Some uses of the Farris Transform in mathematics and phylogenetics - A review

Dress, A., Huber, K. T. and Moulton, V. ORCID: (2007) Some uses of the Farris Transform in mathematics and phylogenetics - A review. Annals of Combinatorics, 11 (1). pp. 1-37. ISSN 0218-0006

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In 1970, Farris introduced a procedure that can be used to transform a tree metric into an ultra metric. Since its discovery, Farris’ procedure has been used extensively within phylogenetics where it has become commonly known as the Farris transform. Remarkably, the Farris transform has not only been rediscovered several times within phylogenetics, but also in other fields. In this paper, we will review some of its various properties and uses. The paper is divided into four parts and, altogether, 12 sections. In the first part, we introduce a standardized scheme for classifying those dissimilarity mappings to which the Farris transform can be applied—a scheme that has evolved over the years, but has apparently not been spelled out before in sufficient detail. In the second part, we will discuss how a straightforward generalization of the Farris transform naturally arises in T-Theory. The third part describes how this generalized Farris transform can be used to approximate dissimilarities by tree metrics. And in the final part, we describe some further, “non-standard” applications of the Farris transform.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: Vishal Gautam
Date Deposited: 05 Apr 2011 07:35
Last Modified: 02 Feb 2023 11:30
DOI: 10.1007/s00026-007-0302-5

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