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Archiver > GENEALOGY-DNA > 2010-02 > 1265846514


From:
Subject: Re: [DNA] MRCA Estimates
Date: Thu, 11 Feb 2010 00:01:54 +0000 (UTC)
In-Reply-To: <1068441842.2232861265846443361.JavaMail.root@sz0002a.westchester.pa.mail.comcast.net>


>From: "Charles Acree" < >
>...However, as we all know, MRCA predictions can often mislead when applied to the genealogical time-frame (roughly the past millennium).
>In our Acree surname project, for instance, MRCA statistics have proven totally inapplicable. Of the nineteen of us ...who descend from a common Acree ancestor born 300 years ago (affirmed by genealogical documentation)...Seven of us match 46/46 (by Ancestry.com's count); five match 45/46; and six match 44/46. (The nineteenth matches 12/12.)

My response:



Dear Charles,



It seems that you bark at a wrong tree, so to speak. Mutations in your family haplotypes are all correct from a point of a MRCA determination. However, you want to see mutations in specific haplotypes of your family members. This is not going to happen. Mutations are wild and occur wherever statistics almighty clicks. There can be two mutations, and even three mutations in one nephew and none in another one.  Do not look for any sense in that statistics.



This is apparently a root of frustration of many genealogists. On some strange reason they look for well-ordered mutations following the family tree. This is not going to happen.



However, collectively, mutations obey some very simple rules. Let's take a look at your example. As I understand, 18 members of your extended family who have a common ancestor 300 years ago have - collectively - 5+12 = 17 17 mutations in their 46-marker haplotypes. In other words, the average number of mutations in those 18 individuals equal to 17/18/46 = 0.0205 mutations per marker. Average mutations rates for extended haplotypes typically group around 0.002 mutations per marker per generations of 25 years (I calibrate those rates using 25 years per generation; this is a fixed mathematical value and not an actual length of a generation). For 12-marker haplotypes it equals to 0.00183, for 25-marker ones it is 0.00183, for 37-marker ones it is of 0.00243, for 67-marker ones it is 0.00216. For the 46-marker haplotypes it is 0.00190 mutations per marker per generation.



Therefore, a common ancestor of your family lived 0.0205/0.00190 = 11 generations ago, that is 11x25 = 275 years ago. With a properly calculated margin of error it is 275+/-135 years ago with 95% confidence (two sigma, that is +/-49.5% for this particular case).  As you see, it nicely matches with 300 years when your common ancestor was born, as confirmed by documents. I would suggest not to go tooooo far by noting that 275 years ago your common ancestor was 25 year old, and this was a right time for him to have children.           


Furthermore, there is an even easier way to estimate a timespan to your common ancestor. For this, I often use the logarithmic method, which is a very simple and convenient tool, particularly with recently recent common ancestors. All what you do is to divide the total number of individuals (18 in your case) by the total number of unmutated haplotypes (7 in your case), take a natural logarithm and divide by the mutation rate for the whole haplotype (0.0019x46 = 0.0874 in your case).For your particular case we get: [ln(18/7)]/0.0874 = 11 generations to a common ancestor, that is 11x25 = 275 years ago. As you see, it is exactly the same figure as we obtained above by counting mutations. Here we did not count mutations, just simply counted unmutated haplotypes.



This simple case again demonstrates that there is nothing mysterious in counting mutations, and that we count them correctly - time and again. In fact all that you need to do is an average number of mutations per marker. And, of course, the mutation rate constant for the haplotype format you employ. They are given above for four typical cases. The full list which I use contains 31 haplotype formats.   



Regards,



Anatole Klyosov



*****************************************

Spirited discussion of the value and methodology of Most Recent Common Ancestor (MRCA) statistical inference is worthwhile because those estimates can be helpful, particularly with regard to pre-historic times. However, as we all know, MRCA predictions can often mislead when applied to the genealogical time-frame (roughly the past millennium).

In our Acree surname project, for instance, MRCA statistics have proven totally inapplicable. Of the nineteen of us (mostly and impressively, 4th-8th cousins) who descend from a common Acree ancestor born 300 years ago (affirmed by genealogical documentation), none of us has a genetic distance (GD) from the mode greater than two, and all of us share the distinguishing, invaluable partial-repeat at DYS385b that I've mentioned. Seven of us match 46/46 (by Ancestry.com's count); five match 45/46; and six match 44/46. (The nineteenth matches 12/12.)

Two participants have an uncle/nephew relationship. Guess what their match is. No, you got it wrong. The uncle is one of those who matches the mode 44/46 - differing from his nephew in two (fast-mutating) markers (GD=2, one up, one down).

Charles Acree




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