A measure of the denseness of a phylogenetic network

The concept of phylogenetic denseness bears critically on the accuracy of evolutionary pathways inferred from experimentally sequenced proteins isolated from extant species. In this paper I develop an objective measure, rho, of denseness to supplement previous intuitive concepts and which permits one to use this concept in comparing the quality of different evolutionary reconstructions. This measure is used to examine several published phylogenetic trees: insulin, alpha-hemoglobin, beta-hemoglobin, myoglobin, cytochrome c, and the parvalbumin family. The paper emphasizes 1) the importance of denseness in accurately estimating the number of nucleotide replacements which separate homologous sequences when this estimation is made by the method of parsimony, 2) the value of this concept in assessing the quality of those estimates, and 3) the use of this concept as a biologically practical heuristic method for identifying poorly studied regions in a phylogenetic tree, whether or not the tree was obtained by the parsimony method.