#173: By Half!!

Dear Friends: I noticed that some of my blogs are displaying weird…Wordpress is jumbling up paragraphs for some reason…grrrrr. I will attempt to fix this when I see it, but checking all 172 previous posts is not on the agenda at present…it’s only the internet after all!

173.1  It’s always beneficial to go back and review the basics…today, it’s half-cousins…which is what, for the sake of brevity, I will say instead of half-first cousins. This simplification is of course wrong from a strictly genealogical standpoint, but it is perfectly acceptable in this context…and as we are constantly reminded these days, context is everything! And in that same context, I will, for the most part, call 1st cousins simply cousins. Try not to grimace….

173.2   Mothers and fathers, sons and daughters, brothers and sisters, grandparents and grandchildren…these concepts we latch onto at a very early age. Aunts, uncles, and cousins come next, and for many people that’s where it stops, unfortunately. But this second step is a very significant one…your father has a brother, just like you do, and that grown-up brother has a family…wife and children…just like your father does. That brother also has parents like you do and like your father does…except those parents are the same as your father’s parents. All you need really to complete the picture is to consider that your father also has aunts, uncles, and cousins…thus these same patterns happen all over again, and to your grandparents as well, and before you know it your family tree is fleshed out. All that’s left to learn is the correct terminology to use…it ain’t exactly rocket science.

173.3  OK…there is one additional wrinkle…that of half-siblings, who share just one parent, not both. And the offspring of half-siblings are half-cousins…with only one grandparent in common, while full cousins have 2.

173.4  And at this point I should acknowledge that there are a few people who will deny…sometimes with surprising vehemence…that such a thing as a half-cousin even exists. To them, you’re either a cousin or you’re not. To an extent, they have a point. In the parallel case of half-siblings, those that I have known considered their half-siblings to be just siblings…This is my brother Blackie…we have different mothers…like that. There is nothing wrong with this in the context of everyday social intercourse. Same with considering half-cousins as cousins. The trouble occurs in a genealogical context, when you start documenting who’s related to who and how.

173.5  Say for example that you have determined that among your ancestors, A and B are cousins…A’s father and B’s father are brothers. Then as you’re adding on generations downwards, you start noticing middle names that are clearly surnames…but matching none in A’s father’s or mother’s line. Then the penny drops…A’s father and B’s father are in fact half-brothers, and A and B are half-cousins. That’s a whole line of descent you would have missed…even more important if that newly discovered line hooks up further back with the lines you were aware of. Today of course you have the medical angle…for transplants or what-have-you, a half-cousin is less related to you than a full cousin, but more related than a 2nd cousin, etc.

chart 611

173.6  At any rate, take a look at Chart 611b…this dates back to my earliest blogs, and employs a type of diagram which I call a “Parental Tree”…in contrast, Chart 611a I have just now created, using the same style…it’s a “Family Tree.” I use the word “family” in the fast-becoming old-fashioned sense of a mother and a father, married with children.  A Parental tTree is just that…it indicates who is the parent of whom, without regard for marriage per se…altho, the double lines in the Family Tree can also represent a reproductive union, not necessarily solemnified by a ceremony.

173.7  These 2 types of charts are better suited to different situations. As we will see, when a bunch of adults are having children “among” themselves, the Parental Tree works better. For example, in Chart 611a, if the father with 2 wives has a 3rd wife, or even a 4th, how would you connect them? On the other hand, when there are more than 2 offspring involved, the Family Tree is preferable…just imagine the rat’s nest of criss-crossing lines if the parents under “Single 1C” in Chart 611b had 10 kids instead of 2.

173.8  In terms of genealogical analysis, the thing I like about half-cousins is you get more bang for your buck…what I mean is, with just a slight bit of added complication, you get a whole wealth of fascinating complexity…perhaps more than you might have expected! And we’ll begin with double cousins, as in Chart 612.

chart 612

173.9  On the left, full double cousins…A’s father and Z’s father are brothers from one family…their mothers are sisters from another family. A and Z are related as cousins on “both sides”…a phenomenon seen more often in days gone by, when families tended to marry between themselves. I myself have an example in my family…2 of my maternal grandfather’s father’s brothers married sisters…Louis and Clement Jr. Berube to Adele and Lydia Talon. As you can see on the right of Chart 612, you can have the same arrangement with a pair of half-brothers and half-sisters, resulting in double half-cousins…and this is just the tip of the iceberg…half-brothers can marry full sisters, full cousins, half-cousins, on and on. Notice the tell-tale X shape with the fulls, and the W shape with the halfs.

chart 314 re

173.10  Woo hoo! We get to reuse* a chart from Related How Again? #91interestingly, “first cousins” on the left uses a hybrid of the Family Tree and Parental Tree diagrams…you can do what you like, as long as it shows clearly what’s going on. The point here is that double half-cousins are as much related to each other as cousins…1/16 + 1/16 = 1/8…and notice that in each case X and Y share 2 grandparents, labeled A and B. That A and B procreated together in one case, and with others in the other, is irrelevant from the mathematical standpoint. This is why defining “1st cousins” as sharing 2 grandparents is so problematic…double half-cousins share 2 grandparents but are not 1st cousins…seeing is believing, nez pah?

