The parameters of Menzerath-Altmann law in genomes

TL;DR

This study investigates the relationship between genome size and chromosome number across various organisms, revealing that the Menzerath-Altmann law does not generally follow a simple power law with an exponent of -1, except in some cases.

Contribution

It provides a detailed analysis of the parameters of Menzerath-Altmann law in genomes, challenging the notion that mean chromosome length is a trivial power function of chromosome number.

Findings

Exponent of -1 is unlikely for many organism groups.

Adding an exponential component improves fit in several groups.

Parameters deviate significantly from power law with exponent -1 in most cases.

Abstract

The relationship between the size of the whole and the size of the parts in language and music is known to follow Menzerath-Altmann law at many levels of description (morphemes, words, sentences...). Qualitatively, the law states that 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 Menzerath-Altmann law in genomes deviate significantly from a power law with a -1 exponent with the exception of birds and cartilaginous fishes.