Y-chromosomal Aaron - Does A CMH Prove Cohen Ancestry?

Does A CMH Prove Cohen Ancestry?

One source of early confusion was a widespread popular notion that only Cohens or only Jews could have the Cohen Modal Haplotype. It is now clear that this is not the case. The Cohen Modal Haplotype (CMH), whilst notably frequent amongst Cohens, is also far from unusual in the general populations of haplogroups J1 and J2 with no particular link to the Cohen ancestry. These haplogroups occur widely throughout the Middle East and beyond. Thus, while many Cohens have haplotypes close to the CMH, a greater number of such haplotypes worldwide belong to people with no likely Cohen connection at all.

Statistically the value of matching the CMH can be assessed using Bayes' theorem, which in its odds form can be written:

In words, this says that the odds in favour of Cohen ancestry C (i.e., the probability of having Cohen ancestry, divided by the probability of not having Cohen ancestry), having observed some piece of data D, is given by the odds one would assign given only one's initial information I, multiplied by the probability of having observed D if C is true, divided by the probability of having observed D if C is false.

(In fact, for convenience we shall work with the reciprocal of this equation, i.e. work in terms of odds against, rather than odds on).

The proportion of the whole male Jewish population that has Cohen ancestry has been estimated at 5%. So if we take that 5% as our initial estimate of the probability of shared Cohen ancestry, then on the basis of the data above:

• Not belonging to haplogroups D or E improves the odds for a Sephardic Jew from 19/1 against to (19/1)*(0.85/1.00) = 16.2/1 against (a 5.8% probability)
• Not belonging to haplogroups D,E,P,Q or R takes the odds to (19/1)*(0.63/0.88) = 13.6/1 against (6.8% probability).
• Membership of Haplogroup J improves the odds to (19/1)*(0.37/0.75) = 9.4/1 against (9.6% probability).
• Being within the CMH.1 group takes the odds to (19/1)*(0.14/0.61) = 4.4/1 against (18.7% probability).
• A full 6/6 match takes the odds to (19/1)*(0.10/0.56) = 3.4/1. (22.7% probability).

Even a full 6/6 match for the 6 marker CMH thus cannot "prove" Cohen ancestry. It can only somewhat strengthen a previously existing belief. But for populations where the background probability assessment of shared Cohen ancestry must be vanishingly low, such as almost all non-Jews, even a full 6/6 match makes only a small difference. For individuals in such populations, the CMH probably indicates Haplogroup J, but a completely different ancestry to the Kohanim.