Proper gromov transforms of metrics are metrics

In phylogenetic analysis, a standard problem is to approximate a given metric by an additive metric. Here it is shown that, given a metric D defined on some finite set X and a non-expansive map f : X R, the one-parameter family of the Gromov transforms D,f of D relative to f and that starts with D for large values of and ends with an additive metric for = 0 consists exclusively of metrics. It is expected that this result will help to better understand some standard tree reconstruction procedures considered in phylogenetic analyis. Keywords and Phrases: Metrics, additive metrics, additive metrics, ultra metrics Farris transforms, Gromov transforms, phylogenetic analysis, phylogenetic combinatorics

• Type: Journal
• Year: 2002
• Where: APPML
• Authors: Andreas W. M. Dress
• Keywords: Additive Metrics, APPML 2002, Metrics Farris Transforms, Phylogenetic Analysis