Only ours are methodologically valid. It’s a common creationist tactic to fling around big numbers to ‘disprove’ evolution: for instance, I’ve had this mysterious Borel’s Law (that anything with odds worse than 1 in 10^{50} can never happen) thrown in my face many times, followed by the declaration that the odds of the simplest organism forming by chance are 1 in 10^{340,000,000}. It’s complete nonsense, of course — their calculations all ignore the reality of the actual events, assuming that everything must form spontaneously and all at once, which is exactly the opposite of how probability plays a role in evolution. It’s annoying and inane, and the creationists never seem to learn…perhaps because the rubes they pander to are easily dazzled by even bogus mathematics, so they keep doing it.

We’re going to have to start firing back. Doug Theobald, a long-time contributor to Talk.Origins and the Panda’s Thumb, has written a very nice paper testing the likelihood that all life on earth is *not* related by common descent, and he comes up with some numbers of many digits to support evolutionary theory. Nick Matzke has a summary, and the story has been written up for National Geographic.

Basically, the idea is this: take a small set of known, conserved proteins that are shared in all organisms, not restricting ourselves to one kingdom or one phylum, but grabbing them all. In this paper, that data set consists of 23 proteins from 12 taxa in the Big Three domains: Bacteria, Archaea, and Eukarya. Then set up many different models to explain the relationships of these species. For instance, you could organize them into the classic single tree, where all are related, or you could model them as three independent origins, for each of Bacteria, Archaea, or Eukarya, or you could postulate other combinations, such as that Bacteria arose independently of Archaea and Eukarya, which share a common ancestor. Finally, you tell your computer to do a lot of statistics on the models, asking how likely it is that two independent groups would each arrive at similar sequences, rating each of the models for parsimony and accuracy against the evidence.

And the winner is…common ancestry, with one branching tree! This is what we expected, of course, and what Theobald has done is to test our assumptions, always a good thing to do.

More complicated permutations of these models were also tried. What if there were a significant amount of horizontal gene transfer? Would that make multiple origins of modern life more likely? He was testing models like the ones below, where the dotted lines represent genes that leap across taxa to confuse the issue.

The answer here is that they don’t. These models can also be evaluated by statistical methods, and the best fit is again the one on the right, with a single ancestral root. People might recall the infamous “Darwin was wrong” cover from New Scientist—well, these results say that New Scientist was wrong, the existence of extensive horizontal gene transfer does not negate the fact of common descent.

So what’s the big number? There are lots of them in the paper, since it evolves many comparisons, but Theobald distills it down to just the odds that bacteria have an independent origin from Archaea and eukaryotes:

But, based on the new analysis, the odds of that are “just astronomically enormous,” he said. “The number’s so big, it’s kind of silly to say it”–1 in 10 to the 2,680th power, or 10 followed by 2,680 zeros.

One in 10^{2680}? Hey, aren’t those odds a little worse than Borel’s criterion of one in 10^{50}?

Stay tuned to the Panda’s Thumb. Apparently, once he finishes up the trifling business of wrapping up a semester’s teaching, Theobald will be putting up a synopsis of his own and answering questions online.

Theobald D (2010) A formal test of the theory of universal common ancestry. Nature 465(13):219-222.