Page 419 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 419
MATHEMATICS IN BIOLOGY AND MEDICINE (MS-35)
Lines of descent in a Moran model with frequency-dependent selection
and mutation
Luigi Esercito, lesercito@techfak.uni-bielefeld.de
Bielefeld University, Germany
Coauthors: Ellen Baake, Sebastian Hummel
Dealing with the interplay of mutation and selection is one of the important challenges in pop-
ulation genetics. We consider two variants of the two-type Moran model with mutation and
frequency-dependent selection, namely a scheme with nonlinear dominance (of the fit type)
and another with what we name the fittest-type-wins scheme. We show the equivalence of the
two variants and pursue the latter for further analysis. In particular, we trace the genealogy of
a sample of individuals backward in time, via an appropriate version of the so-called ances-
tral selection graph (ASG), originally introduced by Krone and Neuhauser (1997). We use the
information contained in mutation events to reduce the ASG to the parts that are informative
with respect to the type distribution of the present population and their ancestors, respectively.
This leads to the killed ASG and the pruned lookdown ASG in this setting, which we use to
derive representations for the (factorial) moments of the type distribution and the ancestral type
distribution; we do so by connecting forward and backward graphical models via duality rela-
tionships. Finally, we show how the results carry over to the diffusion limit.
References
[1] Baake, Ellen, Luigi Esercito, and Sebastian Hummel. "Lines of descent in a Moran model
with frequency-dependent selection and mutation." arXiv preprint arXiv:2011.08888
(2020).
Evolutionary escape and evolutionary suicide in host-pathogen systems
Eva Kisdi, eva.kisdi@helsinki.fi
University of Helsinki, Finland
Can pathogens drive their hosts extinct? Can hosts evolutionarily escape their pathogens? The
most basic models answer both questions in the negative. Here I review a number of possi-
bilities how evolution may nevertheless lead to the extinction of the host or of the pathogen.
Possible mechanisms driving extinction include Allee effects, population structure and condi-
tional behaviour of the hosts. These models showcase examples of simple models exhibiting
rich behaviour and leading to results previously thought to be unlikely.
Mathematical Modelling of the impact of Quarantine and Isolation-based
control interventions on the Transmission Dynamics of Lassa fever
Chinwendu Emilian Madubueze, ce.madubueze@gmail.com
Federal University of Agriculture, Makurdi, Nigeria
Coauthor: Emmanuel A. Bakare
Lassa fever is an acute viral hemorrhagic fever caused by the Lassa virus. It was first discovered
in Nigeria in 1969 when two missionary nurses died of Lassa fever. Lassa fever infection is
417
Lines of descent in a Moran model with frequency-dependent selection
and mutation
Luigi Esercito, lesercito@techfak.uni-bielefeld.de
Bielefeld University, Germany
Coauthors: Ellen Baake, Sebastian Hummel
Dealing with the interplay of mutation and selection is one of the important challenges in pop-
ulation genetics. We consider two variants of the two-type Moran model with mutation and
frequency-dependent selection, namely a scheme with nonlinear dominance (of the fit type)
and another with what we name the fittest-type-wins scheme. We show the equivalence of the
two variants and pursue the latter for further analysis. In particular, we trace the genealogy of
a sample of individuals backward in time, via an appropriate version of the so-called ances-
tral selection graph (ASG), originally introduced by Krone and Neuhauser (1997). We use the
information contained in mutation events to reduce the ASG to the parts that are informative
with respect to the type distribution of the present population and their ancestors, respectively.
This leads to the killed ASG and the pruned lookdown ASG in this setting, which we use to
derive representations for the (factorial) moments of the type distribution and the ancestral type
distribution; we do so by connecting forward and backward graphical models via duality rela-
tionships. Finally, we show how the results carry over to the diffusion limit.
References
[1] Baake, Ellen, Luigi Esercito, and Sebastian Hummel. "Lines of descent in a Moran model
with frequency-dependent selection and mutation." arXiv preprint arXiv:2011.08888
(2020).
Evolutionary escape and evolutionary suicide in host-pathogen systems
Eva Kisdi, eva.kisdi@helsinki.fi
University of Helsinki, Finland
Can pathogens drive their hosts extinct? Can hosts evolutionarily escape their pathogens? The
most basic models answer both questions in the negative. Here I review a number of possi-
bilities how evolution may nevertheless lead to the extinction of the host or of the pathogen.
Possible mechanisms driving extinction include Allee effects, population structure and condi-
tional behaviour of the hosts. These models showcase examples of simple models exhibiting
rich behaviour and leading to results previously thought to be unlikely.
Mathematical Modelling of the impact of Quarantine and Isolation-based
control interventions on the Transmission Dynamics of Lassa fever
Chinwendu Emilian Madubueze, ce.madubueze@gmail.com
Federal University of Agriculture, Makurdi, Nigeria
Coauthor: Emmanuel A. Bakare
Lassa fever is an acute viral hemorrhagic fever caused by the Lassa virus. It was first discovered
in Nigeria in 1969 when two missionary nurses died of Lassa fever. Lassa fever infection is
417
