Finally I uploaded a third our paper on the analysis of quasispecies model. Here all the links together:
- Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution (This text deals with the symmetric or permutation invariant fitness landscape and mutations and reproduction events are separated. This text was recently accepted by Mathematical Biosciences, DOI: 10.1016/j.mbs.2014.08.006. It contains all the main ideas and long introduction to the whole field.)
- On the behavior of the leading eigenvalue of Eigen’s evolutionary matrices (This paper is about general non permutation invariant fitness landscapes and classical Eigen’s model when mutations and reproduction events occur at the same time. Probably the main contribution of this paper is that we came up with a conjecture about a very general formula for the error threshold. More analysis is necessary at access the validity of this conjecture)
- Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model (This paper proposes a heuristic technique to find the quasispecies distribution in the infinite sequence length limit. Surprisingly, a lot of well known results can be obtained in a very straightforward way. Plus new analytical results are given. At some level it looks “to simple to be true” and I am quite worried about reviewers’ opinions on this text.)
- Here are the slides from my last presentation on the subject; these are quite full and give a short exposition of the first and third paper above. I am planning to give an hour long talk in our department colloquium this fall, and these slides will serve as a starting point for my (longer) presentation.