Proper gromov transforms of metrics are metrics Original Research Article

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 nonexpansive map f : X → View the MathML source, the one-parameter family of the Gromov transforms DΔ,f of D relative to f and Δ that starts with D for large values of Δ and ends with an additive metric for Δ = 0 consists exclusively of metrics. It is expected that this result will help to better understand some standard tree reconstruction procedures considered in phylogenetic analysis.