This thesis deals with the mathematical modeling of evolutionary processes that take
place in heterogeneous populations. Its leitmotif is the response of complex ensembles
of replicating entities to multiple (and often opposite) selection pressures. Even though
the specific problems addressed in different chapters belong to different organizational
levels—genome, population, and community—all of them can be conceptualized as the
evolution of a heterogeneous population—let it be a population of genomic elements,
viruses, or prokaryotic hosts and phages—facing a complex environment. As a result,
the mathematical tools required for their study are quite similar. In contrast, the strategies
that each population has discovered to perpetuate vary according to the different
evolutionary challenges and environmental constraints that the population experiences.
Along this thesis, there has been a special interest on connecting theoretical models
with experimental results. To that end, most of the work presented here has been
motivated either by laboratory findings or by the bioinformatic analysis of sequenced
genomes. We strongly believe that such a multidisciplinary approach is necessary in
order to improve our knowledge on how evolution works. Moreover, experiments are a
must when it comes to propose antiviral strategies based on theoretical predictions, as
we do in Chapter 3. This thesis is structured in two main blocks. The first one focuses on studying instances
of viral evolution under the action of mutagenic drugs, paying particular attention
to their possible application to the development of novel antiviral therapies. This
block comprises chapters 2 and 3; the former dicussing the phenomenon of lethal defection
and stochastic viral extinction; the latter dealing with the optimal way to combine
mutagens and inhibitors in multidrug antiviral treatments. The second block is devoted
to the study of the evolutionary forces underlying genome structure. In chapter 4, we
propose a mechanism through which multipartite viruses could have originated. Interestingly,
the pathway leading to genome segmentation shares some steps with lethal
defection, but each outcome is reached at specific environmental conditions. Chapter 5
analyses the abundance distributions of transposable elements in prokaryotic genomes,
with the aim of determining the key processes involved in their spreading. We explicitly
explore the hypothesis that transposable elements follow a neutral dynamics, with a
negligible fitness cost for their host genomes. A higher level of organization is studied
in Chapter 6, where an agent based coevolutionary model based on Lotka-Volterra interactions
is used to investigate the evolutionary dynamics of the prokaryotic antiviral
immunity system CRISPR-Cas. This chapter also examines the environmental factors
that are responsible for its maintenance or loss. Finally, Chapter 7 summarizes the main
results obtained along the thesis and sketches possible lines of work based on them