#8: Uncles Are Grand, Cousins Get Removed…Not My Fault

8.1  Relatively few basic words comprise the kinship system in the English language:

father…mother
son…daughter
uncle…aunt
nephew…niece
parent…child
brother…sister
sibling…cousin

If you have a relative that isn’t one of these, you describe that relative by modifying one of these…making it a compound word or a phrase. You’ll notice that the first 10 of these words are in blue…they span 2 generations…the other 4 are in red…they are the same generation.  I did it this way because in English, the way you modify these basic words is different, depending on whether it’s your generation or not.

8.2  For your generation…brothers, sisters, and siblings are just that…and cousins are modified with 1st, 2nd, 3rd, etc….depending on how far back you need to go to find the 2 siblings from which you and your cousin are descended.

8.3  Not your generation….grand goes up or down 1 generation…sometimes a one word compound like grandfather, granddaughter…sometimes a 2 word phrase like grand aunt, grand nephew. Great grand goes up or down 2 generations, then additional greats are added for each additional generation. And here we come to an area of disagreement…

8.4  …which is, what to call your father’s uncle. Commonly, the term is “great uncle”…similarly, your grandfather’s uncle is your “great great uncle,” and on up the tree. There are 2 problems with this. First, as you start to pile on the greats, you see a disconnect…for example, your great great grandfather’s brother is your great great great uncle…that’s 2 people of the same generation, one with 2 greats, one with 3 greats. Wouldn’t it be easier all the way around if the greats in each generation were in sync? Um…yeah. Thus genealogists prefer the term “grand uncle,” in direct correspondence with grandfather. This way, between the 2 brothers of a generation in your direct line, the greats will always match.

8.5  The best argument for doing it this way… apart from the clarity and consistency of it…is this: You have a grand father, but no great father. So why should you have a great uncle?

8.6  The second problem is something that I suspected, and a quick google count confirmed it: if there is somebody you call your “great uncle,” he most likely calls you his “grand nephew”…next, your “great great uncle” has you as his “great grand nephew”…again, the greats are out of whack. And heck, I even found one case where a chart said “grand uncle” and “great uncle” were 2 different things, 2 different generations from you…talk about Murphy’s Law in action!  So using greats and grands the same way with uncle/nephew as you do with father/son is the answer, pure and simple…altho there exist legal decisions that say a great uncle is the same thing as a grand uncle, where wills are concerned, etc. But I say, why complicate your life?

chart 1

8.7  Looking back at Chart 1, this was meant as a general reference chart…3-in-1 actually, showing how each of your relatives is related to you, to your father, and to your grandfather. Chart 19  below simplifies this…it shows each relative’s relation to you…altho in the triangular left-hand corners, it does give that person’s relation to your direct ancestor of that generation. But one thing I wanted to do was to make your direct line of ancestors moving up from you vertical, instead of diagonal, and that’s accomplished by making the box representing each preceding direct ancestor larger than the one beneath it…with the pleasant result that everyone below a “long box” is a direct descendant of the person in that long box.

chart 19

8.8  There are several ways to abbreviate multiple greats for the sake of convenience…a great great great grandfather can be a 3 great grandfather…a 3rd great grandfather…or a 3G grandfather. I prefer the 3G approach, but you’ll encounter all these ways, so expect them.

8.9   Now we’ve accounted for many of your relatives…all of those in your generation…all of those in your direct line, both up and down…and all of the siblings of your direct ancestors, along with the descendants of your siblings. What’s left are the relatives belonging to the same generation as those in your direct line, apart from their siblings…all of those are cousins of some degree…the same as all the relatives in your generation, apart from your siblings, are some sort of cousin to you. Thus we find your father’s 1st cousin, 2nd cousin, 3rd cousin, etc. And your grandfather’s 1st, 2nd, 3rd cousin…and your great grandfather’s, and on up.

