TY  - JOUR
A1  - Casanova Soberón, Adrián González
A1  - Kurt, Noemi
A1  - Pérez, José Luis
T1  - The ancestral selection graph for a Λ-asymmetric Moran model
T2  - Theoretical population biology
N2  - Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanisms, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of one type is larger than the other. The higher reproductive success may stem from either more frequent reproduction, or from larger numbers of offspring, and is encoded in a measure Λ for each of the two types. Λ-reproduction here means that a whole fraction of the population is replaced at a reproductive event. Our approach consists of constructing a Λ-asymmetric Moran model in which individuals of the two populations compete, rather than considering a Moran model for each population. Provided the measure are ordered stochastically, we can couple them. This allows us to construct the central object of this paper, the Λ−asymmetric ancestral selection graph, leading to a pathwise duality of the forward in time Λ-asymmetric Moran model with its ancestral process. We apply the ancestral selection graph in order to obtain scaling limits of the forward and backward processes, and note that the frequency process converges to the solution of an SDE with discontinuous paths. Finally, we derive a Griffiths representation for the generator of the SDE and use it to find a semi-explicit formula for the probability of fixation of the less beneficial of the two types.
KW  - Moran model
KW  - Ancestral selection graph
KW  - Duality
KW  - Λ-coalescent
KW  - Fixation probability
Y1  - 2024
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/83472
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-834722
SN  - 0040-5809
VL  - 2024
IS  - In Press, Corrected Proof
PB  - Elsevier
CY  - Amsterdam
ER  -