Evolvability Analysis: Distribution of Hyperbiobs in a Variable-Length Protein Genotype Space

A variable-length protein genotype space (the whole amino-acid sequence space) is mathematically analyzed and a lower threshold density for adequate connectivity of functional (viable) genotypes is estimated. Functional genotypes are assumed to distribute as a ‘hyperblob’ which means a cluster or an island, and connectivity between hyperblobs is estimated using the theory of regular languages and the random graph theory. It is shown that the logarithmic value of the threshold density approximately decreases with an increase in the genotype length