Darwinian selection, limitations

It is obvious that such a ruthless all-or-none decision could neither be a consequence of random production nor result from interactions as they are responsible for chemical equilibrium, which always settles on finite concentration ratios. It is indeed the peculiar mechanism of the reproduction process far from equilibrium that accounts for the fact of survival, and this mechanism is even active when the competitors are degenerate in their selective values, that is, if they are neutral competitors. In this limiting case, considered to be very important for the evolution of species, Darwin s principle indeed reduces to the mere tautology survival of the survivor. Nevertheless, there are, even here, systematic quantitative regularities in the way that macroscopic populations of wild types rise and fall in a deterministic manner (as far as the process, not the particular copy choice, is concerned), which make it anything but a trivial correlation. This case of neutral selection has been called non-Darwinian. It should be emphasized, however, that Darwin was well aware of this possibility and described it verbally in a quite adequate way. The precise formulation of a theory of neutral selection, which then allows us to draw quantitative conclusions on the evolution of species is an achievement of the second half of this century. Kimura [2] has pioneered this new branch of population genetics. 

The typical outcome of quasi-species behavior is natural selection in the Darwinian sense. We believe that it should be possible to adapt the quasispecies model to any situation where natural selection in the Darwinian sense plays a major role. Hence the model may be generalized so as to include all kinds of horizontal gene transfer typical for recombination. The model as presented is essentially a deterministic model that holds only for a sufficiently large population size. This limitation and a possible way to overcome it will be the subject of the final section. 

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