Ancestral processes with selection: Branching and Moran models

Ellen Baake, and Robert Bialowons. "Ancestral processes with selection: Branching and Moran models." Banach Center Publications 80.1 (2008): 33-52. <http://eudml.org/doc/281943>.

@article{EllenBaake2008,
abstract = {We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyse the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population is traced back into the past. The second approach is the Moran model with selection. Here, the population has constant size N. Individuals reproduce (at rates depending on their types), the offspring inherits the parent's type, and replaces a randomly chosen individual (to keep population size constant). Independently of the reproduction process, individuals can change type. As in the branching model, we consider the ancestral lines of single individuals chosen from the equilibrium population. We use analytical results of Fearnhead (2002) to determine the explicit properties, and parameter dependence, of the ancestral distribution of types, and its relationship with the stationary distribution in forward time.},
author = {Ellen Baake, Robert Bialowons},
journal = {Banach Center Publications},
keywords = {multitype branching; mutation-selection model; ancestral selection graph},
language = {eng},
number = {1},
pages = {33-52},
title = {Ancestral processes with selection: Branching and Moran models},
url = {http://eudml.org/doc/281943},
volume = {80},
year = {2008},
}

TY - JOUR
AU - Ellen Baake
AU - Robert Bialowons
TI - Ancestral processes with selection: Branching and Moran models
JO - Banach Center Publications
PY - 2008
VL - 80
IS - 1
SP - 33
EP - 52
AB - We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyse the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population is traced back into the past. The second approach is the Moran model with selection. Here, the population has constant size N. Individuals reproduce (at rates depending on their types), the offspring inherits the parent's type, and replaces a randomly chosen individual (to keep population size constant). Independently of the reproduction process, individuals can change type. As in the branching model, we consider the ancestral lines of single individuals chosen from the equilibrium population. We use analytical results of Fearnhead (2002) to determine the explicit properties, and parameter dependence, of the ancestral distribution of types, and its relationship with the stationary distribution in forward time.
LA - eng
KW - multitype branching; mutation-selection model; ancestral selection graph
UR - http://eudml.org/doc/281943
ER -