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Invariant manifolds of Competitive Selection–Recombination dynamics

Baigent, S; Seymenoğlu, B; (2020) Invariant manifolds of Competitive Selection–Recombination dynamics. Nonlinear Analysis: Real World Applications , 53 , Article 103054. 10.1016/j.nonrwa.2019.103054. Green open access

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Abstract

We study the two-locus-two-allele (TLTA) Selection-Recombination model from population genetics and establish explicit bounds on the TLTA model parameters for an invariant manifold to exist. Our method for proving existence of the invariant manifold relies on two key ingredients: (i) monotone systems theory (backwards in time) and (ii) a phase space volume that decreases under the model dynamics. To demonstrate our results we consider the effect of a modifier gene β on a primary locus α and derive easily testable conditions for the existence of the invariant manifold.

Type: Article
Title: Invariant manifolds of Competitive Selection–Recombination dynamics
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.nonrwa.2019.103054
Publisher version: https://doi.org/10.1016/j.nonrwa.2019.103054
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Invariant manifolds, Population genetics, Selection-Recombination model, Monotone systems
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10084528
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