Evolution on distributive lattices

Details Evolution on distributive lattices Evolution on distributive lattices

2005-11-23

arxiv.org/abs/q-bio/0511039v2

Biology

Quantitative Biology

Populations and Evolution

22 pages, 4 figures; minor corrections, moved details to appendix. Final version to appear in Journal of Theoretical Biology

Scientific paper

10.1016/j.jtbi.2006.03.013

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.

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