Computation of the Observed Spectral Sequence Spectrum for Nucleotide Sequence Alignments

Abstract

Phylogenetics deals with the task of reconstructing all the ancestral relations among a set of lineages. For any given phylogenetic tree that explains their evolution, subject to the Kimura Three Parameters Model, Hadamard Conjugation is an equation that relates its tree weights (within a matrix Q) to its substitution patterns distribution (within a matrix P) on leaves. In practice, the latter matrix is approximated via the DNA sequence alignment. Some challenges have to be faced in the process such as filling the gaps when they exist. Throughout this manuscript, it is provided fully explanation of how the matrix P can be approximated. The authors contribute to the scientific community with one library running on Maple to lead with these tasks. We conclude this work with a fully developed example focused on three spieces of orchids of the genus Lophiarella distributed in southwestern Mexico and northwestern Mesoamerica for which we obtained the matrix P.

Appendix

Voucher information and GenBank accesion numbers on nrITS DNA for taxa used in Sect. 3:

• Lophiarella flavovirens, Mexico, Colima, Carnevali 7270 (CICY), JQ319734;

• Lophiarella microchila, Mexico, Chiapas, Carnevali 7643 (CICY), JQ319735;

• Lophiarella splendida, Guatemala, Carnevali 7232 (CICY), JQ319736.

Nucleotide sequences, as they were used on Maple, are: