When is Menzerath-Altmann law mathematically trivial? A new approach
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Ramon Ferrer-i-Cancho
,
Antoni Hernández-Fernández
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.
Acknowledgments
This article has benefited enormously from the comments of anonymous reviewers. We are grateful to P. Delicado, R. Gavaldà and E. Pons for their valuable mathematical insights. We owe the counterexample showing that uncorrelation does not imply mean independence to P. Delicado. We are also grateful to G. Bel-Enguix and N. Forns for helpful discussions. This work was supported by the grant Iniciació i reincorporació a la recerca from the Universitat Politècnica de Catalunya, the grants BASMATI (TIN2011-27479-C04-03) and OpenMT-2 (TIN2009-14675-C03) from the Spanish Ministry of Science and Innovation and the grant 2/0038/12 from the VEGA funding agency (JM).
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©2014 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Research Articles
- When is Menzerath-Altmann law mathematically trivial? A new approach
- Covariate adjusted differential variability analysis of DNA methylation with propensity score method
- P-value calibration for multiple testing problems in genomics
- Robust methods to detect disease-genotype association in genetic association studies: calculate p-values using exact conditional enumeration instead of simulated permutations or asymptotic approximations
- Markovianness and conditional independence in annotated bacterial DNA
- Exploring homogeneity of correlation structures of gene expression datasets within and between etiological disease categories
- Corrigendum
- Biological pathway selection through Bayesian integrative modeling
Artikel in diesem Heft
- Frontmatter
- Research Articles
- When is Menzerath-Altmann law mathematically trivial? A new approach
- Covariate adjusted differential variability analysis of DNA methylation with propensity score method
- P-value calibration for multiple testing problems in genomics
- Robust methods to detect disease-genotype association in genetic association studies: calculate p-values using exact conditional enumeration instead of simulated permutations or asymptotic approximations
- Markovianness and conditional independence in annotated bacterial DNA
- Exploring homogeneity of correlation structures of gene expression datasets within and between etiological disease categories
- Corrigendum
- Biological pathway selection through Bayesian integrative modeling
