Non-ultrametric phylogenetic trees shed new light on Neanderthal introgression.

Ultrametric spaces are widely used to depict evolutionary times in phylogenetic trees since they assume that every population/species is located at the tips of bifurcating branches of the same length. The discrete branching of ultrametric trees permits the measurement of distances between pairs of individuals that are proportional to their divergence time. Here the traditional ultrametric concept of bifurcating and divergent phylogenetic tree is overturned and a new type of non-ultrametric diagram is introduced. The objective of this study is the description of gene flows in branching species/populations in terms of converging trees instead of bifurcating trees. To provide an operational example, the paleoanthropological issue of the date of Neanderthal genome's introgression in non-African humans is examined. Neanderthals and ancient humans are not anymore two species that exchange chunks of DNA, rather become a single, novel cluster of extant hominins that must be considered by itself. The novel converging, non-ultrametric phylogenetic trees permit the calibration of molecular clocks with a twofold benefit. When the date of the branching of two population/species from a common ancestor is known, the novel approach allows to calculate the time of subsequent introgressions. On the contrary, when the date of the introgression between two population/species is known, the novel approach allows to detect the time of their previous branching from a common ancestor.