2014
Ferrer-i-Cancho, R.; Hernández-Fernández, A.; Baixeries, J.; Dębowski, Ł.; Mačutek, J.
When is Menzerath-Altmann law mathematically trivial? A new approach Journal Article
In: Statistical Applications in Genetics and Molecular Biology, vol. 13, no. 6, pp. 633-644, 2014.
Abstract | Links | BibTeX | Tags: genomes, Menzerath's law
@article{Ferrer2012h,
title = {When is Menzerath-Altmann law mathematically trivial? A new approach},
author = {R. Ferrer-i-Cancho and A. Hernández-Fernández and J. Baixeries and Ł. Dębowski and J. Mačutek},
doi = {10.1515/sagmb-2013-0034},
year = {2014},
date = {2014-01-01},
journal = {Statistical Applications in Genetics and Molecular Biology},
volume = {13},
number = {6},
pages = {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's law},
pubstate = {published},
tppubtype = {article}
}
2013
Ferrer-i-Cancho, R.; Forns, N.; Hernández-Fernández, A.; Bel-Enguix, G.; Baixeries, J.
The challenges of statistical patterns of language: the case of Menzerath's law in genomes Journal Article
In: Complexity, vol. 18, no. 3, pp. 11-17, 2013.
Abstract | Links | BibTeX | Tags: genomes, Menzerath's law
@article{Ferrer2012f,
title = {The challenges of statistical patterns of language: the case of Menzerath's law in genomes},
author = {R. Ferrer-i-Cancho and N. Forns and A. Hernández-Fernández and G. Bel-Enguix and J. Baixeries},
doi = {10.1002/cplx.21429},
year = {2013},
date = {2013-01-01},
journal = {Complexity},
volume = {18},
number = {3},
pages = {11-17},
abstract = {The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and genomes as a tendency of the mean size of the parts to decrease as the number of parts increases in many situations. This statistical regularity emerges also in the context of genomes, for instance, as a tendency of species with more chromosomes to have a smaller mean chromosome size. It has been argued that the instantiation of this law in genomes is not indicative of any parallel between language and genomes because (a) the law is inevitable and (b) noncoding DNA dominates genomes. Here mathematical, statistical, and conceptual challenges of these criticisms are discussed. Two major conclusions are drawn: the law is not inevitable and languages also have a correlate of noncoding DNA. However, the wide range of manifestations of the law in and outside genomes suggests that the striking similarities between noncoding DNA and certain linguistics units could be anecdotal for understanding the recurrence of that statistical law.},
keywords = {genomes, Menzerath's law},
pubstate = {published},
tppubtype = {article}
}
Ferrer-i-Cancho, R.; Baixeries, J.; Hernández-Fernández, A.
Erratum to "Random models of Menzerath-Altmann law in genomes" (BioSystems 107 (3), 167-173) Journal Article
In: Biosystems, vol. 111, no. 3, pp. 216-217, 2013.
Links | BibTeX | Tags: genomes, Menzerath's law
@article{Ferrer2012g,
title = {Erratum to "Random models of Menzerath-Altmann law in genomes" (BioSystems 107 (3), 167-173)},
author = {R. Ferrer-i-Cancho and J. Baixeries and A. Hernández-Fernández},
doi = {10.1016/j.biosystems.2013.01.004},
year = {2013},
date = {2013-01-01},
journal = {Biosystems},
volume = {111},
number = {3},
pages = {216-217},
keywords = {genomes, Menzerath's law},
pubstate = {published},
tppubtype = {article}
}
Baixeries, J.; Hernández-Fernández, A.; Forns, N.; Ferrer-i-Cancho, R.
The parameters of Menzerath-Altmann law in genomes Journal Article
In: Journal of Quantitative Linguistics, vol. 20, no. 2, pp. 94-104, 2013.
Abstract | Links | BibTeX | Tags: genomes, Menzerath's law
@article{Baixeries2012b,
title = {The parameters of Menzerath-Altmann law in genomes},
author = {J. Baixeries and A. Hernández-Fernández and N. Forns and R. Ferrer-i-Cancho},
doi = {10.1080/09296174.2013.773141},
year = {2013},
date = {2013-01-01},
journal = {Journal of Quantitative Linguistics},
volume = {20},
number = {2},
pages = {94-104},
abstract = {The relationship between the size of the whole and the size of the parts in language and music is known to follow the Menzerath-Altmann law at many levels of description (morphemes, words, sentences,...). Qualitatively, the law states that the larger the whole, the smaller its parts, e.g. the longer a word (in syllables) the shorter its syllables (in letters or phonemes). This patterning has also been found in genomes: the longer a genome (in chromosomes), the shorter its chromosomes (in base pairs). However, it has been argued recently that mean chromosome length is trivially a pure power function of chromosome number with an exponent of -1. The functional dependency between mean chromosome size and chromosome number in groups of organisms from three different kingdoms is studied. The fit of a pure power function yields exponents between -1.6 and 0.1. It is shown that an exponent of -1 is unlikely for fungi, gymnosperm plants, insects, reptiles, ray-finned fishes and amphibians. Even when the exponent is very close to -1, adding an exponential component is able to yield a better fit with regard to a pure power-law in plants, mammals, ray-finned fishes and amphibians. The parameters of the Menzerath-Altmann law in genomes deviate significantly from a power law with a -1 exponent with the exception of birds and cartilaginous fishes.},
keywords = {genomes, Menzerath's law},
pubstate = {published},
tppubtype = {article}
}
2012
Baixeries, J.; Hernández-Fernández, A.; Ferrer-i-Cancho, R.
