st. augustine on outbreeding

here is st. augustine from his The City of God Against the Pagans on outbreeding (and a bit on inbreeding). it’s a little “I’m My Own Grandpa” in places, but augustine’s basic point is that it’s good that people marry out (eg. avoid marrying their close cousins) because in doing so, they increase the number of connections which they have with other individuals — and if everyone in a society does this, there will be larger and broader networks of individuals with common goals and interests, etc., etc., all of which will “bind social life more effectively” and, hopefully, help create the city of god here on earth as much as possible. never mind the possible evolutionary effects.

st. thomas aquinas refers to these passages in his Summa Theologica in his discussion on the merits of outbreeding (but maybe not too much outbreeding!).

source: Augustine: The City of God Against the Pagans, Books 1-13 [pgs. 665-667]:

“16 – That the present law pertaining to marriage between blood-relations could not apply to the men of the earliest times

“After the first marriage of the man made from the dust and his wife, created from the man’s side, the human race had need of the union of males and females in order to multiply itself by begetting offspring. But there were then no other human beings apart from those who had been born of the first two. Therefore, men took their sisters as wives. In ancient times, this was acceptable, because done under the compulsion of necessity; now, however, it is damnable because forbidden by religion. For affection is now given its proper place, so that men, for whom it is beneficial to live together in honourable concord, may be joined to one another by the bonds of diverse relationships: not that one man should combine many relationships in his sole person, but that those relationships should be distributed among individuals, and should thereby bind social life more effectively by involving a greater number of persons in them. Thus, ‘father’ and ‘father-in-law’ are the names of two different relationships; and so the ties of affection extend to a greater number of persons when each has one man as his father and another as his father-in-law. When brothers and sisters were joined together in marriage, however, the one man Adam was compelled to be both father and father-in-law to his sons and daughters. So too, his wife Eve was both mother-in-law and mother to her children of both sexes; whereas if there had been two women, one as mother and the other as mother-in-law, the bond of social affection would have operated more widely. Again, a sister also, because she had become a wife as well, united two relationships in herself, whereas if these had been distributed between two people, one a sister and the other a wife, the number of persons bound together in the closeness of fellowship would have been increased. But this state of affairs could not exist when the only human beings were brothers and sisters, the children of the first human couple. It could exist only when there was a plentiful suppoly of women who could be wives without also being sisters. Then, not only was there no longer any need for brothers and sisters to marry; it also became unlawful for them to do so. For if the grandchildren of the first human beings, who by that time could have taken their cousins as wives, were joined in marriage to their sisters, there would then not have been two relationships united in one person, but three; which relationships should be distributed among different individuals, in order to unite a greater number in the closness of affection. For the marriage of brothers with sister would then have made one man the father, father-in-law and uncle of his own children. By the same token, his wife would be the mother, aunt and mother-in-law of their shared children. And the children themselves would be not only brothers and sisters and spouses to one another, but also cousins, as being the offspring of brothers and sister. If, however, each of these relationships were assigned to a different individual, they would then connect nine people instead of three to each of them. For one man would have one person as his sister, another as his wife, another as his cousin, another as his father, another as his uncle, another as his father-in-law, another as his mother, another as his aunt, and another as his mother-in-law; and so the social bond would extend not merely to a small group, but ever more widely, to connect a large number more closely together.

“We notice also that, as the human race has increased and multiplied, this rule has come to be observed even among the impious worshippers of many false gods. For although their perverse laws may permit brothers and sisters to marry, their actual custom is better, and they prefer to shun the freedom to do this. In the first ages of the human race, it was generally permitted to take a sister in marriage; but this practice is now so much deplored that it is as though it could never have been lawful. For what achieves most in influencing or offending human sensibilities is custom; and, in this case, custom restrains us from immoderate lust, so that men are right when they judge it wicked to disregard or transgress custom. For if it is wicked to pass beyond the boundary of one’s own property out of greed for possession, how much more wicked is it to subvert a moral boundar out of lust for sexual intercourse! We have also found that, for moral reasons, marriages between cousins are rare even in our own times, because, even though such marriages are permitted by law, the degree of kinship involved in them is only one step away from that of brother and sister. Such marriages were not prohibited by divine Law, and they have not yet been forbidden by human law either;[82] but abhorrence was felt for an act which, though lawful, bordered on the unlawful because marriage with a cousin seemed to be almost the same as marriage with a sister. For cousins are called brothers and sisters even among themselves, because of the closeness of their blood relationship, which is almost that of full brothers and sisters.