8.10  Could we call these cousins grand cousins, great grand cousins, and so on? Bad move, since again the generations would be out of sync…”grand” for your cousin would mean of your father’s generation…but “grand” for your uncle would mean of your grandfather’s generation. Well, that’s the technical analysis of it…who knows why language evolves the way it does? In English, we use the word removed…meaning the number of generations removed from you…once removed for your father’s generation, twice removed for your grandfather’s generation, 3 times removed for your great grandfather’s generation, and like that.

8.11  Yes, your uncle could be thought of as your brother once removed…and your grand uncle as your brother twice removed…we simply don’t do it that way…it is what it is.

8.12  But here’s what trips people up…if someone is your 1st cousin once removed, you are their 1st cousin once removed…but now, “1st cousin once removed” seems to mean 2 different things: from you to him, your father’s 1st cousin…but from him to you, his 1st cousin’s son. Or looked at strictly from your point of view, your 1C 1R could be somebody of an older generation, your father’s 1st cousin…or somebody of a younger generation, your 1st cousin’s son.

8.13  And indeed, as this terminology was developing, some people felt that it should only go one way…your father’s 1st cousins was your 1C 1R, but you weren’t his! Trouble is, what were you to him? Opinions differed, and it was a fine mess to say the least. Thus, the terms ascending and descending came to be tacked on, indicating whether this 1C 1R was back generations from you…or down generations from you. Again, we have the system we have…there are others, like in Spanish where 1C 1R ascending is 2nd uncle…1C 1R descending is 2nd nephew…and since language is always evolving, who know what we’ll say in 50 or 100 years? And this 2nd uncle/nephew system is occasionally seen in English, but it hasn’t taken hold in general. Watch this space.

chart 20

8.14  So now that we know what they’re called…how closely are we related? Chart 20 is your Coefficient of Relationship Cheat Sheet…and these CR’s are applied in Chart 21…enjoy, dear friends… 😉 😉

chart 21


wicked ballsy

Dear Stolf: Your post about the Bee Super Sisters, who had a CR of 3/4 as compared to ½ for full siblings was interesting. But with people, isn’t there a thing called “Three-Quarter Siblings” …is that the same thing? …from Stumpy, Lake Hoochimakoochi River, Georgia. 

chart 22

Dear Stumpy: You’re right, there is…and such a relationship is shown in Chart 22. But while Abner and Zeke here would be called “three-quarter siblings,” that term is misleading, since their CR is not 3/4 but rather 3/8. Consider: half-siblings share one parent, and each has another parent they don’t share…here, Abner and Zeke have the same mother but different fathers. Usually, half-siblings are related only thru just the common parent they share…but here, their 2 different fathers are related to each other…they are in fact brothers. This is one example of Enhanced Half-Siblings…Abner and Zeke are related by 1/4 (as half-siblings) thru their mothers, and 1/8 (as 1st cousins) thru their fathers.

Total CR 1/4 + 1/8 = 3/8. But you’ll notice that 3/8 is half-way between 1/2 and 1/4…which is to say, half way between 4/8 and 2/8. Abner and Zeke are the equivalent of half way between full brothers and half-brothers…hence the term “three-quarter brothers.” And I was careful to say “the equivalent of” because in point of fact Abner and Zeke are both half-brothers and 1st cousins, and that’s all they are. Now one person having children with each of a pair of siblings was more common in olden days than today…hence the special name. But Abner and Zeke do not have a CR of 3/4…for that we would need people having children with people they are related to, not often seen, despite the customary jokes, even along the Lake Hoochimacoochi River.

In other words, think animal husbandry…and here’s a quiz…sketch out a Parental Tree where Abner and Zeke have a CR of 5/8…hint: call them Atlas and Zeus…answer next time.

