TY  - JOUR
A1  - Boenkost, Florin
A1  - Casanova Soberón, Adrián González
A1  - Pokalyuk, Cornelia
A1  - Wakolbinger, Anton
T1  - Haldane’s formula in Cannings models: the case of moderately weak selection
T2  - Electronic journal of probability
N2  - We introduce a Cannings model with directional selection via a paintbox construction and establish a strong duality with the line counting process of a new Cannings ancestral selection graph in discrete time. This duality also yields a formula for the fixation probability of the beneficial type. Haldane’s formula states that for a single selectively advantageous individual in a population of haploid individuals of size N the probability of fixation is asymptotically (as N→∞) equal to the selective advantage of haploids sN divided by half of the offspring variance. For a class of offspring distributions within Kingman attraction we prove this asymptotics for sequences sN obeying N−1≪sN≪N−1/2, which is a regime of “moderately weak selection”. It turns out that for sN≪N−2/3 the Cannings ancestral selection graph is so close to the ancestral selection graph of a Moran model that a suitable coupling argument allows to play the problem back asymptotically to the fixation probability in the Moran model, which can be computed explicitly.
KW  - ancestral selection graph
KW  - Cannings model
KW  - directional selection
KW  - probability of fixation
KW  - sampling duality
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/81748
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-817481
SN  - 1083-6489
VL  - 26
SP  - 1
EP  - 36
PB  - EMIS ELibEMS ; Univ. of Washington, Mathematics Dep.
CY  - [Madralin] ; Seattle, Wash.
ER  -