Infinitely long branches and an informal test of common ancestry

Background: The evidence for universal common ancestry (UCA) is vast and persuasive. A phylogenetic test has been proposed for quantifying its odds against independently originated sequences based on the comparison between one versus several trees. This test was successfully applied to a well-supported homologous sequence alignment, which was however criticized on the basis of simulations showing that alignments without any phylogenetic structure could mislead its conclusions. Results: Here we present a simplified version of this same counterexample, which can be interpreted as a tree with arbitrarily long branches, and where the UCA test fails again. We also present another case whereby any sufficiently similar alignment will favour UCA irrespective of the true independent origins for the sequences. Finally, we present a class of frequentist tests that perform better than the purportedly formal UCA test. Conclusion: Despite claims to the contrary, we show that the counterexamples successfully detected a drawback of the original UCA test, of relying on sequence similarity. In light of our own simulations, we therefore conclude that the UCA test as originally proposed should not be trusted unless convergence has already been ruled out a priori.