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Copyright © 2011 Mark John, All Rights Reserved

 

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#7: More Tinker-Toys

7.1   Many sites on the internet will take a stab at explaining double cousins, which is to say, double 1st cousins…of those that go onto double 2nd cousins, most (but not all!) realize there are 2 different kinds…reviewing Charts 11 and 12 below. Only one I’ve found adds the third kind…well, actually let’s call it the third basic kind. Some folks include double-half cousins as another kind…as well as the offspring of identical twins, which are genealogically cousins, but genetically much more closely related…something we’ll get into in 2 weeks.

chart 11:12

7.2   But really, double half-2nd cousins are not double 2nd cousins…and more than a half-brother is a full brother…so Chart 18 diagrams the third kind, what I call Sesquilineal double 2nd cousins. Sesqui- means one and a half, most commonly encountered in the word sesquicentennial, a 150th anniversary. And this kind is sort of half-way between uni- and bi-…a hybrid if you will.

chart 18

7.3  But before anything else, we should verify that Abner and Zeke are indeed 2nd cousins 2 ways. As you can see, they’re father’s are 1st cousins, since those grandfathers are brothers…way 1, check. And Abner’s mother is a sibling of Zeke’s father, since those grandmothers are sisters…way 2, check. The question is, what exactly is going on here? Below, I’ve redrawn the charts to highlight a particular feature which will provide the answer.

chart 18 AB

7.4  In Chart 18-A,  Zeke’s father X is a 1st cousin to Abner’s mother C…the mothers of X and C are sisters. In Chart 18-B, I’ve juggled things around to show that Zeke’s father X is also a 1st cousin to abner’s father BX and B have fathers who are brothers. But here’s the key: these 2 cousins of X‘s are on different sides of X‘s family…B on his father’s side, C on his mother’s side. B and C are not related to each other…they are cousins to X on opposite sides of X‘s family…and we all have, unless a parent is an only child, 2 sets of unrelated 1st cousins…children of our father’s siblings and children of our mother’s siblings.

chart 18-C

7.5  Looked at from the point of view of B and C, they happen to share a 1st cousin…but they share nothing else…no aunts, uncles, or grandparents in common. Now from where Abner sits, his father’s uncle married his mother’s aunt…unusual, but again, this uncle and aunt are not related. And from Zeke’s viewpoint, one of his father’s paternal cousins married one of his father’s maternal cousins…cousins on opposite sides of his father’s family…as seen in Chart 18-C, rearranged yet another way.

chart 17-A

7.6  Similarly, the 3 ways of being double 3rd cousins diagrammed in Chart 17 can be expanded to 6 ways, in Chart 17-A. Once again, notice the “crossover”…now it’s split between 2 different generations. And if you were to move Abner and Zeke up into the position of their parents’ generation, you would have the corresponding double 2nd cousins versions…uni-, bi-, and sesqui-lineal. So far, I don’t have names for all these double 3rd cousins arrangements…and there’ll be even more, for double 4th cousins and so on…maybe someday!

7.7  Now technically speaking, there is a fourth way you could have double 2nd cousins…but I don’t count it, and for a very important reason. When analyzing kinship connections, I take the relationships that are given to be as such…and by that I mean, these relations exist but no others. For example, if Abner and Zeke are 1st cousins, and Alice and Zelda are 1st cousins, I assume they are related in no other ways…each is related to his or her cousin by a CR of 1/8. Were Alice and Zelda double 1st cousins, it would be 1/4…twice as close as Abner and Zeke…but if that’s not stated, that’s not assumed.

7.8  Thus the 4th way to have double 2nd cousins is if single1st cousins were to marry each other. In this case, Abner’s father and Zeke’s mother are 1st cousins…so the boys are 2nd cousins one way…but also Abner’s mother and Zeke’s father are 1st cousins, so they are 2nd cousins a second way. Trouble is, they are also siblings. Their CR is not that of double 2nd cousins…1/32 + 1/32 = 1/16…but instead 1/32 + 1/32 + 1/2 = 9/16. That these “four” parents are actually the same 2 individuals doesn’t matter…CRs are cumulative…another word for it is “additive,” which means you add them together.

7.9  Reminds me of a bar bet…Abner and Zelda are 2nd cousins…both are of legal age and neither is married. In all 50 states 2nd cousins can get married, but Abner and Zelda cannot…why not? The answer of course is that they’re also siblings!