“To the patriarchs of antiquity, it was a matter of religious duty to ensure that the bonds of kinship should not gradually become so weakened by the succession of the generations that they ceased to be bonds of kinship at all. And so they sought to reinforce such bonds by means of the marriage tie before kinship became too remote, thereby calling kinship back, so to speak, as it fled. Thus, when the world was now full of people, although they did not like to marry sisters with whom they had either a father or a mother or both parents in common, they nonetheless liked to take wives from within their own family. Who would doubt, however, that the state of things at the present time is more virtuous, now that marriage between cousins is prohibited?[83] And this is not only because of the multiplication of kinship bonds just discussed: it is not merely because, if one person cannot stand in a dual relationship when this can be divided between two persons, the number of family ties is thereby increased. In addition, there is present in man a certain sense of honour, which is both natural and laudable, which prompts him not to direct towards a woman whom he is bound to respect and honour as a kinswoman that lust — and lust it is, even though necessary for procreation — which, as we see, occasions shame even within the chastity of marriage.

“[82] Marriage between cousins was, in fact, prohibited by the Emperor Theodosius I (see Ps. – Aurelius Victor, ‘Epitome de caesaribus’, 48; Ambrose, ‘Epist.’ 60,5. This is a fact that Augustine seems to remember in the next paragraph. See also Plutarch, ‘Quaest. Rom.’, 108.

“[83] See n. 82.”

previously: st. augustine and st. thomas aquinas and thomas aquinas on too much outbreeding

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the canonical family tree

following up on a reader request, here is an extended family tree for ya with names (boy, it's HARD to pick names for kids!).

everything is from the point-of-view of “jack” (ego). i went for double-barrelled names in order to give some sort of hint as to any given individual’s relationship to jack. so, his father’s brother (his paternal uncle) is “frank bob.” and his father’s brother’s daughter (his paternal first-cousin) is “frances betty” (see what i did there?).

here they all are (click on charts for LARGER images – should open in new tab/window):

now, in father’s brother’s daughter marriage (i can see your eyes glazing over already!), jack marries his uncle frank’s daughter, cousin frances. in a society where this is a common practice (eg. arab world), they do this over and over again, although maybe not in every generation. if it were every generation, it would look like this:

so, all of the jacks marry their cousins frances betty. see how the lineage keeps folding back in on itself? this is some close inbreeding.

also, see the left side of the canonical family tree? — where uncle mike and aunt martha are? mom’s brother and sister? that side of the family tree doesn’t really exist in an fbd system, ’cause mom’s brothers and sisters are ALSO dad’s paternal cousins. in an fbd system, the left side of the family tree should really be over on the right side. (*facepalm*) maybe i’ll try to draw that one day. it’s no wonder that most peoples in the world consider fbd marriage to be too incestuous — interesting that most people figured that out and avoid it.

now, here’s mother’s brother’s daughter marriage, the most common variant of cousin marriage and the most common form found (traditionally) in china:

again, all of the jacks marry their mother’s brother’s daughter (mbd) — mary beth. but this time, dad is NOT related to mom’s side of the family via his patrilineage. this is a sort-of inbreeding, but not so close as fbd marriage above. not always within the same lineage. mom’s brother, mike, is probably married to a woman from some other lineage, so cousin mary beth is not so closely related to jack. dad’s brother, frank, on the other hand, is probably also married to a woman from the patrilineage, so (in fbd marriage) jack and frances betty are probably more closely genetically related.

what the canonical family tree needs, really, are surnames. (why didn’t i think of that sooner?!)

imagine the fbd marriage system above — jack’s new wife, cousin frances betty, doesn’t have to change her last name ’cause she’s in the same patrilineage as jack. jack smith, let’s say, marries his father’s brother’s daughter — uncle frank bob smith’s daughter, cousin frances betty smith. see?

in the mbd marriage system, on the other hand, jack smith marries his mother’s brother’s daughter — uncle mike bill jones’ daughter, cousin mary beth jones. mary beth needs to change her name ’cause she’s from another patrilineage. like confucius say marriage is “the union of two surnames, in friendship and in love.”

previously: genealogical terminology

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mother’s brother’s daughter marriage

so, i found out that mother’s brother’s daughter (matrilateral cross cousin) marriage is, apparently, the most common form of cousin marriage globally.

