MAXIMUM-LIKELIHOOD MODELS FOR COMBINED ANALYSES OF MULTIPLE SEQUENCE DATA

Models of nucleotide substitution were constructed for combined analys es of heterogeneous sequence data (such as those of multiple genes) fr om the same set of species. The models account for different aspects o f the heterogeneity in the evolutionary process of different genes, su ch as differences in nucleotide frequencies, in substitution rate bias (for example, the transition/transversion rate bias), and in the exte nt of rate variation across sites. Model parameters were estimated by maximum likelihood and the likelihood ratio test was used to test hypo theses concerning sequence evolution, such as rate constancy among lin eages (the assumption of a molecular clock) and proportionality of bra nch lengths for different genes. The example data from a segment of th e mitochondrial genome of six hominoid species (human, common and pygm y chimpanzees, gorilla, orangutan, and siamang) were analyzed. Nucleot ides at the three codon positions in the protein-coding regions and fr om the tRNA-coding regions were considered heterogeneous data sets. St atistical tests showed that the amount of evolution in the sequence da ta reflected in the estimated branch lengths can be explained by the c odon-position effect and lineage effect of substitution rates. The ass umption of a molecular clock could not be rejected when the data were analyzed separately or when the rate variation among sites was ignored . However, significant differences in substitution rate among lineages were found when the data sets were combined and when the rate variati on among sites was accounted for in the models. Under the assumption t hat the orangutan and African apes diverged 13 million years ago, the combined analysis of the sequence data estimated the times for the hum an-chimpanzee separation and for the separation of the gorilla as 4.3 and 6.8 million years ago, respectively.