7.10  And this gets around to why sibling marriages are frowned on…the offspring are not only siblings, but double 1st cousins…CR of 1/2 + 1/8 + 1/8 = 3/4. You’ve heard I’m sure that such inbreeding results in offspring that are “too closely related.” Now you know how much is “too close”…busy bees, nez pah?  Next week, cousins who aren’t your cousins…because they’re removed…peace out…

Wicked Ballsy

alice zelda

So anywho…last week I showed you what Abner and Zeke looked like…what about Alice and Zelda? Why not…just be careful what you ask for, that’s all’s I’m sayin’…

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Copyright © 2011 Mark John, All Rights Reserved

#6: World of Tinker-Toys

tinker toy6.1 The challenge in #4  was to make a Parental Tree outlining double half-1st cousins. On the left of Chart 13, we’ve started with the basic diagram for half-1st cousins , outlined in Yellow from Chart 8b. Abner and Zeke are half-cousins on their fathers’ side because their fathers are half-brothers. To make Abner and Zeke double half-cousins, they need to be half-cousins on their mothers’ side as well. We do this by making their mothers half-sisters…adding a maternal grandfather Abner and Zeke share, and 2 maternal grandmothers they don’t share…marked on Chart 13 with a green X. The resulting diagram is a little messy…a bit of judicious shifting around yields the diagram on the right, the added grandparents still marked with a green X so you can verify where they were.

chart 13

6.2   Below we compare the “Tinker-Toys for double-1st cousins (Chart 9) and double half-1st cousins (Chart 13). As you can see, Abner and Zeke are double 1st cousins when their fathers are brothers and their mothers are sisters. They are double half-1cousins when their parents’ relationship is half-siblings instead of full siblings. This difference is clearly illustrated by the double X and double W connections between the grandparents’ and parents’ generations.

chart 13A

6.3  With these patterns in mind, we move on to half-2nd cousins…simply change the grandfathers in Chart 10-B  from full brothers X to half-brothers W and we’re done. For half-3rd, half-4th, half-5th cousins just shift the W back a generation.

chart 14

6.4  Now in this context, the word “double” has described a relationship that Abner and Zeke share twice, once on their fathers’ side, once on their mothers’ side. But it was the same relationship…1st cousins, half-2nd cousins, whatever it may be. Do the relationships on either side have to be the same? The answer is no…as seen in Chart 15. We call this double cousin relationship irregular, since the 2 sides are different…regular would be if they’re the same. And now, the word “cousin” is being used in a looser sense…it means some type of cousin…in this case 1st and half-1st.

chart 15

6.5  Thus, there can be such a thing as triple cousins, and some families describe themselves as such. A typical example of triple cousins is shown in Chart 16A…Abner and Zeke are double 2nd cousins on their fathers’ side and single 1st cousins on their mothers’ side. There is no relationship per se of which they are “triple”…which is to say, there is no relationship they share 3 times…triple 1st cousins is impossible, since we only have 2 sides to our family, not 3. Abner and Zeke can be 1st cousins thru their fathers and 1st cousins thru their mothers…there are no relations left for that third 1st cousin relationship.

chart 16 A

6.6  On the other hand, since 2nd cousins are descended from the siblings of grandparents, and everybody has 4 grandparents, there can be triple 2nd cousins…in Chart 16A, Abner and Zeke’s mothers are sisters…simply make them 1st cousins, and the boys are now 2nd cousins 3 ways. Make the mothers double 1st cousins…like the fathers are…and now Abner and Zeke are quadruple 2nd cousins….quadruple because there are 4 grandparents. And if you’re thinking, well heck, there are also 8 great grandparents for 3rd cousins…yup, you’re on the right track, my friend!