i looked at father’s brother’s daughter marriage before, and noted one interesting feature in which ego’s paternal uncle (his father’s brother) got to pass his y-chromosome on to his daughter’s male children when she married her paternal cousin (because ego shares his paternal uncle’s y-chromosome). this is something a man wouldn’t normally be able to do (since his daughters don’t inherit his y-chromosome). so, fbd marriage is a really good deal for the paternal uncle.

what happens in mother’s brother’s daughter (mbd) marriage?

well, first of all, the y-chromosome doesn’t really matter here because ego doesn’t share a y-chromosome with any of his maternal relatives (unless everyone’s really inbred!).

in the case of x-chromosomes, ego inherits just one x-chromosome from his mother — an x that is a recombination of her two x-chromosomes. so, let’s track her two x-chromosomes.

in the case of ego’s mom’s maternal x-chromosome (i.e. the one she inherited from her mom), ego’s mother’s brother shares an x-chromosome similar, but not identical, to the one that ego’s mom has. (each of them inherited a recombined x-chromosome from their mother.) he passes an (almost) intact copy on to his daughter (the mbd), while ego gets part of his mom’s maternal x-chromosome recombined. the result looks like this (click on images for LARGER versions):

so there’s a few bonuses for several individuals here:

– some of ego’s x-chromosomal dna passes on to ego’s son via ego’s wife (the mbd) — normally a male doesn’t pass any x-chromosomal dna onto his sons;
– ego’s daughters get an extra amount of his x-chromosomal dna via their mother — another way of looking at it is that the mbd gets to pass on an extra amount of her x-chromosomal dna via ego;
– both ego’s mom and his maternal uncle get extra amounts of their x-chromosomal dna in their female grandchildren, and ego’s mom gets to pass some of her x-chromsomal dna on to her son’s male children, something she normally wouldn’t have been able to do.

ok. so that was one of ego’s mom’s x-chromosomes. what about the other one? the other one she inherited from her father, so she doesn’t share it with her brother. so it looks like this:

not very exiciting.

buuuuuut, what if ego’s dad had also married his mbd? that’s how they do it, ya know.

then it would look like this:

as you can see, ego’s father would also get to contribute some of his x-chromosomal dna to his female grandchildren’s genomes (via ego’s mother), something he wouldn’t have done otherwise.

so, that’s a short summary of what happens with the x- and y-chromosomal dna in mother’s brother’s daughter marriage. let me know if you see anything else of interest — or if you see an error in something i wrote here (i am experiencing a bit of a cupcake-induced brain fog after today’s festivities (~_^) ).

previously: father’s brother’s daughter marriage and coefficients of relationship – cousin marriage – grandparents

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coefficients of relationship – cousin marriage – grandparents

ok. back to business.

last time i regaled you with my new-and-improved coefficients of relationship/relatedness for the nuclear family members in all forms of cousin marriage (from the p.o.v. of a guy) — MBD (mother’s brother’s daughter) marriage, MZD (mother’s sister’s daughter) marriage, FBD (father’s brother’s daughter) marriage, and FZD (father’s sister’s daughter) marriage. (here’s a key to all the terms if you want to follow along. i also had neat diagrams of the four forms of cousin marriage in the previous post just in case, like me, you’re a visual sort-of person.).

now i’ve added the brothers & sisters as well as the grandparents. here we go (click on chart for LARGER image):

again, all of the family members (probably) share the most dna (i.e. alleles) in MZD marriage, and (ignoring the “no inbreeding at all” category) they share the least in FBD and FZD marriage. from what i’ve read, maternal cousin marriage is the most common globally (not in the middle east, tho), but i’m not sure which one — i.e. if it’s MBD or MZD. i’ll get back to you on that one. (see update below.)

to just repeat exactly what i said in the previous post (’cause i’m too lazy to write up something new and exciting):

the calculations are based on the fact that there is differential x- and y-chromosome inheritance from fathers and mothers to sons and daughters. this seems to matter in an inclusive fitness sort-of way between grandmothers and their grandchildren, so why not between all the other members of the family?

throw inbreeding into the mix, and you wind up with the members of some families being more related to one another than members of other families depending on the type of inbreeding (see chart).

here’s a couple of examples of how i did the math. please, tell me if you think my logic is wrong (very possible) and/or my calculations are wrong (very probable!).

first of all, the percentages of autosomal, x- and y-chromosomal dna that men and women have (based on the vega genome browser) are:

