Maximum likelihood estimation is known to be provably consistent under a wide variety of conditions (Wald 1949), but several authors have argued that these conditions do not apply to estimating the tree topology since tree topologies are discrete, not continuous, parameters (Yang 1996; Siddall 1998; Farris 1999). However, Swofford et al. (2001) argue that Wald’s conditions do apply and Yang (1994), Chang (1996), and Rogers (2001) prove that maximum likelihood is consistent under different assump