Phylogenetic invariants for stationary base composition

Changing base composition during the evolution of biological sequences can mislead some of the phylogenetic inference techniques in current use. However, detecting whether such a process has occurred may be difficult, since convergent evolution may lead to similar base frequencies emerging from different lineages. To study this situation, algebraic models of biological sequence evolution are introduced in which the base composition is fixed throughout evolution. Basic properties of the associated algebraic varieties are investigated, including the construction of some phylogenetic invariants.