  We consider the directed evolution of a population after an intervention that
has significantly altered the underlying fitness landscape. We model the space
of genotypes as a distributive lattice; the fitness landscape is a real-valued
function on that lattice. The risk of escape from intervention, i.e., the
probability that the population develops an escape mutant before extinction, is
encoded in the risk polynomial. Tools from algebraic combinatorics are applied
to compute the risk polynomial in terms of the fitness landscape. In an
application to the development of drug resistance in HIV, we study the risk of
viral escape from treatment with the protease inhibitors ritonavir and
indinavir.
