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Titlebook: Spatial Fleming-Viot Models with Selection and Mutation; Donald A. Dawson,Andreas Greven Book 2014 Springer International Publishing Switz

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Lecture Notes in Mathematicshttp://image.papertrans.cn/s/image/873496.jpg
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https://doi.org/10.1007/978-3-319-02153-960J70,92D15,92D25,60J80,60J85; ; Dual processes; Emergence of rare mutants; Fleming-Viot processes; Mutat
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,Emergence with , ≥ 2 Lower Order Types (Phases 0,1,2),ce 1 between the two types (Section 8). It remains to determine in this Section 9 and the next Section 10 respectively what is the effect of having .Both of these cases are going to exhibit some new phenomenon and challenges not present in the two-type model. What are the effects of having more than two types precisely?
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Neutral Evolution on ,, After Fixation (Phase 3),. So far we have discussed in Sections 8–10 the Phases 0, 1 and 2 and we now have to deal here in this section with the next Phase 3 (and in the next Section 12 with Phase 4). In Subsection 11.1 we describe the result, then in 11.2 give the proof.
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,Mean-Field Emergence and Fixation of Rare Mutants in the Fisher–Wright Model with Two Types,The systematic analysis of the model is rather complex and we therefore build up the theory in levels, in order to make the main theme more visible. The present section is the overture of the whole symphony.
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Formulation of the Main Results in the General Case,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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A Basic Tool: Dual Representations,An important technical tool in our analysis are various new representations of the marginal distributions of the basic processes in terms of expectations under the appropriate . respectively . dual processes.
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