Large sets of genotypes give rise to the same phenotype because phenotypic expressionis highly redundant. Accordingly, a population can accept mutations without alteringits phenotype, as long as the genotype mutates into another one on the same set. BylinkinLarge sets of genotypes give rise to the same phenotype because phenotypic expressionis highly redundant. Accordingly, a population can accept mutations without alteringits phenotype, as long as the genotype mutates into another one on the same set. Bylinking every pair of genotypes that are mutually accessible through mutation, geno-types organize themselves into neutral networks (NN). These networks are known to beheterogeneous and assortative, and these properties affect the evolutionary dynamics ofthe population. By studying the dynamics of populations on NN with arbitrary topol-ogy we analyze the effect of assortativity, of NN (phenotype) fitness, and of networksize. We find that the probability that the population leaves the network is smallerthe longer the time spent on it. This progressive "phenotypic entrapment" entails asystematic increase in the overdispersion of the process with time and an accelerationin the fixation rate of neutral mutations.[+][-]