TY  - INPR
A1  - Casanova Soberón, Adrián González
A1  - Kurt, Noemi
A1  - Pérez, José Luis
T1  - The ancestral selection graph for a Λ-asymmetric Moran model
T2  - arXiv
N2  - Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, 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. 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. Under certain conditions, that we call the ``partial order of adaptation'', we can couple these measures. 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. Interestingly, the construction also provides a connection to the theory of optimal transport. 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 discontinous 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
KW  - optimal transport
Y1  - 2023
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/83480
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-834800
UR  - https://arxiv.org/abs/2306.00130v1
IS  - 2306.00130 Version 1
PB  - arXiv
ER  -