Dawkins4 argued that even though it may, at first, seem unlikely that such a complex structure as the eye evolved by selection, it could have been realized by a long sequence of small evolutionary steps driven by selection. Theobald2 mentions that statistically significant sequence similarity can arise from factors other than common ancestry, such as convergent evolution due to selection, but such factors were not taken into account in his ‘formal’ test to reject the independent origins hypothesis.

Table 1 shows that the formal test provides support for a common origin of two putatively unrelated genes, mitochondrial cytb and nd2, with no homology. However, we believe that this result should not be regarded as evidence of the ultimate common ancestry of cytb and nd2. This raises a question mark as to the effectiveness of the formal test applied by Theobald2. It should be noted that, because alignment gives a bias for common ancestry, we did not make an alignment between cytb and nd2. To reject the separate origins hypothesis of the domains of life, it would be indispensable to develop a more ‘biological’ test to show that even by improving the model of the separate origins by taking into account biological factors such as the possibility of convergent evolution due to selection, the UCA hypothesis is still supported by the AIC. To do this, it is necessary to develop an entirely new methodological framework of molecular phylogenetics that is different from the conventional framework that neglects convergent and parallel evolution. Notably, there have been many reported cases of convergent and parallel evolution misleading molecular phylogenetic inference5,6,7,8,9, and such a method is needed for molecular phylogenetics in general.

Table 1 A formal test of the common ancestry between mitochondrial genes cytb and nd2