  Large sets of genotypes give rise to the same phenotype because phenotypic
expression is highly redundant. Accordingly, a population can accept mutations
without altering its phenotype, as long as thegenotype mutates into another one
on the same set. By linking every pair of genotypes that are mutually
accessible through mutation, genotypes organize themselves into neutral
networks (NN). These networks are known to be heterogeneous and assortative,
and these properties affect the evolutionary dynamics of the population. By
studying the dynamics of populations on NN with arbitrary topology we analyze
the effect of assortativity, of NN (phenotype) fitness, and of network size. We
find that the probability that the population leaves the network is smaller the
longer the time spent on it. This progressive "phenotypic entrapment" entails a
systematic increase in the overdispersion of the process with time and an
acceleration in the fixation rate of neutral mutations. We also quantify the
variation of these effects with the size of the phenotype and with its fitness
relative to that of neighbouring alternatives.
