The Parameters of the Menzerath-Altmann Law in Genomes

Abstract

The relationship between the size of the whole and the size of the parts in language and music is known to follow the Menzerath-Altmann law at many levels of description (morphemes, words, sentences, …). Qualitatively, the law states that the larger the whole, the smaller its parts, e.g. the longer a word (in syllables) the shorter its syllables (in letters or phonemes). This patterning has also been found in genomes: the longer a genome (in chromosomes), the shorter its chromosomes (in base pairs). However, it has been argued recently that mean chromosome length is trivially a pure power function of chromosome number with an exponent of −1. The functional dependency between mean chromosome size and chromosome number in groups of organisms from three different kingdoms is studied. The fit of a pure power function yields exponents between −1.6 and 0.1. It is shown that an exponent of −1 is unlikely for fungi, gymnosperm plants, insects, reptiles, ray-finned fishes and amphibians. Even when the exponent is very close to −1, adding an exponential component is able to yield a better fit with regard to a pure power-law in plants, mammals, ray-finned fishes and amphibians. The parameters of the Menzerath-Altmann law in genomes deviate significantly from a power law with a −1 exponent with the exception of birds and cartilaginous fishes.