title: A remarkable nonlinear invariant for evolution with heterogeneous rates.
abstract: A model for DNA or protein sequence evolution is proposed where each position belongs to one of two distinct classes. The two classes evolve at different rates. For a phylogeny on four species, we find a cubic function of 4-tuple occurrence frequencies that is nontrivially invariant no matter what the proportion of positions in each rate class. This result refutes the major criticism of nonlinear polynomial invariants.
authors.affiliation: Centre de recherches mathématiques, Université de Montréal, Québec, Canada.
authors.forename: V
authors.initials: V
authors.lastname: Ferretti
authors.forename: D
authors.initials: D
authors.lastname: Sankoff
mesh_terms: D004247:DNA / Q000235:genetics; D019143:Evolution, Molecular; D016014:Linear Models; D008433:Mathematics; D008957:Models, Genetic; D017711:Nonlinear Dynamics; D010802:Phylogeny; D011506:Proteins / Q000235:genetics; D013269:Stochastic Processes
chemical_list: D011506:Proteins; D004247:DNA