#4: Double or Nothing

4.1  Last week’s puzzle: I wanted to know how it is possible for your nephew by blood to be your wife’s 1st cousin by blood, without anybody marrying a blood relative. The answer is Chart 6…and it’s interesting that this arrangement can be arrived at in 2 different ways. The way I figured it initially was this: Your brother has a son, who is your nephew. That nephew has cousins on your side of the family, who are related to you…but he also has cousins on his mother’s side, who are not  related to you. One of these cousins on his mother’s side could be Zelda, the daughter of your brother’s sister-in-law Alice…and you marry Zelda. Now your blood nephew is also your wife’s blood 1st cousin.

chart 6

4.2  But a second sequence of events leads to the same thing: You marry Zelda, then your brother marries your wife’s aunt (Alice’s sister) and has a son…again, this son is your blood nephew and your wife’s blood 1st cousin. Pretty cool, if I do say so myself.

4.3  Today we are going to double up and double down…with half-cousins and double cousins.  But first, a word about the diagrams I use to illustrate family trees and interrelations. There are many ways to do this…I primarily use 2, which I call a Family Tree (seen below as Chart 7-A) and a Parental Tree (Chart 7-C.) The difference may seem slight, but it can prove a very big deal when charting out complicated cases, trust me. That difference is: in a Family Tree, 2 people who have an offspring are connected by a symbol…it could be a single horizontal line, a double line, an X, an X with lines, any number of things. This connective symbol implies a marriage…but that’s not necessarily the case, neither today nor a 1000 years ago. So think of it as a biological union…recalling Robert Louis Stevenson’s definition of marriage: a friendship recognized by the police… 🙂 😉

chart 7

4.4  The important point is that the offspring of such a union are connected to the union, not to the 2 parents that make up that union…as you can see in Chart 7-A…and as a result, siblings are connected to each other, as for example are the fathers of Abner (A) and Zeke (Z). With a Parental Tree, no symbol represents a biological union…parents are connected directly to their offspring…in fact, there are NO connecting lines other than parent/child…as seen in Chart 7-C. In general, Family Trees work best for outlining real families, especially where there are multiple siblings, uncles, nephews, etc. Parental Trees can provide a clearer picture when analyzing specific types of relationships…but as you will notice in Chart 7-B, these 2 types of charts can be mixed and hybridized to your heart’s content…so let’s introduce…

chart 8

4.5   half-cousins, or more specifically, half-1st cousins. They are the offspring of half-siblings…for example, the son of your father’s half-brother is your half-1st cousin. The main difference between 1st cousins and half-1st cousins is this: since full brothers have the same 2 parents, their sons…1st cousins…will then have the same 2 grandparents, their fathers’ parents. On the other hand, half-1st cousins will share only 1 grandparent…that being the parent their father share as half-brothers…as in Chart 8-A where Abner and Zeke have the same paternal grandfather but difference paternal grandmothers. Comparing with Chart 8-B, this produces 2 difference kinds of diagrammatic structures…for the Family Tree, one individual has a biological union with 2 different people, left and right…whereas the Parental Tree displays a W formation at the top…and contrast that with the X formation for full 1st-cousins in Chart 7-C.

4.6  I ought to mention that there are some people who think the concept of half-relations is a needlessly complicated one…surprisingly, some even argue that there is no such thing as half-relations! True, many people with half-relations regard these relatives as full relations in casual conversation…others will specify the exact relationship…different people do it different ways. If you grew up in the same household as your half-brother, he’s certainly your “brother.” At the same time, I doubt that you ever really think of yourself and your brother as having the same 2 biological parents…when the plain fact is that you don’t.

4.7  In olden days, when extended kinship was more important, these distinctions were crucial. And they can still be today…with the prevalence of organ transplants, the degree of compatibility is based on the closeness of the relationship…and siblings share 1/2 their genes…half-siblings 1/4…1st cousins 1/8…and half-1st cousins 1/16. BTW, it appears that some “half-deniers” base their belief on what is for Western society now an obsolete practice, that of reckoning kinship thru only one parent, and in our case, one’s father. Thus 2 sons with the same father were “brothers”…who the mothers were, the same or different, was not relevant. This is called unilineal, kinship thru one line…today, we consider ourselves related to both sides of our family, bilineal, thru 2 lines.

chart 9

4.8  Similarly, if you mention double cousins, the response from some people will be: There’s no such thing!  Unless of course they have them in their own family, in which case they know perfectly well what double cousins are: 1st cousins thru both sides of the family…as shown in Chart 9…Abner and Zeke are 1st cousins because their fathers are brothers…but they are also 1st cousins because their mothers are sisters. And it could also be a brother and a sister from one family marrying a sister and a brother from another family. This happened much more often in the past, especially when parents arranged marriages for their children…people had bigger families, didn’t move around as much, so the pool of potential mates was limited. Thus several unions between the Smiths and the Jones’s would not be unusual…especially if the first one worked out well! It was what was called 2 families having “close ties.”

