Invariant manifolds of Competitive Selection–Recombination dynamics

Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Stephen Baigent, Belgin SeymenoğluAbstractWe 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.

Source: Nonlinear Analysis: Real World Applications - October 24, 2019 Category: Research Source Type: research