An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets

G. William Moore, M. Goodman, J. Barnabas

Research output: Contribution to journalArticle

Abstract

The problem of constructing a dendrogram depicting phylogenetic relationships for a collection of contemporary species is considered. An approach was developed based on the additive hypothesis in which each "length" between two species can be described by the shortest sum of lengths for the individual links on the dendrogram topology which connect the two species. The additive hypothesis holds equally well if the dendro gram is replaced by its corresponding (rootless) network. Network topologies are defined set theoretically in terms of the initial, contemporary species, and a coefficient is defined for each point of any conceivable network. It is proved mathematically that each point of an additive network gives a coefficient value of zero, whereas each point not belonging to an additive network gives a coefficient value greater than zero. This suggests an iterative procedure in which "false" network points are replaced by "true" ones, or more generally in which "very false" network points are replaced by "nearly true" ones. The first procedure follows from the mathematical proof and the second is confirmed by simulation. Since most real data sets are not additive in the strict sense, a real data example was presented in which the iterative procedure produced a plausible network topology.

Original languageEnglish (US)
Pages (from-to)423-457
Number of pages35
JournalJournal of Theoretical Biology
Volume38
Issue number3
DOIs
StatePublished - 1973
Externally publishedYes

Fingerprint

Dendrogram
Topology
topology
Iterative Procedure
Network Topology
Coefficient
Zero
Phylogenetics
Datasets
phylogeny

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets. / Moore, G. William; Goodman, M.; Barnabas, J.

In: Journal of Theoretical Biology, Vol. 38, No. 3, 1973, p. 423-457.

Research output: Contribution to journalArticle

@article{e63460ded502494bae26a7a1645428a7,
title = "An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets",
abstract = "The problem of constructing a dendrogram depicting phylogenetic relationships for a collection of contemporary species is considered. An approach was developed based on the additive hypothesis in which each {"}length{"} between two species can be described by the shortest sum of lengths for the individual links on the dendrogram topology which connect the two species. The additive hypothesis holds equally well if the dendro gram is replaced by its corresponding (rootless) network. Network topologies are defined set theoretically in terms of the initial, contemporary species, and a coefficient is defined for each point of any conceivable network. It is proved mathematically that each point of an additive network gives a coefficient value of zero, whereas each point not belonging to an additive network gives a coefficient value greater than zero. This suggests an iterative procedure in which {"}false{"} network points are replaced by {"}true{"} ones, or more generally in which {"}very false{"} network points are replaced by {"}nearly true{"} ones. The first procedure follows from the mathematical proof and the second is confirmed by simulation. Since most real data sets are not additive in the strict sense, a real data example was presented in which the iterative procedure produced a plausible network topology.",
author = "Moore, {G. William} and M. Goodman and J. Barnabas",
year = "1973",
doi = "10.1016/0022-5193(73)90251-8",
language = "English (US)",
volume = "38",
pages = "423--457",
journal = "Journal of Theoretical Biology",
issn = "0022-5193",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - An iterative approach from the standpoint of the additive hypothesis to the dendrogram problem posed by molecular data sets

AU - Moore, G. William

AU - Goodman, M.

AU - Barnabas, J.

PY - 1973

Y1 - 1973

N2 - The problem of constructing a dendrogram depicting phylogenetic relationships for a collection of contemporary species is considered. An approach was developed based on the additive hypothesis in which each "length" between two species can be described by the shortest sum of lengths for the individual links on the dendrogram topology which connect the two species. The additive hypothesis holds equally well if the dendro gram is replaced by its corresponding (rootless) network. Network topologies are defined set theoretically in terms of the initial, contemporary species, and a coefficient is defined for each point of any conceivable network. It is proved mathematically that each point of an additive network gives a coefficient value of zero, whereas each point not belonging to an additive network gives a coefficient value greater than zero. This suggests an iterative procedure in which "false" network points are replaced by "true" ones, or more generally in which "very false" network points are replaced by "nearly true" ones. The first procedure follows from the mathematical proof and the second is confirmed by simulation. Since most real data sets are not additive in the strict sense, a real data example was presented in which the iterative procedure produced a plausible network topology.

AB - The problem of constructing a dendrogram depicting phylogenetic relationships for a collection of contemporary species is considered. An approach was developed based on the additive hypothesis in which each "length" between two species can be described by the shortest sum of lengths for the individual links on the dendrogram topology which connect the two species. The additive hypothesis holds equally well if the dendro gram is replaced by its corresponding (rootless) network. Network topologies are defined set theoretically in terms of the initial, contemporary species, and a coefficient is defined for each point of any conceivable network. It is proved mathematically that each point of an additive network gives a coefficient value of zero, whereas each point not belonging to an additive network gives a coefficient value greater than zero. This suggests an iterative procedure in which "false" network points are replaced by "true" ones, or more generally in which "very false" network points are replaced by "nearly true" ones. The first procedure follows from the mathematical proof and the second is confirmed by simulation. Since most real data sets are not additive in the strict sense, a real data example was presented in which the iterative procedure produced a plausible network topology.

UR - http://www.scopus.com/inward/record.url?scp=0015594566&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0015594566&partnerID=8YFLogxK

U2 - 10.1016/0022-5193(73)90251-8

DO - 10.1016/0022-5193(73)90251-8

M3 - Article

C2 - 4632522

AN - SCOPUS:0015594566

VL - 38

SP - 423

EP - 457

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 3

ER -