The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem

Cordero F (2017)
MARKOV PROCESSES AND RELATED FIELDS 23(2): 313-324.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity, without any rescaling of parameters or time. We first prove that the latter converges, uniformly in compacts in probability, to the solution of an ordinary differential equation, which is explicitly solved. Next, we study the stability properties of its equilibrium points. Moreover, we show that the fluctuations of the proportion of fit individuals, after a proper normalisation, satisfy a uniform central limit theorem in [0, infinity). As a consequence, we deduce the convergence of the corresponding stationary distributions.
Stichworte
Moran model; mutation-selection models; limit of large populations; central limit theorem; density dependent populations
Erscheinungsjahr
2017
Zeitschriftentitel
MARKOV PROCESSES AND RELATED FIELDS
Band
23
Ausgabe
2
Seite(n)
313-324
ISSN
1024-2953
Page URI
https://pub.uni-bielefeld.de/record/2916163

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Cordero F. The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS. 2017;23(2):313-324.
Cordero, F. (2017). The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS, 23(2), 313-324.
Cordero, F. (2017). The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS 23, 313-324.
Cordero, F., 2017. The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS, 23(2), p 313-324.
F. Cordero, “The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem”, MARKOV PROCESSES AND RELATED FIELDS, vol. 23, 2017, pp. 313-324.
Cordero, F.: The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem. MARKOV PROCESSES AND RELATED FIELDS. 23, 313-324 (2017).
Cordero, Fernando. “The Deterministic Limit of the Moran Model: a Uniform Central Limit Theorem”. MARKOV PROCESSES AND RELATED FIELDS 23.2 (2017): 313-324.