Exact solutions of evolution models

The methods and models of evolutionary dynamics have a lot of applications in interdisciplinary research. We need in advanced evolution theory to understand complexity growth during the biological evolution, artificial intelligence, cancer, socio-dynamics.

We review the quasispecies theory, including the case of fluctuating fitness landscapes, and the relation with the statistical physics. We use the statistical physics methods to derive rigorous, exact solutions or qualitatively to get some insights of deep aspects of evolution. From the statistical physics perspectives the advanced evolution phenomenon is on the same level of complexity as the Maxwell demon or higher, and not less complex at least as the strings.