#99: 7/8ths of What Again?

chart 346 again

99.1  Last week I left you with a real-world example of “7/8th brothers”…a couple of bulls from a sale last year, and asked how closely they were related. But what’s the big deal about 2 individuals that share 7 of 8 great grandparents? That’s very close to 8 of 8 great grandparents, you see? Practically the same thing…sort of…kind of…like…so how can you go wrong?

99.2  And what’s so wonderful about sharing 8 of 8 great grandparents? Well, it definitely means you’re blood relatives…and at least closer than if you shared fewer great grandparents than that…or none at all…duh. As far as livestock goes…horses, cattle, etc…the sharing of grandparents (quarter fractions) and great grandparents (eighth fractions) predates the modern understanding of genetics by hundreds if not thousands of years. The problem is, what if all your great grandparents are…you should pardon the expression…bum steers? An animal sharing those ancestors would most likely also be a loser.

99.3  So the point was to share ancestors, and as many as possible, with a prize animal…a top performer, a classic specimen. Then presumably your animal would have similar characteristics to the celebrated one…not guaranteed of course, but chances were great, or so the thinking went. Thus the exact Coefficient of Relationship between 2 individuals with the same 8 great grandparents wasn’t the issue…the identity and lineage of those great grandparents was.

99.4  And I say that because sharing 8 great grandparents does not translate into any one specific CR…it can cover a wide range. The most obvious that would come to mind would be full siblings, with a CR of 1/2, as in Chart 347.

chart 347

99.5  Notice that between the siblings’ parents’ generations (2 individuals) and great grandparents’ generation (8 individuals)…there are 4 individuals making up the grandparents’ generation. That’s standard of course for full siblings. But in Chart 348A, there are 5 individuals in the grandparents’ generation…6 in B and C…7 in D…and 8 in E. In all these cases, the 2 “siblings” at the bottom still share 8 great grandparents…but now their CR’s are as follows, converting to 32nds so as to compare with ½ = 16/32…A 11/32…B 10/32…C 6/32…D 5/32…and E 4/32. Case E are quadruple 2nd cousins, the genetic equivalent of 1st cousins…cases C and D are more closely related than 1st cousins at 4/32…and A and B are more closely related than half-siblings at 8/32.

chart 348

99.6  And tho I haven’t illustrated it, there is another case of sharing 8 great grandparents with just 4 individuals in the grandparents’ generation: that of so called “3/4 siblings” (in human terms now)…which are half-way between full and half-siblings, with a CR of 3/8 = 12/32. And as we have seen many, that times consists of half-siblings thru one parent and full 1st cousins thru the other parents…i.e., 2 individuals who share one parent, with the 2 non-shared parents being siblings.

chart 349

99.7  Even so, we haven’t exhausted all the possibilities yet…how about a tag-team configuration like that on the maternal side of Chart 349. And if you find that hard to follow, I’ve broken it down for you in Chart 350…it’s just 2 different men each having a child with each of 2 different women.

chart 350

Now when a/b and c/d have a child, those 2 offspring have the same 4 grandparents, just in 4 different combinations…and there is no interbreeding involved…no one has has a child with someone they are related to. Those 2 offspring are quadruple half-1st cousins with a CR of 1/4, the equivalent of half-siblings…and their offspring get a quarter of that, or 1/16…that’s on the maternal side. On the paternal side they’re half-siblings…for a total CR of 5/16 or 10/32…the same as Chart 348B.

chart 351

99.8  But wait…I’m still not thru! So far we’ve been assuming that the 8 great grandparent slots are filled by 8 different individuals…what if some of those slots get doubled up? After all, in our original bull example of 7 of 8, 2 of the slots were filled by one chart 352individual. With 8 of 8, we would get, for example, Chart 351, with a CR of 9/16 or 18/32…and notice that now there is interbreeding…the  2 individuals in the parents’ generation are 1st cousins, so the bottom 2 individuals are full siblings as well as double 2nd cousins. Chart 352 takes this to its logical extreme, just 2 individuals filling 8 great grandparents slots, with a final CR of 7/8 or 28/36.

