#46: More of David, by Half

46.1  Last week were were flexing our genealogical muscles with a chart of descendants of the Biblical King David…and I left you with the question of how Jeush (O) and Abijah (P) are related, given that they have the same father, their mothers are both half-1st cousins and 2nd cousins, and the father is both half-1st cousin and 2nd cousin to one of the mothers, but just half-1st cousin to the other…whew!

46.2  And this seems like a reasonable time to review the genealogical concept of “half-relations.”

46.3  Suppose Abe and Zoë say that their grandfathers were brothers. That would make then 2nd cousins, the offspring of 1st cousins, as shown in Chart 152a. Now this is correct as far as it goes, as long as we bear in mind that it is a short-hand for Chart 152b…which is to say, we take them at their word, and assume by “brothers” they mean “full brothers.” And as we see in Chart 152c, the grandfathers could be half-brothers, so that their children would be half-1st cousins, and Abe and Zoë half-2nd cousins.

46.4  Now all the half-siblings I’ve ever met called their half-siblings their “siblings”…brothers or sisters. Further discussion night reveal that they have “different mothers,” in which case you could say: Oh, so you’re half-siblings…to which they might reply: Yeah, technically, but we don’t think of it that way. This illustrates the difference between genealogical terminology and “everyday” terminology…thus for example you might introduce your 1st cousin once removed as your cousin, or your uncle, or your father’s cousin, or your father’s 1st cousin…but probably not as your 1st cousin once removed. But every family has different customs and habits…which may vary between individuals within the same family.

46.5  The significance of Chart 152 is this: it’s somewhat sloppy to say that the closest common ancestor of 2nd cousins is a great grandparent…if they are full 2nd cousins, they would have 2 common great grandparents…they would share both a great grandfather and a great grandmother, as in 152b. If not, then we have 152c, where the grandfathers are half-brothers, the parents half-1st cousins, and Abe and Zoë half-2nd cousins. Here their closest common ancestor is literally one person, not 2…but in general, we assume we are dealing with full relations unless told otherwise, for simplicity’s sake.

46.6  And what does it matter, really? Well, in everyday life, it may matter a lot, a little, or not at all. But in genealogy and kinship it is very significant…full siblings share all their ancestors…one does not have a relative in the past that the other doesn’t…both in the mother’s line and the father’s line. For half-siblings, there are 3 lines of descent, not 2, and they only share one of them. This certainly could be crucial from a genetic or medical standpoint…less so from a matrimonial standpoint today, but that could still be relevant depending on your religion, personal beliefs, or the laws where you live.

46.7  But where it gets really interesting is with the “clue” I gave you last week for O and P’s relationship: “Enhanced Half-Siblings.” (Sorry, but there is no “everyday” term for this!)  Most of the time, half-brothers with the same father will have mothers who are unrelated. But the mothers could be related, as in Chart 153 where they are sisters….making  Bob and Cal 1st cousins as well as half-brothers. Now you might object: How can they be 1st cousins if they’re “already something else,” in this case, half-brothers?

46.8  Well, as was hinted at in the 3 diagrams of Chart 152, it’s because from a genealogical standpoint, full siblings are “Double Half-Siblings.” It’s thought of this way: you can have the same mothers (half-siblings), the same fathers (half-siblings), or both (full siblings.) Another way to put this would be that full siblings are half-siblings on one side, and half-siblings on the other side…while with “actual” half-siblings, they are half-siblings only on one side, and not related on the other. In the case of Bob and Cal, they are related on both sides…half-brothers on their father’s side…and 1st cousins on their mothers’ side. (And if you’re thinking that technically full siblings could be considered a form of Enhanced Half-Siblings…well, you’re right, but please don’t think that way! It’s bad enough that they’re Double Half-Siblings, you know?)

46.9  The Coefficient of Relationship for full sibs is ½…for half-sibs is 1/4…and not surprisingly, for Bob and Cal’s type of Enhanced Half-Sibs, it’s 3/8, which is half-way between 4/8 (½) and 2/8 (1/4). Of course, the 2 parents can be related in other ways besides siblings…half-sibs, 1st cousins, half-1st cousins, 2nd cousins, both half-sibs and 1st cousins (!!)…the possibilities are endless.

