Solving the migration-recombination equation from a genealogical point of view

Alberti F, Baake E, Letter I, Martinez S (2021)
Journal of mathematical biology 82(5): 41 .

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Alberti, FredericUniBi; Baake, EllenUniBi; Letter, I; Martinez, S
Abstract / Bemerkung
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of large numbers setting. We relate this dynamics (forward in time) to a Markov chain, namely a labelled partitioning process, backward in time. This way, we obtain a stochastic representation of the solution of the migration-recombination equation. As a consequence, one obtains an explicit solution of the nonlinear dynamics, simply in terms of powers of the transition matrix of the Markov chain. The limiting and quasi-limiting behaviour of the Markov chain are investigated, which gives immediate access to the asymptotic behaviour of the dynamical system. We finally sketch the analogous situation in continuous time.
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of mathematical biology
Band
82
Ausgabe
5
Art.-Nr.
41
eISSN
1432-1416
Page URI
https://pub.uni-bielefeld.de/record/2953579

Zitieren

Alberti F, Baake E, Letter I, Martinez S. Solving the migration-recombination equation from a genealogical point of view. Journal of mathematical biology. 2021;82(5): 41 .
Alberti, F., Baake, E., Letter, I., & Martinez, S. (2021). Solving the migration-recombination equation from a genealogical point of view. Journal of mathematical biology, 82(5), 41 . https://doi.org/10.1007/s00285-021-01584-4
Alberti, F., Baake, E., Letter, I., and Martinez, S. (2021). Solving the migration-recombination equation from a genealogical point of view. Journal of mathematical biology 82:41 .
Alberti, F., et al., 2021. Solving the migration-recombination equation from a genealogical point of view. Journal of mathematical biology, 82(5): 41 .
F. Alberti, et al., “Solving the migration-recombination equation from a genealogical point of view”, Journal of mathematical biology, vol. 82, 2021, : 41 .
Alberti, F., Baake, E., Letter, I., Martinez, S.: Solving the migration-recombination equation from a genealogical point of view. Journal of mathematical biology. 82, : 41 (2021).
Alberti, Frederic, Baake, Ellen, Letter, I, and Martinez, S. “Solving the migration-recombination equation from a genealogical point of view”. Journal of mathematical biology 82.5 (2021): 41 .

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