99.9  So much for 8 of 8 great grandparents…CR anywhere from 4/36 to 28/36…thats 1/8 to 7/8. And Lord knows that was just a quick overview…maybe there’s a way to finagle CRs even higher or lower than those.

99.10  But I think you can see that taking that down a step, from 8 of 8 shared great grandparents to 7 of 8, there is going to be a similar spread of possible relationships…with a maximum of 9 individuals in the great grandparents’ generation, and, without interbreeding, between 5 and 8 in the parents’ generation…a typical example being Chart 353, which I calculate at a CR of 7/64. (From last time, FF = thru father’s father, FM = thru father’s mother, MF = thru mother’s father, and MM = thru mother’s mother.)

chart 353

99.11  Except now, the idea of some of those 8 great grandparent slots being filled by the same individuals gets a bit dicey…consider Chart 354. Here, all 8 of Green’s great grandparents are also great grandparents of Orange, yet there is one less “double up,” and so Orange ends up having one great grandparent that Green doesn’t. Is this really 7 of 8? Seems like it should be, even tho only one of the 2 related individuals at the bottom has a unshared or “odd” great grandparent, instead of both having one, as in Chart 353. 

chart 354

99.12  At any event, to answer our quiz…we’ll break it down into components. In Chart 355, we see that Bull 70 and Bull 71 are enhanced half-siblings…they have the same father D and mothers who are related, E and F. And the relationship between mothers E and F is itself one of enhanced half-siblings…the mothers’ have the same father A and mothers who are half-siblings, B and C. Now you can “cypher” this in 2 different ways…E and F are half-siblings thru their father…1/4…and half-1st cousins thru their mothers…1/16. That’s a total CR between E and F of 5/16. Their respective offspring will have a quarter of that, or 5/64…added to the 1/4 70 and 71 get as half-siblings thru their father, for a total of 16/64 + 5/64 = 21/64.

chart 355

99.13  The other way to determine the CR of 70 and 71 is thru their maternal grandparents, without the middle step of figuring the CR of their mothers. Thus they are half-1st cousins thru A and half-2nd cousins thru B and C…a CR of 1/16 + 1/64…which again comes out to 5/64…added to 1/4 from D gives 21/64…it checks.

99.14  Were this a family tree of humans, it might well end there. But a quick check of the grandparents generation reveals that 70 and 71 are not only enhanced half-siblings, but super-enhanced half-siblings…that is, they have the same father, mothers who are related to each other, and mothers who are also related to the shared father. We covered this back in G4BB 46….to review:   

halfs

99.15  Unlikely in human kinship? Not really…consider this scenario: A young couple have several children, then the wife dies. Her sister, the children’s aunt, moves in to help take care of them. She eventually marries the widower and they have a child, resulting in enhanced half-siblings…same father, mothers who were sisters. Now consider this same scenario, except the original couple were 1st cousins…the 2nd wife, being the 1st wife’s sister, is also a 1st cousin of the widower father…result: super-enhanced half-siblings.

chart 356

99.16  So thru Z and A, 70 and 71 are double 2nd cousins…do you see how?

70‘s father D and 71‘s mother F are half-1st cousins = 70 and 71 are half-2nd cousins
70‘s mother E and 71‘s father D are half-1st cousins = 70 and 71 are half-2nd cousins

CR of double half-2nd cousins is 1/64 + 1/64 = 2/64…plus 21/64 from Chart 355…grand total CR 23/64….which is just a shade more distant that “3/4 siblings” or 24/64. Done,  done, and done. Next week…100, and just getting started…

Wicked Ballsy…not!!!

granwhat

Ahem…so much for competent journalism. The “niece” turns out to be a misspelled “gran-niece.” Think about it…what if the headline were about a prominent person’s “son”….but it turned out to be their grandson. You’d call that an out-and-out mistake. So it’s OK to “simplify” grand niece to niece but not grandson to son? Pretty lame, if you ask me.

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Copyright © 2012 Mark John Astolfi, All Rights Reserved

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