Over the last decade or so, there has been a voluminous, and often tiresome, debate about whether recent DNA evidence regarding the origins of Native Americans disproves the Book of Mormon. The debate is wearying for several reasons. To me, a key point is that the DNA evidence isn’t really providing very much new information; scholars have long had a variety of converging sources of data strongly supporting the hypothesis that Native Americans in general come from Siberia. So DNA evidence is a useful piece of reinforcing data but not a revolution in understandings of Native American origins.
However, the specifically Mormon debate is narrower: the issue is whether DNA studies that find no trace of Middle Eastern DNA patterns in current or past Native American populations disprove the Book of Mormon’s account of Nephites and Lamanites. On this point, there are clear answers as long as the question is framed in terms of (generally accepted standards for) proof. If the Book of Mormon hypothesis is taken as implying that Lamanites are the only, or even the main, ancestral source for Native Americans, then the hypothesis is disproven. On the other hand, if the Book of Mormon hypothesis is regarded as claiming that at most a very small proportion of the ancestry of Native Americans is Lehite, then the hypothesis is not disproven. Kevin Barney provides a useful overview of the point here, although readers are welcome to reach these same conclusions at much greater length by reading the extensive material available at the FARMS Review of Books, in Simon Southerton’s book, in Thomas Murphy’s essays, and to some extent in the Ensign.
Let’s take up a better framing of the question: do DNA studies provide evidence regarding the Book of Mormon hypothesis? In fact this is difficult; finding Middle Eastern DNA contributions in pre-Colombian Native American populations wouldn’t prove that the Book of Mormon is true. It would just prove ancient contact between the Middle East and the Americas. So, rather than addressing the “Book of Mormon hypothesis,” let’s address a more tangible hypothesis of which the Book of Mormon hypothesis is a subset. Let’s simply consider the umbrella hypothesis that at least some of the ancestors of at least some Native Americans are from the Middle East.
The standard to use for weighing evidence here is Bayes’ Rule; essentially, it tells us that the probability we should rationally assign to the umbrella hypothesis given the findings of a new DNA study is equal to the probability of those findings given the umbrella hypothesis times the strength of our prior belief in the umbrella hypothesis, divided by the unconditional probability of the findings (which can be calculated as a sum of the probability of the findings given each existing hypothesis about Native American origins multiplied by the prior belief in that hypothesis).
To make things simple, let’s consider only two hypotheses: (a) the hypothesis that at least some Native American ancestry is of Middle Eastern extraction, and (b) the hypothesis that no Native American ancestry is of Middle Eastern extraction. Suppose that some new study emerges which finds no affirmative evidence of Middle Eastern ancestry for Native Americans. How should this affect our belief in hypothesis (a)?
To answer the question, we need four numbers. First, we need to quantify our prior degree of belief in hypothesis (a). Let’s say that we’re 99% confident in this hypothesis before finding out about the new DNA study. Second, we need our prior belief in hypothesis (b); the axioms of probability require that belief to be 1%. Third, we need to determine the probability of a new study showing no affirmative evidence of Middle Eastern ancestry given that there is no Middle Eastern ancestry; this should noncontroversially be set at or near 100%; we’ll go to the extreme, as it doesn’t make much difference for our purposes. Finally, the tough part: what is the probability of a DNA study finding no affirmative evidence of Middle Eastern ancestry for Native Americans if at least some Native Americans have at least some Middle Eastern ancestors?
Different choices for this fourth probability will have huge effects on the rational degree of belief in the umbrella hypothesis that we should hold after observing the new DNA study. Suppose, as Southerton might argue, that the probability should be set at zero. Well, zero times anything else is still zero, so our rational belief in the umbrella hypothesis and by extension the Book of Mormon hypothesis falls to zero. But this is certainly unreasonable; there are obviously a lot of reasons that a given study might fail to uncover evidence of Middle Eastern ancestry even if it exists.
Suppose, by contrast, that, as our Steve P. writes, “the long-term probability of any DNA sequence being represented in a distant descendent is zero.” (Steve’s argument is subtler than this, and I’ll incorporate details in a moment. For the time being, let’s simply take the crudest version of the claim.) In this case, the probability of finding Middle Eastern DNA among Native American populations is zero even under the umbrella hypothesis, so the key conditional probability is 100%; we are certain to fail to find Middle Eastern DNA, no matter what. In this case, our rational belief in the umbrella hypothesis after observing a DNA study that finds no affirmative evidence of Middle Eastern DNA is identically equal to our belief in the hypothesis before observing the data.
Yet, a conditional probability of exactly zero can’t actually be right, either. After all, ancient DNA signatures of one kind or another are in fact found in DNA studies! Steve’s argument is an asymptotic one; for a single slice of DNA code, and if the expected number of children each member of a population has at each generation is less than or equal to one, then after infinitely many generations the probability of finding that slice of DNA code in the population is exactly zero. The asymptotic argument is fragile in two directions. First, if the line with the DNA code in question is growing at all on average from generation to generation, then the probability of finding the DNA code after infinitely many generations is strictly greater than 1. Obviously, the Book of Mormon narrative does suggest at least some degree of growth among Lehite populations, although one might argue that they were perhaps entirely reversed afterwards — but this raises potential questions of its own about the Book of Mormon’s prophesies regarding the restoration of the Lamanites to the gospel. Second, the probability will not actually reach zero in any number of finite generations.
So let’s adopt a conservative estimate of the conditional probability of not seeing any affirmative evidence of Middle Eastern ancestry given that the umbrella hypothesis is true: let’s say the probability is 99.999%. With this arguably reasonable value, our rational belief in the umbrella hypothesis changes, after seeing a new DNA study with no finding of Middle Eastern ancestry, from 99% to 98.99999%. The DNA study isn’t irrelevant, as it does move our rational degree of belief a smidgen, but it’s not a backbreaker given our conditional probabilities. In fact, for such an arrangement of prior beliefs and conditional probabilities, after observing 100,000 studies that all fail to find affirmative evidence of Middle Eastern ancestry, our belief in the umbrella hypothesis drops only to 97.32762%.
This result, though, is substantially dependent on the very high, and rather conservative, conditional probability assigned above. What if our conditional probability is 99.9%, instead of 99.999%, consistent with the fact that Mormons generally would not be absolutely and world-endingly astonished if affirmative evidence of Middle Eastern ancestry were to be found? In this case, a mere 5000 studies that all show no affirmative evidence of the umbrella hypothesis would be sufficient to reduce our belief in that hypothesis to 39.95401%. And if the conditional probability were to be 98% — still reflecting a substantially high likelihood of failure even if the umbrella hypothesis is true — then only a very plausible 250 studies would be needed to reduce our rational belief in the hypothesis to 38.80404%.
In other words, a great deal depends on the conditional probability of finding evidence of Middle Eastern ancestry in a particular study given that the Book of Mormon is historical. Apologists have successfully established that this probability is low. It’s implausible to set this probability at exactly zero. The precise value it should have is hard to determine, and it matters a lot. The Galton-Watson equilibrium if each generation averages 1.1 descendents per ancestor is about a 20% chance of a single individual’s DNA signature surviving, a probability that is clearly large enough to make DNA evidence relevant to belief in the Book of Mormon (although not determinitive until at least 50 studies have been done), so the range of at present plausible values almost certainly includes some that would sway rational belief.