Emergence of random selections in evolution of biological populations

If a biological population is fragmented in small isolated groups, there may emerge an evolution phenomenon independent from natural selection. Limited number of individuals and their isolation allow a completely random variation in their genetic frequencies, in such a way to have the predominance of some genes and the disappearance of others in next generations, independently on the convenience of the predominant genes for the individuals. This statistical phenomenon is called founder effect, or bottleneck effect (in ecological dynamics). As an advancement in the study of dynamics of bio-molecular populations, and more in general of biological growing, in this paper we focus on the statistical phenomenon that a small sample of a heterogeneous population of species has a distribution of the species different than that in the original population, and independently on the initial distribution, after few steps of sampling and growing, an homogeneous population emerges, where only one of the initial species is present. This phenomenon is strictly related to the founder effect, attested in species evolution, which describes what happens when a few individuals of a population live isolated for several generations: a new colony is generated by a dominant (called founder) species. 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. (C) 2020 Published by Elsevier B.V.