On the stationary distribution of the block counting process for population models with mutation and selection

Cordero F, Moehle M (2019)
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 474(2): 1049-1081.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck| Englisch
 
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Abstract / Bemerkung
We consider two population models subject to the evolutionary forces of selection and mutation, the Moran model and the A-Wright-Fisher model. In such models the block counting process traces back the number of potential ancestors of a sample of the population at present. Under some conditions the block counting process is positive recurrent and its stationary distribution is described via a linear system of equations. In this work, we first characterise the measures A leading to a geometric stationary distribution, the Bolthausen-Sznitman model being the most prominent example having this feature. Next, we solve the linear system of equations corresponding to the Moran model. For the A-Wright-Fisher model we show that the probability generating function associated to the stationary distribution of the block counting process satisfies an integro differential equation. We solve the latter for the Kingman model and the star-shaped model. (C) 2019 Elsevier Inc. All rights reserved.
Erscheinungsjahr
2019
Zeitschriftentitel
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Band
474
Ausgabe
2
Seite(n)
1049-1081
ISSN
0022-247X
eISSN
1096-0813
Page URI
https://pub.uni-bielefeld.de/record/2934596

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Cordero F, Moehle M. On the stationary distribution of the block counting process for population models with mutation and selection. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 2019;474(2):1049-1081.
Cordero, F., & Moehle, M. (2019). On the stationary distribution of the block counting process for population models with mutation and selection. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 474(2), 1049-1081. doi:10.1016/j.jmaa.2019.02.004
Cordero, F., and Moehle, M. (2019). On the stationary distribution of the block counting process for population models with mutation and selection. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 474, 1049-1081.
Cordero, F., & Moehle, M., 2019. On the stationary distribution of the block counting process for population models with mutation and selection. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 474(2), p 1049-1081.
F. Cordero and M. Moehle, “On the stationary distribution of the block counting process for population models with mutation and selection”, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 474, 2019, pp. 1049-1081.
Cordero, F., Moehle, M.: On the stationary distribution of the block counting process for population models with mutation and selection. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 474, 1049-1081 (2019).
Cordero, Fernando, and Moehle, M. “On the stationary distribution of the block counting process for population models with mutation and selection”. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 474.2 (2019): 1049-1081.