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A unified and universal explanation for Levy laws and 1/f noises.

ABSTRACT: Lévy laws and 1/f noises are shown to emerge uniquely and universally from a general model of systems which superimpose the transmissions of many independent stochastic signals. The signals are considered to follow, statistically, a common--yet arbitrary--generic signal pattern which may be either stationary or dissipative. Each signal is considered to have its own random transmission amplitude and frequency. We characterize the amplitude-frequency randomizations which render the system output's stationary law and power-spectrum universal--i.e., independent of the underlying generic signal pattern. The classes of universal stationary laws and power spectra are shown to coincide, respectively, with the classes of Lévy laws and 1/f noises--thus providing a unified and universal explanation for the ubiquity of these classes of "anomalous statistics" in various fields of science and engineering.

SUBMITTER: Eliazar I

PROVIDER: S-EPMC2709667 | biostudies-literature | 2009 Jul

REPOSITORIES: biostudies-literature

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A unified and universal explanation for Lévy laws and 1/f noises.

Eliazar Iddo I Klafter Joseph J

Proceedings of the National Academy of Sciences of the United States of America 20090713 30

Lévy laws and 1/f noises are shown to emerge uniquely and universally from a general model of systems which superimpose the transmissions of many independent stochastic signals. The signals are considered to follow, statistically, a common--yet arbitrary--generic signal pattern which may be either stationary or dissipative. Each signal is considered to have its own random transmission amplitude and frequency. We characterize the amplitude-frequency randomizations which render the system output's ...[more]

PMID: 19597146

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Project description:BackgroundThe superficial resemblance of phylogenetic trees to other branching structures allows searching for macroevolutionary patterns. However, such trees are just statistical inferences of particular historical events. Recent meta-analyses report finding regularities in the branching pattern of phylogenetic trees. But is this supported by evidence, or are such regularities just methodological artifacts? If so, is there any signal in a phylogeny?MethodologyIn order to evaluate the impact of polytomies and imbalance on tree shape, the distribution of all binary and polytomic trees of up to 7 taxa was assessed in tree-shape space. The relationship between the proportion of outgroups and the amount of imbalance introduced with them was assessed applying four different tree-building methods to 100 combinations from a set of 10 ingroup and 9 outgroup species, and performing covariance analyses. The relevance of this analysis was explored taking 61 published phylogenies, based on nucleic acid sequences and involving various taxa, taxonomic levels, and tree-building methods.Principal findingsAll methods of phylogenetic inference are quite sensitive to the artifacts introduced by outgroups. However, published phylogenies appear to be subject to a rather effective, albeit rather intuitive control against such artifacts. The data and methods used to build phylogenetic trees are varied, so any meta-analysis is subject to pitfalls due to their uneven intrinsic merits, which translate into artifacts in tree shape. The binary branching pattern is an imposition of methods, and seldom reflects true relationships in intraspecific analyses, yielding artifactual polytomies in short trees. Above the species level, the departure of real trees from simplistic random models is caused at least by two natural factors--uneven speciation and extinction rates; and artifacts such as choice of taxa included in the analysis, and imbalance introduced by outgroups and basal paraphyletic taxa. This artifactual imbalance accounts for tree shape convergence of large trees.SignificanceThere is no evidence for any universal scaling in the tree of life. Instead, there is a need for improved methods of tree analysis that can be used to discriminate the noise due to outgroups from the phylogenetic signal within the taxon of interest, and to evaluate realistic models of evolution, correcting the retrospective perspective and explicitly recognizing extinction as a driving force. Artifacts are pervasive, and can only be overcome through understanding the structure and biological meaning of phylogenetic trees. Catalan Abstract in Translation S1.

Dataset Information

A unified and universal explanation for Levy laws and 1/f noises.

Publications

A unified and universal explanation for Lévy laws and 1/f noises.

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