Bürger, Mathematical properties of mutation-selection models. Genetica 102/103, 279–298 (1998)

    Google Scholar 

  3. D.A. Dawson, A. Greven, Multiple time scale analysis of hierarchically interacting systems, in A Festschrift to Honor G. Kallianpur (Springer, Berlin, 1993a), pp. 41–50

    Google Scholar 

  4. D.A. Dawson, A. Greven, Multiple time scale analysis of interacting diffusions. Probab. Theory Relat. Fields 95, 467–508 (1993b)

    Article  MathSciNet  MATH  Google Scholar 

  5. D.A. Dawson, A. Greven, Hierarchical models of interacting diffusions: multiple time scale phenomena. Phase transition and pattern of cluster-formation. Probab. Theory Rel. Fields 96, 435–473 (1993c)

    Article  MathSciNet  MATH  Google Scholar 

  6. D.A. Dawson, A. Greven, Multiple space-time scale analysis for interacting branching models. Electron. J. Probab. 1, paper no. 14, 1–84 (1996)

    Google Scholar 

  7. D.A. Dawson, A. Greven, Hierarchically interacting Fleming-Viot processes with selection and mutation: Multiple space time scale analysis and quasi equilibria. Electron. J. Probab. 4, paper no. 4, 1–81 (1999)

    Google Scholar 

  8. D.A. Dawson, A. Greven, J. Vaillancourt, Equilibria and Quasi-equilibria for Infinite Collections of Interacting Fleming-Viot processes. Trans. Am. Math. Soc. 347(7), 2277–2360 (1995)

    MathSciNet  MATH  Google Scholar 

  9. A. Depperschmidt, A. Greven, P. Pfaffelhuber, Tree-valued Fleming-Viot dynamics with mutation and selection. Ann. Appl. Probab. 22, 2560–2615 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. S.N. Ethier, T.G. Kurtz, Coupling and ergodic theorems for Fleming-Viot processes. Ann. Probab. 26, 533–561 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Greven, P. Pfaffelhuber, A. Winter, Tree-valued resampling dynamics: Martingale Problems and applications. Probab. Theor. Relat. Fields 155, 787–838 (2013)

    MathSciNet  Google Scholar 

  12. P. Jagers, O. Nerman, The growth and composition of branching populations. Adv. Appl. Probab. 16, 221–259 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  13. P. Seidel, The historical process of the spatial Moran model with selection and mutation. Master thesis, Department of Math., Erlangen, Germany, 2008

    Google Scholar 

  14. P. Seidel, The historical process of interacting Fleming-Viot processes with selection (in preparation)

    Google Scholar 

  15. T. Shiga, Uchiyama, Stationary states and the stability of the stepping stone model involving mutation and selection. Probab. Theory Relat. Fields 73, 87–117 (1986)

    MathSciNet  MATH  Google Scholar 

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Dawson, D.A., Greven, A. (2014). Formulation of the Main Results in the General Case. In: Spatial Fleming-Viot Models with Selection and Mutation. Lecture Notes in Mathematics, vol 2092. Springer, Cham. https://doi.org/10.1007/978-3-319-02153-9_4

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