A new theory of phylogeny inference through construction of multidimensional vector space

Abstract

Here, a new theory of molecular phylogeny is developed in a multidimensional vector space (MVS). The molecular evolution is represented as a successive splitting of branch vectors in the MVS. The end points of these vectors are the extant species and indicate the specific directions reflected by their individual histories of evolution in the past. This representation makes it possible to infer the phylogeny (evolutionary histories) from the spatial positions of the end points. Search vectors are introduced to draw out the groups of species distributed around them. These groups are classified according to the nearby order of branches with them. A law of physics is applied to determine the species positions in the MVS. The species are regarded as the particles moving in time according to the equation of motion, finally falling into the lowest-energy state in spite of their randomly distributed initial condition. This falling into the ground state results in the construction of an MVS in which the relative distances between two particles are equal to the substitution distances. The species positions are obtained prior to the phylogeny inference. Therefore, as the number of species increases, the species vectors can be more specific in an MVS of a larger size, such that the vector analysis gives a more stable and reliable topology. The efficacy of the present method was examined by using computer simulations of molecular evolution in which all the branch- and end-point sequences of the trees are known in advance. In the phylogeny inference from the end points with 100 multiple data sets, the present method consistently reconstructed the correct topologies, in contrast to standard methods. In applications to 185 vertebrates in the α-hemoglobin, the vector analysis drew out the two lineage groups of birds and mammals. A core member of the mammalian radiation appeared at the base of the mammalian lineage. Squamates were isolated from the bird lineage to compose the outgroup, while the other living reptilians were directly coupled with birds without forming any sister groups. This result is in contrast to the morphological phylogeny and is also different from those of recent molecular analyses.