4.9  Other people wonder, upon hearing of double cousins for the first time, if it’s even legal. Naturally, it is…since no one is marrying someone they’re biologically related to. True, some religions used to have…and others still do have…prohibitions against marrying in-laws. In Chart 9, assuming A‘s parent were married first, Z‘s father would then be marrying his sister-in-law’s sister. Whether in-law relations, technically called affines, actually spread out that far is debatable. The traditional rule has tended to be: affines of affines are not affines…in other words, your brother’s wife is your sister-in-law…your wife’s sister is your sister-in-law…but your brother’s wife’s sister and your wife’s brother’s wife are nothing to you. If you did do it that way, it could theoretically spread to everybody…and they’d be nobody left to marry…

4.10  Now unless you have this in your own family, double 1st cousins present some unique features that probably never occurred to you. For example, most people have 2 unrelated sets of 1st cousins, those on their father’s side and those on their mother’s side. Double 1st cousins have just one set….each is the other’s “other side.” Likewise “single” 1st cousins have 1 pair of grandparents they share, and each has another pair they do not share. Double 1st cousins share both pairs of grandparents…there are no “other” grandparents, again because the “other” sides coincide. It’s actually kind of neat when you think about it.

4.11  And here’s the important part: double 1st cousins are more closely related than single 1st cousins…not surprisingly, twice as related. That’s clear enough to see…for example, in Chart 9  double 1st cousins Abner and Zeke get all their genes from just 4 people, 2 pairs of grandparents…for single 1st cousins, there would be 2 more pairs of grandparents at that generational level…3 pairs in all, of which the single 1st cousins would share only 1 pair.

4.12  What’s called the Coefficient of Relationship or CR of 2 relatives tells how many genes, on average, they have in common. If you’ll recall your high school biology, you get half your genes from your father and half from your mother. So the CR between a parent and child is 50%, stated  fractionally as 1/2. I mentioned other common CRs in 4.7. For collateral relatives, that is those who aren’t your direct ancestors or descendants, these CRs are approximate…but with 20,000 genes, it averages out.

4.13  And this leads to one of the most important principles of genetics…and thus genealogy: Coefficients of Relationship are cumulative…which means if 2 people are related to each other in more than one way, both ways count. The passing down of genes thru one path is independent from another path…it holds whether another path is there or not. Thus, double 1st cousins are related as 1st cousins twice…1/8 + 1/8 = 1/4…and they are thus as closely related as half-siblings. But careful: they are NOT half-siblings…any more than your brother is your father, even tho both are related to you by a CR of 1/2.

4.14  And as a practical matter, one must give props to the state of North Carolina…about half the states allow 1st cousins to marry, with varying degrees of qualifications. But only the Tar Heels have noticed that double 1st cousins are as closely related as half-siblings…and since no jurisdiction allows half-siblings to marry, North Caroline prohibits double 1st cousins, while allowing “single” 1st cousins. And that, dear friends, can be described only as “astute,” I don’t care who you are…

chart 10

4.15   I know…some folks throw up their hands and say: Woof! Too much for me! Too much like math!  But if you’re with me so far, and digging it, it’s time to get real down ‘n’ dirty. Chart 9 showed the ONLY way 2 individuals can be double 1st cousins. But with more distant cousins, it gets more complicated. Chart 10  is 2nd cousins. We’ll analyze what happens when they double up in 2 weeks…next week I have a bee I gotta get out of my bonnet. For now, here are 2 different ways you can be be double 2nd cousinsit would be worthwhile to study Charts 11 and 12…contrast and compare, as they say…

chart 11 chart 12

4.16  And after you’ve pondered these for a while, here’s a quiz: sketch out a parental chart showing the relationship between double half-1st cousins…be seeing you!

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Copyright © 2011 Mark John, All Rights Reserved

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