Random models of Menzerath-Altmann law in genomes.

Recently, a random breakage model has been proposed to explain the negative correlation between mean chromosome length and chromosome number that is found in many groups of species and is consistent with Menzerath-Altmann law, a statistical law that defines the dependency between the mean size of the whole and the number of parts in quantitative linguistics. Here, the central assumption of the model, namely that genome size is independent from chromosome number is reviewed. This assumption is shown to be unrealistic from the perspective of chromosome structure and the statistical analysis of real genomes. A general class of random models, including that random breakage model, is analyzed. For any model within this class, a power law with an exponent of -1 is predicted for the expectation of the mean chromosome size as a function of chromosome length, a functional dependency that is not supported by real genomes. The random breakage and variants keeping genome size and chromosome number independent raise no serious objection to the relevance of correlations consistent with Menzerath-Altmann law across taxonomic groups and the possibility of a connection between human language and genomes through that law.