# Infinitely Long Branches and an Informal Test of Common Ancestry

## TL;DR

This paper examines a test for universal common ancestry and finds it unreliable under certain conditions, proposing better alternatives.

## Contribution

A simplified counterexample and improved frequentist tests for evaluating universal common ancestry.

## Key findings

- A simplified counterexample shows the UCA test can fail with long branches.
- Simulations reveal the test can wrongly favor UCA even when sequences are independent.
- Proposed frequentist tests outperform the original UCA test in reliability.

## Abstract

The evidence for universal common ancestry (UCA) is vast and persuasive, and a phylogenetic test was proposed for quantifying its odds against independently originated sequences based on the comparison between one and several trees [1]. This test was successfully applied to a well-supported homologous sequence alignment, being however criticized once simulations showed that even alignments without any phylogenetic structure could mislead its conclusions [2]. Despite claims to the contrary [3], we believe that the counterexample successfully showed a drawback of the test, of relying on good alignments.

Here we present a simplified version of this counterexample, which can be interpreted as a tree with arbitrarily long branches, and where the test again fails. We also present another simulation showing circumstances whereby any sufficiently similar alignment will favor UCA irrespective of the true independent origins for the sequences. We therefore conclude that the test should not be trusted unless convergence has already been ruled out a priori. Finally, we present a class of frequentist tests that perform better than the purportedly formal UCA test.