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Re-equilibration on Higher Level E 1 (Phase 4)

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

Abstract

Having now handled phases 0,1,2,3, in this section we are concerned with Phase 4 (recall Subsubsection 4.2.1 for the five phases scenario), that is, the time regime in which the mean-field model on spatial level 2 is concentrated on the second fitness level (E 1 types) and approaches a McKean–Vlasov mutation-selection equilibrium but before the emergence of the third fitness level (E 2-types) in a typical spatial 1-ball. This will then also serve as Phase 0 for the transition E 1E 2 in a model at spatial scale 2 which will be considered in the next section.

Keywords

  • Fitness Level
  • Path Space
  • Martingale Problem
  • Exponential Moment
  • Uniform Topology

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References

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Dawson, D.A., Greven, A. (2014). Re-equilibration on Higher Level E 1 (Phase 4). 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_12

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