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Mathematical models of host-parasite co-evolution

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Schenk,  Hanna
Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Schenk, H. (2019). Mathematical models of host-parasite co-evolution. PhD Thesis, University of Lübeck, Lübeck.


Cite as: https://hdl.handle.net/21.11116/0000-0003-C9AD-8
Abstract
An important driver of evolution is the selection pressure that results from interactions
between species. One such interaction is the antagonistic relationship
of hosts and parasites, characterised by a strong disadvantage for the host and
an often essential gain for the parasite. This thesis extends various mathematical
models on host-parasite co-evolution by detailing verbally formulated theories
and testing model robustness. The models illuminate biological mechanisms and
provide long term evolutionary dynamics that are hard to capture experimentally.
Within the same population hosts can be differentially susceptible and parasites
are often specific to certain host types. Therefore, those parasites that can
infect the most common host are temporarily the best adapted, but later, when
another host is more common, a different parasite is the momentary winner. The
resulting oscillations of type abundances within a population are called Red Queen
dynamics.
In the first part of this work, Red Queen dynamics are examined under various
mathematical and biological assumptions. Relative changes within a population
are displayed using evolutionary game theory, but including population dynamics
the equations become comparable to the Lotka-Volterra system for predator-prey
dynamics. In the first project, these oscillations show chaotic properties when
the number of types (dimensions) increases and when oscillation amplitudes are
large. In the second project, both constant and changing population size models
are derived from individual interactions and compared for their biological and
mathematical properties. The stochastic dynamics result in diversity loss, which
is sped up in the changing population size models, but can be counteracted by
re-emerging extinct types. The effect is especially unpredictable under intermediate
population sizes, when deterministic attractive dynamics are balanced with
stochastic diffusion.
In the second part, selection pressure on both species either to evade infection
by the parasite or to find new ways to exploit the host is examined separately.
The first project is concerned with the evolution of a bacterial host. Experiments
have shown that the success of phage (parasite) infecting bacteria (host) depends
on the physiological status of the host. Including important dependencies in an
established model for phage infection introduces a bi-stability for the presence of
phage. A numerical invasion analysis reveals that a slow growing bacterial mutant
can invade a resident population of fast growing hosts and in some cases even
remove the phage infection completely.
In the final project, a model for bacterial persistence, a survival strategy of the
parasite, is developed together with empiricists. Bacteria related to Crohn’s disease are compared to harmless bacteria. The strategies of bacteria to form dormant
stages and evade stress are formulated using ordinary differential equations. The
model is fitted to laboratory data to reveal important growth and switch parameters.
The pathogenic bacteria are more stress-resistant and withstand antibiotic
treatment by forming more dormant stages within the human immune system than
their harmless relatives.
Overall, the models presented here showcase the diverse utility of mathematics
and theory in evolutionary biology. Red Queen dynamics are tested for robustness
and discussed for their applicability and implications. The evolutionary advantage
of both host and parasite strategies are mechanistically founded and the final
integration of laboratory data and theoretical reasoning presents a successful interdisciplinary
collaboration.