Random models of Menzerath-Altmann law in genomes Journal Article
In: Biosystems, vol. 107, pp. 167-173, 2012.
Abstract | Links | BibTeX | Tags: genomes, Menzerath's law
@article{Baixeries2012a,
title = {Random models of Menzerath-Altmann law in genomes},
author = {J. Baixeries and A. Hernández-Fernández and R. Ferrer-i-Cancho},
doi = {10.1016/j.biosystems.2011.11.010},
year = {2012},
date = {2012-01-01},
journal = {Biosystems},
volume = {107},
pages = {167-173},
abstract = {Recently, a random breakage model has been proposed to explain the negative correlation between mean chromosome length and chromosome number that is found in many groups of species and is consistent with Menzerath-Altmann law, a statistical law that defines the dependency between the mean size of the whole and the number of parts in quantitative linguistics. Here, the central assumption of the model, namely that genome size is independent from chromosome number is reviewed. This assumption is shown to be unrealistic from the perspective of chromosome structure and the statistical analysis of real genomes. A general class of random models, including that random breakage model, is analyzed. For any model within this class, a power law with an exponent of -1 is predicted for the expectation of the mean chromosome size as a function of chromosome length, a functional dependency that is not supported by real genomes. The random breakage and variants keeping genome size and chromosome number independent raise no serious objection to the relevance of correlations consistent with Menzerath-Altmann law across taxonomic groups and the possibility of a connection between human language and genomes through that law.},
keywords = {genomes, Menzerath's law},
pubstate = {published},
tppubtype = {article}
}
2011
Hernández-Fernández, A.; Baixeries, J.; Forns, N.; Ferrer-i-Cancho, R.
Size of the whole versus number of parts in genomes Journal Article
In: Entropy, vol. 13, no. 8, pp. 1465-1480, 2011.
Abstract | Links | BibTeX | Tags: genomes
@article{Hernandez2011a,
title = {Size of the whole versus number of parts in genomes},
author = {A. Hernández-Fernández and J. Baixeries and N. Forns and R. Ferrer-i-Cancho},
doi = {10.3390/e13081465},
year = {2011},
date = {2011-01-01},
journal = {Entropy},
volume = {13},
number = {8},
pages = {1465-1480},
abstract = {It is known that chromosome number tends to decrease as genome size increases in angiosperm plants. Here the relationship between number of parts (the chromosomes) and size of the whole (the genome) is studied for other groups of organisms from different kingdoms. Two major results are obtained. First, the finding of relationships of the kind "the more parts the smaller the whole" as in angiosperms, but also relationships of the kind "the more parts the larger the whole". Second, these dependencies are not linear in general. The implications of the dependencies between genome size and chromosome number are two-fold. First, they indicate that arguments against the relevance of the finding of negative correlations consistent with Menzerath-Altmann law (a linguistic law that relates the size of the parts with the size of the whole) in genomes are seriously flawed. Second, they unravel the weakness of a recent model of chromosome lengths based upon random breakage that assumes that chromosome number and genome size are independent. It is known that chromosome number tends to decrease as genome size increases in angiosperm plants. Here the relationship between number of parts (the chromosomes) and size of the whole (the genome) is studied for other groups of organisms from different kingdoms. Two major results are obtained. First, the finding of relationships of the kind “the more parts the smaller the whole” as in angiosperms, but also relationships of the kind “the more parts the larger the whole”. Second, these dependencies are not linear in general. The implications of the dependencies between genome size and chromosome number are two-fold. First, they indicate that arguments against the relevance of the finding of negative correlations consistent with Menzerath-Altmann law (a linguistic law that relates the size of the parts with the size of the whole) in genomes are seriously flawed. Second, they unravel the weakness of a recent model of chromosome lengths based upon random breakage that assumes that chromosome number and genome size are independent.},
keywords = {genomes},
pubstate = {published},
tppubtype = {article}
}
2009
Ferrer-i-Cancho, R.; Forns, N.
The self-organization of genomes Journal Article
In: Complexity, vol. 15, no. 5, pp. 34-36, 2009.
Abstract | Links | BibTeX | Tags: genomes, Menzerath's law
@article{Ferrer2009e,
title = {The self-organization of genomes},
author = {R. Ferrer-i-Cancho and N. Forns},
doi = {10.1002/cplx.20296},
year = {2009},
date = {2009-01-01},
journal = {Complexity},
volume = {15},
number = {5},
pages = {34-36},
abstract = {Menzerath-Altmann law is a general law of human language stating, for instance, that the longer a word, the shorter its syllables. With the metaphor that genomes are words and chromosomes are syllables, we examine if genomes also obey the law. We find that longer genomes tend to be made of smaller chromosomes in organisms from three different kingdoms: fungi, plants, and animals. Our findings suggest that genomes self-organize under principles similar to those of human language.},
keywords = {genomes, Menzerath's law},
pubstate = {published},
tppubtype = {article}
}
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