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

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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)

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.

Suggested Citation

  • Ferrer-i-Cancho Ramon & Hernández-Fernández Antoni & Baixeries Jaume & Dębowski Łukasz & Mačutek Ján, 2014. "When is Menzerath-Altmann law mathematically trivial? A new approach," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(6), pages 633-644, December.
    • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:6:p:12:n:1
    DOI: 10.1515/sagmb-2013-0034
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    References listed on IDEAS

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