Molecular data support a rapid radiation of aphids in the Cretaceous and multiple origins of host alternation

A maximum likelihood method for inferring evolutionary trees from DNA sequence data was developed by Felsenstein (1981). In evaluating the extent to which the maximum likelihood tree is a significantly better representation of the true tree, it is important to estimate the variance of the difference between log likelihood of different tree topologies. Bootstrap resampling can be used for this purpose (Hasegawa et al. 1988; Hasegawa and Kishino 1989), but it imposes a great computation burden. To overcome this difficulty, we developed a new method for estimating the variance by expressing it explicitly. The method was applied to DNA sequence data from primates in order to evaluate the maximum likelihood branching order among Hominoidea. It was shown that, although the orangutan is convincingly placed as an outgroup of a human and African apes clade, the branching order among human, chimpanzee, and gorilla cannot be determined confidently from the DNA sequence data presently available when the evolutionary rate constancy is not assumed.

DNA sequence evolution through nucleotide substitution may be assimilated to a stationary Markov process. The fundamental equations of the general model, with 12 independent substitution parameters, are used to obtain a formula which corrects the effect of multiple and parallel substitutions on the measure of evolutionary divergence between two homologous sequences. We show that only reversible models, with six independent parameters, allow the calculation of the substitution rates. Simulation experiments on DNA sequence evolution through nucleotide substitution call into question the effectiveness of the general model (and of any other more detailed description); nevertheless, the general model results are slightly superior to any of its particular cases.