Quantitative measure of randomness and order for complete genomes

We propose an order index, ϕ, which gives a quantitative measure of randomness and order of complete genomic sequences. It maps genomes to a number from 0 (random and of infinite length) to 1 (fully ordered) and applies regardless of sequence length. The 786 complete genomic sequences in GenBank were found to have ϕ values in a very narrow range, ϕ_g=0.031_−0.015^+0.028. We show this implies that genomes are halfway toward being completely random, or, at the “edge of chaos.” We further show that artificial “genomes” converted from literary classics have ϕ’s that almost exactly coincide with ϕ_g, but sequences of low information content do not. We infer that ϕ_g represents a high information-capacity “fixed point” in sequence space, and that genomes are driven to it by the dynamics of a robust growth and evolution process. We show that a growth process characterized by random segmental duplication can robustly drive genomes to the fixed point.