When is Menzerath-Altmann law mathematically trivial? A new approach

Ferrer-i-Cancho Ramon (), Hernández-Fernández Antoni, Baixeries Jaume, Dębowski Łukasz and Mačutek Ján
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Ferrer-i-Cancho Ramon: Complexity and Quantitative Linguistics Lab, LARCA Research Group, Departament de Ciències de la Computació, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, Jordi Girona Salgado 1-3, 08034 Barcelona (Catalonia), Spain
Hernández-Fernández Antoni: Complexity and Quantitative Linguistics Lab, LARCA Research Group, Departament de Ciències de la Computació, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, Jordi Girona Salgado 1-3, 08034 Barcelona (Catalonia), Spain Departament de Lingüística General, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona (Catalonia), Spain
Baixeries Jaume: Complexity and Quantitative Linguistics Lab, LARCA Research Group, Departament de Ciències de la Computació, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, Jordi Girona Salgado 1-3, 08034 Barcelona (Catalonia), Spain
Dębowski Łukasz: Institute of Computer Science, Polish Academy of Sciences, ul. Jana Kazimierza 5, 01-248 Warszawa, Poland
Mačutek Ján: Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia

Statistical Applications in Genetics and Molecular Biology, 2014, vol. 13, issue 6, 633-644

Abstract: Menzerath’s law, the tendency of Z (the mean size of the parts) to decrease as X (the number of parts) increases, is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z=Y/X, which would imply that Z scales with X as Z∼1/X. That scaling is a very particular case of Menzerath-Altmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z∼1/X in genomes. The most powerful test is a new non-parametric one based upon the correlation ratio, which is able to reject Z∼1/X in nine out of 11 taxonomic groups and detect a borderline group. Rather than a fact, Z∼1/X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.

Keywords: genomes; Menzerath-Altmann law; Monte Carlo methods; power-laws (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1515/sagmb-2013-0034

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