46.10  Now we’re pretty much ready to tackle the relationship between O and P, except for one hitch: unlike “normal” Enhanced Half-Siblings, the 2 sides of the family are related to each otherwhich is to say, the common parent on one side and the 2 parents on the other side are in fact related, over and above the 2 parents on one side being related to each other…duh!…that’s why O and P are such a tangle! So let’s approach it from a simplified case, then apply what we learn to O and P.

46.11  But before the “simplified case,” we need the “super-simplified case,” that of Double First Cousins. And here we can state, as per Chart 154, the DOUBLING RULE:

A’s father is brother of Z’s father  = 1st cousins
A’s mother is sister of Z’s mother = 1st cousins

So A and B are 1st cousins “on both sides of the family”…hence Double 1st Cousins, with a CR of 1/8 + 1/8 = 1/4. or the equivalent of half-brothers.

46.12  Now let’s look at the “Super-Enhanced” Half-Brothers…in Chart 155, we have taken “Normal” Enhanced Half-Brothers Bob and Cal from Chart 153, and made both sides of their families related…in this case their father A is 1st cousin to their mothers Y and Z.

46.13  What this does is add a Double Cousin relationship to Bob and Cal, and to make this relationship clearer to see, in Chart 156 I have moved A over to the other side…and as I have done in the past, his “background” is a different color to indicate that this part of the chart has been duplicated.

Now if you apply the DOUBLING RULE, you will see that Bob and Cal are indeed Double 2nd Cousins, on top of everything else…

Bob’s father is 1st cousin of Cal’s mother  = 2nd cousins
Bob’s mother is 1st cousin of Cal’s father  = 2nd cousins

This is tricky, since the 2 individuals I’ve underlined above are the same person…but this makes no difference to the Double 2nd Cousin relationship. Taking the extreme example of Cleopatra and her sister Berenice (she had 5 siblings, altho whether full or half or some of each is unknown, so we’ll assume full)…their parents where brother and sister…so Cleo and Berry were both sisters and Double 1st cousins. Thus Bob and Cal are half-brothers, 1st cousins, and Double 2nd cousins, for a CR of 1/4 + 1/8 + 1/32 + 1/32 = 7/16, which is just slightly less related than if they were full brothers = 8/16 or ½.

46.14  And now at last we are prepared to look at O and P…and what I have done is to recast their relationship in the form of the Super-Enhanced Bob and Cal diagram in Chart 156,  so that we may compare and contrast, as they say. To start with, we see in Chart 157 that O and P are half-brothers on their father N’s side, with a CR of 1/4. The relationship between their mothers is a complicated one (see the chart after 46.1)…2nd cousins on one side, half-1st cousins on the other…so we will instead use their CR of 3/32…how convenient! The offspring of 2 related individuals have one quarter of the CR of their parents, so thru their mothers O and P have a CR of 3/128…O and P are 3rd cousins (1/128) and half-2nd cousins (1/64 or 2/128)… 1/128 + 2/128 = 3/128…whoo hoo, it checks!

46.15  Finally, applying the DOUBLING RULE, we see that while O and P are related in 2 ways, they are not the same ways, since their father is related to their mothers in different ways…

                         P’s father is 3/32 to O’s mother  = 3/128  (remember, 1/4th)
P’s mother is 1/16 to O’s father  = 1/64  (ditto…)

So taken all together, O and P have a CR of 1/4 (thru father) + 3/128 (thru mothers) + 1/64 + 3/128 (the irregular double cousin relationship, since their fathers and mothers are related)…for a grand total of 40/128…somewhere between half and full siblings, but closer to half…and all I can say is…Hallelujah and Amen!  Next week, why Cousins are 1/8 and not 1/4….see yez…

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Copyright © 2011 Mark John Astolfi, All Rights Reserved

 

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