6.7  Of course these multiple cousin relationships I’ve described are regular…each is the same degree of cousin. In Chart 16A, the triple cousins are irregular since they are not all the same…2nd cousins twice and 1st cousins once. Yes, it must be obvious by now that I do not now nor have I ever suffered from math-o-phobia…quite the contrary! And it is my firm belief that if things are simply explained, and built up from the basic to the more complicated, one step at at time, you needn’t suffer either…

chart 16 B

6.8  To make the relationships in Chart 16A easier to see, we can move Zeke and his father below Zeke’s paternal grandfather, as seen in Chart 16B. It should by now have dawned on you that the possible combinations are practically endless…for example, in Chart 16B, if the boys’ paternal grandfathers were 1st cousins instead of brothers, Abner and Zeke would be a different combination of irregular triple cousins: 3rd, 2nd, and 1st!

6.9  And owing to the fact that our family trees grow “wider” as we go back thru past generations, variations start to appear. We have seen that there is only one way you can get 1st cousins cousins or 2nd cousins. This is true for all of what I call numbered cousins…3rd, 4th, 5th, etc. If Abner and Zeke are any degree of numbered cousin…and “single” or just once…there is only one way that can happen: each has a direct ancestor who is a brother to the other’s direct ancestor…how far back determines the degree. There is only one way to be double 1st cousins as well…but when we move on to double 2nd cousins, things begin to split off…

chart 11

6.10  …which is what we saw with Charts 11 and 122 different ways Abner and Zeke can be double 2nd cousins. Bilineal and Unilineal are terms that crop up in many genealogical contexts…bi means 2…uni mean 1…and lineal refers to a line of direct ancestors…all connected by a series of parent/child relationships. In Chart 11, Abner and Zeke have fathers who are 1st cousins, hence they are 2nd cousins…they also have mothers who are 1st cousins, so they are again 2nd cousins…double 2nd cousins, 2nd cousins 2 ways, thru 2 lines of descent…bilineal.

chart 12

6.11  In Chart 12, Abner and Zeke have fathers who themselves are double 1st cousins…thus Abner and Zeke are double 2nd cousins thru only one line, their fathers’…unilineal. Now you might wonder if there 2 types of double 2nd cousins really amount to the same thing…are the Coefficients of Relationship equal? They are…1/16 in either case…that’s twice the CR of single 2nd cousins, 1/32.

6.12  But to confirm these 2 different forms of double 2nd cousins amount to the same genetic relationship, we simply check for grandparents who are siblings…that is where 2nd cousins come from after all. In the bilineal case, Abner’s paternal grandfather is the brother of Zeke’s paternal grandfather…that’s 2nd cousins. But also, Abner’s maternal grandfather the brother of Zeke’s maternal grandfather…that’s 2nd cousins again…double 2nd cousins…check! And notice were the bi of bilineal comes in…we went to their father’s fathers and their mother’s fathers…2 lines, father’s and mothers.

6.13  With unilineal…we again find 2 sets of grandparents, shared by Abner and Zeke, who are siblings…in this case, their paternal grandfathers are brothers…and their paternal grandmothers are sisters. But notice, we did this thru Abner and Zeke’s paternal lines only…they have no relation thru their mothers..hence unilineal. The bottom line: to be 2nd cousins, you must share a pair of grandparents…and Abner and Zeke do this twice, whether bilineally or unilineally.

6.14 The key thing to understand is this: in both these cases, there is what I call a “crossover” between 2 family lines…represented by the big wide X in both Charts 11 and 12. The difference is, this crossover comes at different generations…from Abner and Zeke’s parents’ generation for bilineal…from their grandparents’ generation for unilineal. And as is the case for all of genealogy, this “movable” crossover occurs with all degrees of cousins…and Chart 17 show 3 different types of double 3rd cousins…amazing, huh?

chart 17

6.15  And if you’re really sharp-eyed, you might have noticed a seeming discrepancy…in the middle diagram, it says that Abner and Zeke’s fathers are double 2nd cousins…but aren’t they also double 2nd cousins in the diagram on the left? Yes, they are…the difference is, in the middle diagram, no grandparents are double 1st cousins, as they are on the left…instead, there are 2 pairs of single 1st cousin grandparents.

