Emergence of random selections in evolution of biological populations

In this work we propose a mathematical framework (inspired by the Good Turing estimator) for the above phenomenon, and show its emergence also in molecular and bacterial systems, where generations are observable in short times, and the convergence of the population distribution to a single species (in population genetics this process is called fixation) may be achieved in few operational steps. Some DNA based experiments which exhibit this phenomenon are here presented, together with a couple of experiments carried on bacterial systems of genetically modified E.coli strains. Therefore, a relevant evolutionary phenomenon, already confirmed in the literature of population genetics and species evolution, is here mathematically proved and for the first time observed also in (guided) evolution of nano and micro scale biological populations.