When is Menzerath-Altmann law mathematically trivial? A new approach
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 tha...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/27198 |
| Acceso en línea: | https://hdl.handle.net/2117/27198 https://dx.doi.org/10.1515/sagmb-2013-0034 |
| Access Level: | acceso abierto |
| Palabra clave: | Monte Carlo method Genomes Menzerath-Altmann law Power-laws Montecarlo, Mètode de Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica |
| Sumario: | 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. |
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