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