Female genome
6068 Mbp
Autosomal DNA: 5758 Mbp (≈94.89%)
X: 155 Mbp (≈2.55%), XX: 310Mb (≈5.11%)

Male genome
5972 Mbp
Autosomal DNA: 5758 Mbp (≈96.42%)
X: 155 Mbp (≈2.60%), Y: 59 Mbp (≈0.99%), XY: 214 Mbp (≈3.58%)

and here, the calculations for the genetic relatedness between paternal grandfather and son (PGF-s) when there is no inbreeding and in the four different types of cousin marriage:

PGF-s (no inbreeding)
**parents share no dna.
1/4 autosome + y-chromosome = (96.42% x 0.25) + 0.99% = 0.2510

PGF-s (MBD marriage)
**a man and his MBD share 1/8 of their autosomal dna + 1/4 x-chromosomal dna, so a PGF and a grandchild will share an additional 1/32 of their autosomal dna + 1/16 x-chromosomal dna.
1/4 autosome + 1/32 autosome + 1/16 x-chromosome + y-chromosome = (96.42% x 0.25) + (96.42% x 0.03125) + (2.60% x 0.0625) + 0.99% = 0.2827

PGF-s (MZD marriage)
**a man and his MZD share 1/8 of their autosomal dna + 1/4 x-chromosomal dna + 1/8 x-chromosomal dna, so a PGF and a grandchild will share an additional 1/32 of their autosomal dna + 1/16 x-chromosomal dna + 1/32 x-chromosomal dna.
1/4 autosome + 1/32 autosome + 1/16 x-chromosome + 1/32 x-chromosome + y-chromosome = (96.42% x 0.25) + (96.42% x 0.03125) + (2.60% x 0.0625) + (2.60% x 0.03125) + 0.99% = 0.2835

PGF-s (FBD marriage)
**a man and his FBD share 1/8 of their autosomal dna, so a PGF and a grandchild will share an additional 1/32 of their autosomal dna.
1/4 autosome + 1/32 autosome + y-chromosome = (96.42% x 0.25) + (96.42% x 0.03125) + 0.99% = 0.2811

PGF-s (FZD marriage)
**a man and his FZD share 1/8 of their autosomal dna, so a PGF and a grandchild will share an additional 1/32 of their autosomal dna.
1/4 autosome + 1/32 autosome + y-chromosome = (96.42% x 0.25) + (96.42% x 0.03125) + 0.99% = 0.2811

rinse and repeat for all the other family members.

previously: coefficients of relationship – cousin marriage – nuclear family members

update 07/04: apparently, MBD marriage (matrilateral cross cousin marriage) is the most common form of cousin marriage.

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coefficients of relationship – cousin marriage – nuclear family members

so, here are the coefficients of relationship/relatedness (if i’ve done the maths right) for all the nuclear family members in each type of cousin marriage from the point-of-view of a guy — MBD (mother’s brother’s daughter) marriage, MZD (mother’s sister’s daughter) marriage, FBD (father’s brother’s daughter) marriage, and FZD (father’s sister’s daughter) marriage. (here’s a key to the terms so you can keep track of all the players).

notice that the various nuclear family members (probably) share the most dna (i.e. alleles) in MZD marriage, and they share the least in FBD and FZD marriage. (well, they share the least when there’s no inbreeding, but you know what i mean.)

now, here’s what each of the marriage systems looks like. first, MBD:

MZD:

FBD:

FZD:

the calculations are based on the fact that there is differential x- and y-chromosome inheritance from fathers and mothers to sons and daughters. this seems to matter in an inclusive fitness sort-of way between grandmothers and their grandchildren, so why not between all the other members of the family?

throw inbreeding into the mix, and you wind up with the members of some families being more related to one another than members of other families depending on the inbreeding (see chart at top).

here’s a couple of examples of how i did the math. please, tell me if you think my logic is wrong (very possible) and/or my calculations are wrong (very probable!).

first of all, the percentages of autosomal, x- and y-chromosomal dna that men and women have (based on the vega genome browser) are:

Female genome
6068 Mbp
Autosomal DNA: 5758 Mbp (≈94.89%)
X: 155 Mbp (≈2.55%), XX: 310Mb (≈5.11%)

