Abstract
We now introduce the model used in this monograph in general form. Consider a population consisting of multitype individuals divided into colonies (demes) that are located at sites labelled by a countable group \(\Omega _{N}\) (modelling geographic space) and whose types (genotypes) belong to a countable set
The choice of the geographic space \(\Omega _{N}\) defined below is a good caricature (for large N) of a geography around two dimensions as we shall explain later on.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
D.A. Dawson, Measure-valued Markov processes, in École d’Été de Probabilités de Saint Flour XXI. Lecture Notes in Mathematics 1541 (Springer, Berlin, 1993), pp. 1–261
D.A. Dawson, Multilevel mutation-selection systems and set-valued duals (in preparation)
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, L.G. Gorostiza, A. Wakolbinger, Occupation time fluctuations in branching systems. J. Theor. Probab. 14, 729–796 (2001)
A. Depperschmidt, A. Greven, P. Pfaffelhuber, Tree-valued Fleming-Viot dynamics with mutation and selection. Ann. Appl. Probab. 22, 2560–2615 (2012)
S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence (Wiley, New York, 1986)
S.N. Ethier, T.G. Kurtz, The infinitely-many-alleles-model with selection as a measure-valued diffusion, in Lecture Notes in Biomathematics, vol. 70 (Springer, Berlin, 1987), pp. 72–86
S. Gavrilets, Evolution and speciation in a hyperspace: the roles of neutrality, selection, mutation and random drift, in Towards a Comprehensive Dynamics of Evolution - Exploring the Interplay of Selection, Neutrality, Accident, and Function, ed. by J. Crutchfield, P. Schuster (Oxford University Press, Oxford, 1999)
T.E. Harris, On the Theory of Branching Processes (Springer, Berlin, 1963)
P. Jagers, O. Nerman, The growth and composition of branching populations. Adv. Appl. Probab. 16, 221–259 (1984)
M. Kimura, Diffusion model of population genetics incorporating group selection, with special reference to an altruistic trait, in Lecture Notes in Mathematics, vol. 1203 (Springer, Berlin, 1986), pp. 101–118
C. Kipnis, C.M. Newman, The metastable behavior of infrequently observed weakly random one dimensional diffusion processes. SIAM J. Appl. Math. 45, 972–982 (1985)
C.M. Newman, J.E. Cohen, C. Kipnis, Neo-Darwinian evolution implies punctuated equilibria. Nature 315, 400–401 (1985)
S. Sawyer, J. Felsenstein, Isolation by distance in a hierarchically clustered population. J. Appl. Prob. 20, 1–10 (1983)
M.J. Wade, Sewall Wright, gene interaction and the shifting balance theory. Oxf. Surv. Evol. Biol. 8, 35–62 (1992)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Dawson, D.A., Greven, A. (2014). Formulation of the Multitype and Multiscale Model. 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-02153-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02152-2
Online ISBN: 978-3-319-02153-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)