Yaneer Bar-Yam, Mean field theory and the gene centered view of evolution, New England Complex Systems Institute.
While recent years have seen a movement away from the gene centered view of evolution, it continues to have a strong hold on the conceptual foundations of biology. A formal understanding of the strengths and weakness of this view is lacking. In this article we show that the gene- centered view directly corresponds to a mean-field approximation in the reproduction-selection dynamics. This explains both why the gene centered view is useful and limited in application to evolution. Effective gene fitness result from (time dependent) averages over the current organism pool to obtain a mean-field environment for the gene. Such averaging is justified if mixing by sequel reproduction of the population is rapid compared o trait divergence of sub-populations. When trait-divergence is important, the mean field approximation breaks down. The latter is particularly important over larger time scales in understanding the global properties of evolution, where trait divergence and speciation are essential features to be understood.