Male genome
5972 Mbp
Autosomal DNA: 5758 Mbp (≈96.42%)
X: 155 Mbp (≈2.60%), Y: 59 Mbp (≈0.99%), XY: 214 Mbp (≈3.58%)

and here, the calculations for the genetic relatedness between father and son (F-s) when there is no inbreeding and in the four different types of cousin marriage:

F-s (no inbreeding)
**parents share no dna
1/2 autosome + y-chromosome = (96.42% x .5) + 0.99% = 0.4920

F-s (MBD marriage)
**a man and his MBD share 1/8 of their autosomal dna + 1/4 x-chromosomal dna
1/2 autosome + 1/16 autosome + 1/8 x-chromosome + y-chromosome = (96.42% x .5) + (96.42% x 0.0625) + (2.60% x 0.125) + 0.99% = 0.5555

F-s (MZD marriage)
**a man and his MZD share 1/8 of their autosomal dna + 1/4 x-chromosomal dna + 1/8 x-chromosomal dna
1/2 autosome + 1/16 autosome + 1/8 x-chromosome + 1/16 x-chromosome + y-chromosome = (96.42% x .5) + (96.42% x 0.0625) + (2.60% x 0.125) + (2.60% x 0.0625) + 0.99% = 0.5571

F-s (FBD marriage)
**a man and his FBD share 1/8 of their autosomal dna
1/2 autosome + 1/16 autosome + y-chromosome = (96.42% x .5) + (96.42% x 0.0625) + 0.99% = 0.5523

F-s (FZD marriage)
**a man and his FZD share 1/8 of their autosomal dna
1/2 autosome + 1/16 autosome + y-chromosome = (96.42% x .5) + (96.42% x 0.0625) + 0.99% = 0.5523

rinse and repeat for all the other characters.

thnx again to the reluctant apostate for his gallant help! (^_^)

p.s. – of course, there are other family members a guy could marry|mate with — niece, aunt, sister, mother(!), second-cousin, double first-cousin (not uncommon in the arab world), etc. i’ll be gettin’ to those at a later date.

previously: fbd marriage – genetic relatedness amongst nuclear family members and new and improved coefficients of inbreeding and new and improved coefficients of relationship

update 06/08: chart updated ’cause i found a couple of errors in my math (see, i TOLD you!) — with the women (e.g. d-F). should be fixed now. (*hbdchick crosses fingers*)

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fbd marriage – genetic relatedness amongst nuclear family members

ok. so here’s what father’s brother’s daughter (fbd) marriage looks like:

the first thing to notice is that if you marry your fbd (or your fbs if you’re a chick) is that your children are now also your cousins.

yes. ’cause, if your cousins’ children are your cousins (e.g. your first-cousins’ children are your first-cousins once removed), then if you marry your first-cousin, then your kids are your first-cousins once removed.

ok? ok.

now, my question is: how related are these people, genetically?

a guy and his fbd share 1/8th or 12.5% of their autosomal dna (probability says) — and that’s it. they don’t share a y-chromosome like the guy does with his fbs. just 1/8th of their autosomal dna.

so, now we can work how how related these nuclear family members are.

normally (without any inbreeding) this is what the genetic relatedness looks like:

F–s = 1/2 autosome + y-chromosome
F–d = 1/2 autosome + 1 x-chromsome
M–s/d = 1/2 autosome + 1 x-chromsome

with the inbreeding of two first-cousins, though, we have to add in that 1/8th that is shared between them. and, if i have this right (do i have this right, r.a.? anybody?), the new calculation should look like this:

F–s = 1/2 autosome + 1/16th autosome + y-chromosome
F–d = 1/2 autosome + 1/16th autosome + 1 x-chromosome
M–s/d = 1/2 autosome + 1/16th autosome + 1 x-chromsome

the coefficients of relatedness (rounded to four decimal points) i get then are:

F–s/s–F = 0.5523
F–d = 0.5684
d–F = 0.5593
M–s/d = 0.5593
s–M = 0.5684
d–M = 0.5593

in other words, the people above (probably) share a lot more genes than this nuclear family (below) that is not inbred:

F–s/s–F = 0.4920
F–d = 0.5081
d–F = 0.5000
M–s/d = 0.5000
s–M = 0.5081
d–M = 0.5000

that’s all for now!

key to terms.

previously: father’s brother’s daughter marriage and new and improved coefficients of inbreeding

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genealogical terminology

in case you want to follow my ongoing exploration of kinship relationships from a genetic point-of-view, i thought i’d post a handy guide to all the familial relationships — they can, very quickly, get quite confusing in an i’m-my-own-grandpa sort-of way.

