The development of mathematical approaches to the study of
microbial ecology has most often been limited to
mean field studies of predator-prey interactions with a fixed or
limited number of species.  However, there is an incredible
bacterial and viral diversity in natural systems that is neither
well understood nor systematically identified.  In this talk,
I propose a computational and theoretical framework for
analyzing rapid co-evolutionary dynamics in their ecological context.
The aim of such a framework is to predict and test the dynamics of
bacteria and bacteriophage diversity in ecosystems where
both the molecular biology and population dynamics are
well quantified.  The model system under consideration
is the association between E. coli and lambda phage in
continuous culture.  Because lambda phage inserts its prophage
into the bacterial cell via the maltose receptor, a selective pressure
exists for the bacteria to modify its receptor configuration and,
in turn, for the phage to modify its tail fiber.  A mathematical model
of these trait adaptations is developed using the framework
of adaptive dynamics (Dieckmann and Law, J. Math. Bio. 1996).
Analytical solutions of the co-evolutionary model yield conditions for
evolutionary bifurcations leading to distinct quasispecies, conditions
that depend on ecological conditions and biological traits.
The existence of bifurcations leading to stable coexistence
of multiple quasispecies is verified by stochastic Monte Carlo
simulations of populations evolving in a chemostat with
fixed washout rate and inflow resource density.
A necessary condition for bifurcations is for the host-range specificity
of phage to exceed the specificity of bacteria at uptake of maltose, i.e.
diversification occurs for generalist hosts and specialist phage.
Finally, I discuss means to test quantitatively the predictions of
this model under chemostat conditions.