Stable cycling in quasi-linkage equilibrium : fluctuating dynamics under gene conversion and selection. / Russell, Timothy W.; Russell, Matthew J.; Úbeda, Francisco; Jansen, Vincent A. A.

In: Journal of Theoretical Biology, Vol. 477, 21.09.2019, p. 84-95.

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Genetic systems with multiple loci can have complex dynamics. For example, mean fitness need not always increase and stable cycling is possible. Here, we study the dynamics of a genetic system inspired by the molecular biology of recognition-dependent double strand breaks and repair as it happens in recombination hotspots. The model shows slow-fast dynamics in which the system converges to the quasi-linkage equilibrium (QLE) manifold. On this manifold, sustained cycling is possible as the dynamics approach a heteroclinic cycle, in which allele frequencies alternate between near extinction and near fixation. We find a closed-form approximation for the QLE manifold and use it to simplify the model. For the simplified model, we can analytically calculate the stability of the heteroclinic cycle. In the discrete-time model the cycle is always stable; in a continuous-time approximation, the cycle is always unstable. This demonstrates that complex dynamics are possible under quasi-linkage equilibrium.
Original languageEnglish
Pages (from-to)84-95
Number of pages12
JournalJournal of Theoretical Biology
Early online date13 Jun 2019
Publication statusE-pub ahead of print - 13 Jun 2019
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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