Quantitative measure of randomness and order for complete genomes

We propose an order index, phi, 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 phi values in a very narrow range, phi(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 phi's that almost exactly coincide with phi(g), but sequences of low information content do not. We infer that phi(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.