* When I started this blog, I did think I would reuse charts more than I actually do, which is hardly ever…it’s just so much fun drawing new ones, what can I say?

chart 613 173.11  Things really start to get interesting with Chart 613…well, interesting to me…and whose blog is it again? On the left is the double half-cousins diagram from Chart 612…in the middle, ditto from the reusable Chart 314. On the right, I have redrawn the middle diagram by taking grandfather A and moving him down to be on the same level as the other grandparents, which are his generation after all…only thing is, to connect to Y’s mother, we must now cross lines. If as a personal preference you don’t like crossing lines, that’s why the middle diagram exists. But you might ask: are these 3 diagrams really the same thing?

chart 614

173.12  And by identifying the W shapes, one orange, one green, we see that the 3 diagrams are indeed the same…one W is deformed in the middle diagram, and the 2 W’s overlap in the right diagram, but it’s all good. But wait!…we’re just getting warmed up…

chart 615

173.13  In Chart 615a, X and Y are again double half-cousins….that is, they are half-cousins in 2 different ways…first because their fathers are half-brothers thru grandmother B…and second because X’s father and Y’s mother are half-siblings thru grandfather A. We verify this with Chart 615b…the 2 W’s are overlapping even more, but both are there, good as gold. But with  the examples of double half-cousins so far, we had 4 different individuals in the parents’ generation…here we have only 3…does this mean X and Y are even more closely related than “regular” double half-cousins?

173.14  The answer is no, because for 2 people to be related in the first place, they must both have a path to a common ancestor. If you trace it out in Chart 615b, you will find that X and Y each have just one path to common grandfather A…so they are half-cousins there…they also each have just one path to common grandmother B…so they are half-cousins in a second way. Try as you might, you will find no other paths from either X or Y to either A or B…so despite the “doubling up” in the parents’ generation, X and Y are still just double half-cousins, related 1/16 + 1/16 = 1/8. But one thing you will notice is that X’s mother is not shown here…so let’s let our imaginations run wild and suppose that X’s mother is….

chart 616

173.15  …Y’s mother’s half-sister…did you see that coming? OK, in Chart 616a the grandparents have been re-lettered, starting with A on the left…perhaps that’s a tad confusing…but bottom line, X and Y are now half-cousins in 3 different ways! Which is to say, they are triple half-cousins…something that seems strange since with full cousins, double is the most you can do. Doubt it?…don’t, because the 3 W’s in Chart 616b  confirm it. They share 3 grandparents, not 2. Total relationship between X and Y is now 3/16, half-way between 1st cousins (2/16 = 1/8) and half-siblings (4/16 = 1/4). Now looking at Chart 616a, you might wonder if there’s any more genealogical finagling to be done…and noticing the 2 grandfathers on the opposite far ends…X’s maternal grandfather and Y’s paternal grandfather…what if…

chart 617

173.16  …they were the same person?Can’t be done? Sorry, we just did it! X and Y now share 4 grandparents…and they are quadruple half-cousins, related by 1/16 x 4 = 1/4, equivalent to half-siblings. Again, we check the W’s to confirm this…the green and orange W’s in Chart 617b are the same as they were in Chart 616b so I have not redrawn them. The purple W starts out the same, then ricochets over to the other side. And the 4th W, the pink one, is all over the place, but still kosher…it goes down-up-down-up in requisite W fashion. And yes, finally, now we are done…

173.17  …except to state the moral of the story, which is this: the number of grandparents 2 people share is never an accurate way to reckon the degree to which they are related. Proof: siblings share 4 grandparents and are related by ½. Enhanced half-siblings, where they have the same father and their mothers are sisters, also share 4 grandparents…but they are related as half-siblings (thru their father) and 1st cousins (thru their mothers)…1/4 + 1/8 = 3/8. And in Chart 617  we have quadruple half-1st cousins, again sharing 4 grandparents, but related by 1/4. Touche, OK?…and see you next week…

wicked ballsy

wb1

I owe an enormous debt of gratitude to a gentleman named F. M. Lancaster and his website Genetic and Quantitative Aspects of Genealogy…well, he calls it a monograph, and perhaps is was one before it was the other. Written almost 10 years ago, last updated in 2007. Extremely detailed examination of mathematical topics connected with kinship…there are parts that I have yet to fully grasp…but this site took my understanding of and fascination with genealogy to the “next level” as they say today. And one thing to really recommend it is that Mr. Lancaster is not a hobbyist but a college professor of animal breeding and genetics over in the UK, so he knows his stuff, boy. I got the very valuable tool of the Parental Tree…he calls it a Path Tree…and a lot more from him.

wb2

Octuple…count ’em, 8…can you dig it? Brilliant…

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Copyright © 2014 Mark John Astolfi, All Rights Reserved

 

 

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