title: Necessary and sufficient conditions for the existence of linear invariants in phylogenetic inference.
abstract: The necessary and sufficient conditions for the existence of linear invariants under semigroups of probability transition matrices are derived. It is found that a biologically meaningful nucleotide substitution model has linear invariants if and only if it is a submodel of one of the three most general models, which include the so-called balanced and unbalanced transversion models. Each of these three general models is a nucleotide substitution model with six parameters.
authors.affiliation: Center for Demographic and Population Genetics, University of Texas, Houston 77225.
authors.forename: Y X
authors.initials: YX
authors.lastname: Fu
authors.forename: W H
authors.initials: WH
authors.lastname: Li
mesh_terms: D004247:DNA / Q000235:genetics*; D015233:Models, Statistical; D010802:Phylogeny; D011336:Probability
chemical_list: D004247:DNA