title: Evolution on distributive lattices.
abstract: 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.
authors.affiliation: Department of Mathematics, University of California, Berkeley, CA 94720, USA. niko@math.berkeley.edu <niko@math.berkeley.edu>
authors.forename: Niko
authors.initials: N
authors.lastname: Beerenwinkel
authors.forename: Nicholas
authors.initials: N
authors.lastname: Eriksson
authors.forename: Bernd
authors.initials: B
authors.lastname: Sturmfels
mesh_terms: D001499:Bayes Theorem; D005075:Biological Evolution; D019295:Computational Biology / Q000379:methods; D004305:Dose-Response Relationship, Drug; D024882:Drug Resistance, Viral / Q000235:genetics*; D053476:Extinction, Biological; D005838:Genotype; D006678:HIV / Q000187:drug effects* / Q000235:genetics; D017320:HIV Protease Inhibitors / Q000494:pharmacology; D006801:Humans; D008957:Models, Genetic; D009154:Mutation; D018570:Risk Assessment / Q000379:methods
chemical_list: D017320:HIV Protease Inhibitors