  The quasispecies model was introduced in 1971 by Manfred Eigen to discuss the
first stages of life on Earth. It provides an appealing mathematical framework
to study the evolution of populations in biology, for instance viruses. We
present briefly the model and we focus on its stationary solutions. These
formulae have a surprisingly rich combinatorial structure, involving for
instance the Eulerian and Stirling numbers, as well as the up--down
coefficients of permutations.
