Spectral analysis and a closest tree method for genetic sequences
This paper deals with the reconstruction of evolutionary trees from aligned genetic sequences. Nucleotide sequences are assumed to evolve according to Kimura's 3-parameter model [cf. \textit{M. Kimura}, Proc. Natl. Acad. Sci. USA 78, 454-458 (1981; Zbl 0511.92013)] which can be formulated in a group-theoretic context by identifying the set of four nucleotides with the Kleinian group \(\mathbb{Z}_ 2\times \mathbb{Z}_ 2\) and considering colorations of species by elements of this group. The authors define conjugate spectra of sequence data and use discrete Fourier transformation methods to estimate the underlying evolutionary tree. These methods, like the principle of maximum parsimony, have the property of providing a tree which minimizes an explicitly representable function of the data and allow the development of a branch-and-bound algorithm.
scientific article; zbMATH DE number 148552