6.16  But getting back to double 2nd cousins, I must leave you with a “revolting development,” as they used to say on The Life of Riley…there is yet a 3rd type of double 2nd cousins, over and above bilineal and unilineal… Wha–? Yup…tune in again next week…

wicked ballsy

abner zeke

Hey listen…I thought maybe you might like to see what our guinea pigs Abner and Zeke actually look like…sadly, I’ve forgotten which is which, but there you go…

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Copyright © 2011 Mark John, All Rights Reserved

#5: Busy Bees

5.1  The biological realities of human reproduction drive the dynamics of kinship. Other living things have different dynamics…and there are a dizzying array of reproductive methods and strategies, what in biology class we called “life cycles,” remember? There is something called parthenogenesis…which is asexual reproduction. That means, producing offspring without first shuffling of 2 sets of genes, a mother’s and a father’s…producing what we would call today clones. This happens naturally in many lower forms of animals, and even in some crustaceans, fishes, and reptiles. In humans, identical twins are genetically the equivalent of clones.

5.2  There is even something called paedogenesis, or “born pregnant.” This occurs in some  insects…but not in gerbils as is widely believed…altho on Star Trek, it was the case with tribbles! Again, this is asexual or parthenogenic reproduction, and all the offspring are clones. For example, within the body of a pregnant aphid (the grandmother generation), the fetal aphids (the mother generation) are themselves, within their yet-to-born bodies, producing the daughter generation. As you can well imagine, this is primarily to save time.

5.3  You might wonder then, in all of the Natural World, can there be 2 individuals that, while not identical clones, are still more closely related than full siblings would be in human terms? Well, there’s always incest if course…in some animals there are behavioral instincts that work against it, in others there are not. With the selective breeding of domesticated animals, such “back breeding” is an invaluable genetic tool. But outside of that, there are indeed cases of naturally occurring “closer-than-siblings”…and those with bees occur even without the mating of 2 related individuals. The resulting offspring are called “super-sisters.”

chart B1

5.4  First, human genetics…Chart B1 shows the genetic make-up of 2 human sisters, Alice and Zelda. Each of the numbered tabs represent a gene…to make it simple, I show 8 genes…but humans have about 20,000, and bees 10,000.

5.5  Looking at Alice’s mother, she has 16 genes…2 sets of the same 8 genes…the pink ones she got from her mother, the blue from her father. To make Alice, her mother produces an egg, that has just 8 genes, randomly chosen from her pink group and her blue group (the grey arrows.) The same thing happens with Alice’s father…he has yellow genes from his mother, green from his father, and a random mix of those form a sperm cell. Together, the egg and the sperm constitute Alice and her genetic make-up.

5.6  With Alice’s sister Zelda, egg and sperm are formed the same way, from the same set of parental genes, but with a different random mix of the pink, blue, yellow, and green. Thus, the white tabs in the middle show stars where the sisters share the same genes. With only 16 genes they could share 1 or 2…or even 14 or 15…but with 20,000, it averages very close to ½, as I have illustrated.

Chart B2

5.7  Now we do it again, this time with bees, and you’ll notice a difference. Bee 1 and Bee 2 are not clones…they are sexually produced sisters, since each has the same mother and father. But their father was produced from an unfertilized egg and he has only one set of genes. Thus, all the sperm cells he produces will be clones of himself, and of each other…he simply has no other genetic material with which to mix-and-match.

5.8  And actually, his 8 genes should not all be yellow, but a mix of yellows and greens (half from his mother’s mother, half from his mother’s father.) I made them all yellow to emphasize the point that the 2 super-sisters will automatically share half their genes…the entire half that each gets from their father. They will also share, as do humans, roughly half of those they get from their mother, bringing their total shared inheritance to 3/4, as you can see in the center white tabs with stars…of their 16 genes, they share 12…super-sisters!

5.9  Next week, halves and doubles. Till then, stay busy…

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Copyright © 2011 Mark John Astolfi, All Rights Reserved