Unequal crossover dynamics in discrete and continuous time

Redner O, Baake M (2004)
JOURNAL OF MATHEMATICAL BIOLOGY 49(2): 201-226.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an 'imperfect' alignment, in which the shorter sequence has d units without a partner in the longer one, scales like q(d) as compared to 'perfect' alignments where all these copies are paired. The class is parameterized by this penalty factor q. An effectively infinite population size and thus deterministic dynamics is assumed. For the extreme cases q = 0 and q = 1, and any initial distribution whose moments satisfy certain conditions, we prove the convergence to one of the known fixed points, uniquely determined by the mean copy number, in both discrete and continuous time. For the intermediate parameter values, the existence of fixed points is shown.
Stichworte
generating functions; recombination; quadratic operators; unequal crossover; Lyapunov functions; probability
Erscheinungsjahr
2004
Zeitschriftentitel
JOURNAL OF MATHEMATICAL BIOLOGY
Band
49
Ausgabe
2
Seite(n)
201-226
ISSN
0303-6812
Page URI
https://pub.uni-bielefeld.de/record/1607092

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Redner O, Baake M. Unequal crossover dynamics in discrete and continuous time. JOURNAL OF MATHEMATICAL BIOLOGY. 2004;49(2):201-226.
Redner, O., & Baake, M. (2004). Unequal crossover dynamics in discrete and continuous time. JOURNAL OF MATHEMATICAL BIOLOGY, 49(2), 201-226. https://doi.org/10.1007/s00285-004-0273-7
Redner, O., and Baake, M. (2004). Unequal crossover dynamics in discrete and continuous time. JOURNAL OF MATHEMATICAL BIOLOGY 49, 201-226.
Redner, O., & Baake, M., 2004. Unequal crossover dynamics in discrete and continuous time. JOURNAL OF MATHEMATICAL BIOLOGY, 49(2), p 201-226.
O. Redner and M. Baake, “Unequal crossover dynamics in discrete and continuous time”, JOURNAL OF MATHEMATICAL BIOLOGY, vol. 49, 2004, pp. 201-226.
Redner, O., Baake, M.: Unequal crossover dynamics in discrete and continuous time. JOURNAL OF MATHEMATICAL BIOLOGY. 49, 201-226 (2004).
Redner, O, and Baake, Michael. “Unequal crossover dynamics in discrete and continuous time”. JOURNAL OF MATHEMATICAL BIOLOGY 49.2 (2004): 201-226.

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PMID: 15293019
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