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 1 → E 2 in a model at spatial scale 2 which will be considered in the next section.
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References
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)
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)
P. Jagers, O. Nerman, The growth and composition of branching populations. Adv. Appl. Probab. 16, 221–259 (1984)
R.M. Loynes, Extreme values in uniformly mixing stationary stochastic processes. Ann. Math. Stat. 36, 993–999 (1965)
P.A. Meyer, W.A. Zheng, Tightness criteria for laws of semimartingales. Ann. l’Institut Henri Poincaré 20, 353–372 (1984)
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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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DOI: https://doi.org/10.1007/978-3-319-02153-9_12
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