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Bernstein polynomial approximation of fixation probability in finite population evolutionary games

Authors :
Jiyeon Park
Paul K. Newton
Publication Year :
2022
Publisher :
Cold Spring Harbor Laboratory, 2022.

Abstract

We use the Bernstein polynomials of degree d as the basis for constructing a uniform approximation to the rate of evolution (related to the fixation probability) of a species in a two-component finite-population frequency-dependent evolutionary game setting. The approximation is valid over the full range 0 ≤ w ≤ 1, where w is the selection pressure parameter, and converges uniformly to the exact solution as d → ∞. We compare it to a widely used non-uniform approximation formula in the weak-selection limit (w ∼ 0) as well as numerically computed values of the exact solution. Because of a boundary layer that occurs in the weak-selection limit, the Bernstein polynomial method is more efficient at approximating the rate of evolution in the strong selection region (w ∼ 1) (requiring the use of fewer modes to obtain the same level of accuracy) than in the weak selection regime.

Details

Database :
OpenAIRE
Accession number :
edsair.doi...........7b0662efb1bce34290dca4705628b3b6
Full Text :
https://doi.org/10.1101/2022.08.05.502960