The Euclidean Distance in the Space of Genomic Descriptors: A Formal Approach

Genomes are often described through indices and quantitative measures, as well as through distance measures commonly used in comparative analyses. However, the minimal mathematical framework that makes such comparisons possible is not always made explicit, and the calculated distances are sometimes assigned interpretative meanings that are not biologically justified.This study introduces a mathematical approach to represent genomes as elements of an N-dimensional space, starting from a set of classical genomic descriptors. Within this framework, the Euclidean distance represents the simplest possible measure, independently of the biological nature of the descriptors considered. The geometric effects of dimensionality, descriptor redundancy, and scale differences are discussed. In addition, the conditions under which distances can be compared are defined, with particular attention to the role of normalization.The work clearly separates the problem of measurement from that of interpretation, limiting itself to describing the mathematical framework within which distances exist. In particular, a representation of genomes based solely on the frequencies of the four nucleotide bases defines a very simple Euclidean space in which the calculated distances measure only the genomic compositional separation between sequences.