Wagner's canalization model.

Wagner (1996, Does evolutionary plasticity evolve? Evolution 50, 1008-1023.) and Siegal and Bergman, 2002 and Azevedo et al., 2006 have studied a simple model of the evolution of a network of N genes, in order to explain the observed phenomenon that systems evolve to be robust. These authors primarily considered the case N=10 and used simulations to reach their conclusions. Here we investigate this model in more detail, considering systems of different sizes with and without recombination, and with selection for convergence instead of to a specified limit. For the simpler evolutionary model lacking recombination, we analyze the system as a neutral network. This allows us to describe the equilibrium distribution networks within genotype space. Our results show that, given a sufficiently large population size, the qualitative observation that systems evolve to be robust, is itself robust, as it does not depend on the details of the model. In simple terms, robust systems have more viable offspring, so the evolution of robustness is merely selection for increased fecundity, an observation that is well known in the theory of neutral networks.