Multiplicity of phenotypes and RNA evolution.

Motivation Motoo Kimura's neutral theory stipulates that evolution is predominantly driven by neutral mutations. RNA, realizing both genotype (its linear sequence of nucleotides) as well as phenotype (its folded secondary structure) represents a particularly well suited test bed for studying neutrality. This leads to neutral networks of RNA secondary structures, i.e. sets of sequences all of which folding into a fixed phenotype and whose organization plays a crucial role for neutral evolution. In this paper we bring a new perspective to the neutral theory by studying the consequences of the mostly ignored fact that the genotype-to-phenotype map for RNA is often one-to-many. In fact 29.5% of random RNA sequences realize more than one phenotype (minimum free energy structure). We call two genotypes to be quasineutral if their sets of associated phenotypes have non-empty intersection. Results We show that even though the energy profile of quasineutral mutations is almost identical to the neutral ones, a walk in the genotype space whose consecutive steps are quasineutral, can percolate phenotype space and so such walks bridge between neutral and random walks. This provides further evidence that evolution is continuous. We also study how these drift walks transition between neutral networks.