  This chapter gives a synopsis of recent approaches to model and analyse the
evolution of microbial populations under selection. The first part reviews two
population genetic models of Lenski's long-term evolution experiment with
Escherichia coli, where models aim at explaining the observed curve of the
evolution of the mean fitness. The second part describes a model of a
host-pathogen system where the population of pathogenes experiences balancing
selection, migration, and mutation, as motivated by observations of the genetic
diversity of HCMV (the human cytomegalovirus) across hosts.
