Graphs in sequence spaces: a review of statistical geometry

Statistical geometry is a method of comparative sequence analysis of genes. Based on the concept of the sequence space of nucleic acids it computes the geometries of sequence sets, mainly quartets, by combining both the vertical and horizontal information content of the sequences. The geometries can be used to deduce, for example, the degree of tree-likeness of the data set without any a priori assumption of an evolution model. Furthermore, statistical geometry allows to detect varying positional substitution rates in sequences. Applications of the method to tRNA sequences have provided an assessment for the age of the genetic code. Furthermore, applications of statistical geometry to homeoboxes as well as different virus families have helped to assign reliable kinship relationships. In addition, a lower bound for the age of the common ancestor of the human and simian immunodeficiency viruses has been established.