A remarkable nonlinear invariant for evolution with heterogeneous rates.
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.
Ferretti
V
V
Centre de recherches mathématiques, Université de Montréal, Québec, Canada.
Sankoff
D
D
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
D011506:Proteins; D004247:DNA