to start:

and here’s what those codes stand for:

F = father
M = mother
s = son
d = daughter
B = brother
Z = sister
FB = father’s brother (paternal uncle)
FZ = father’s sister (paternal aunt)
MB = mother’s brother (maternal uncle)
MZ = mother’s sister (maternal aunt)
FBD = father’s brother’s daughter (patrilateral parallel cousin, female)
FBS = father’s brother’s son (patrilateral parallel cousin, male)
FZD = father’s sister’s daughter (patrilateral cross cousin, female)
FZS = father’s sister’s son (patrilateral cross cousin, male)
MBD = mother’s brother’s daughter (matrilateral cross cousin, female)
MBS = mother’s brother’s son (matrilateral cross cousin, male)
MZD = mother’s sister’s daughter (matrilateral parallel cousin, female)
MZS = mother’s sister’s son (matrilateral parallel cousin, male)

here’s all about parallel and cross cousins.

and the grandparents:

PGF = paternal grandfather (father’s father)
PGM = paternal grandmother (father’s mother)
MGF = maternal grandfather (mother’s father)
MGM = maternal grandmother (mother’s mother)

also, from the point-of-view of a grandparent, one could refer to the grandchildren as PGS or PGD, for example, depending on the relationship.

capiche?

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new and improved coefficients of inbreeding

so, just the other day i bored you to tears posted (with the invaluable help of the reluctant apostate!) some new and improved coefficients of relationship. (i haven’t quite finished calculating them all — one day, soon, i promise!)

why do i care about all these crazy coefficients of relationship? well, i don’t, really. what i wanted to get at were these other coefficient of inbreeding thingies, but i needed the relationship ones first, so … *sigh* … here we are at last.

without further ado, let me just post the new and improved coefficients of inbreeding that i have, and then i’ll explain afterwards what this is all about (see the previous post for the key to symbols; scroll down for the punchline):

F — s = 0.2460
s — F = 0.2460
F — d = 0.2541
d — F = 0.2500
M — s = 0.2500
s — M = 0.2541
M — d = 0.2500
d — M = 0.2500

B — B (both directions) = 0.2525
Z — Z (both directions) = 0.2564
B — Z = 0.2476
Z — B = 0.2436

PGF — s = 0.1255
s — PGF = 0.1255
PGF — d = 0.1205
d — PGF = 0.1186
MGF — s = 0.1270
s — MGF = 0.1270
MGF — d = 0.1270
d — MGF = 0.1250

PGM — s = 0.1186
s — PGM = 0.1205
PGM — d = 0.1314
d — PGM = 0.1314
MGM — s = 0.1250
s — MGM = 0.1270
MGM — d = 0.1250
d – MGM = 0.1250

FB — s = 0.1255
s — FB = 0.1255
FZ — s = 0.1186
s — FZ = 0.1205
MB — s = 0.1238
s — MB = 0.1238
MZ — s = 0.1282
s — MZ = 0.1303

FB — d = 0.1270
d — FB = 0.1250
FZ — d = 0.1250
d — FZ = 0.1250
MB — d = 0.1238
d — MB = 0.1218
MZ — d = 0.1282
d — MZ = 0.1282

s — FBS = 0.0652
s — FBD = 0.0603
s — MBS = 0.0603
s — MBD = 0.0635
s — FZS = 0.0603
s — FZD = 0.0603
s — MZS = 0.0651
s — MZD = 0.0651

d — FBS = 0.0593
d — FBD = 0.0657
d — MBS = 0.0593
d — MBD = 0.0625
d — FZS = 0.0625
d — FZD = 0.0625
d — MZS = 0.0641
d — MZD = 0.0641

so … eyes glazed over yet? (~_^)

what’s the point? the point is that, following steve sailer and parapundit and stanley kurtz’s leads regarding the effects of inbreeding on human societal behavior, i got to thinking that it’s not just inbreeding that matters but also the type of inbreeding. i think the type of inbreeding is important because we’re not all equally related to all of our relatives.

this very much includes our cousins who, in many societies, also become people’s husbands and wives. so, for instance, i don’t think it’s a coincidence that certain types of behaviors (mostly related to controlling reproduction) occur in societies where there is a high frequency of father’s brother’s daughter marriage.

now, when researchers look at the inbreeding rates in populations, they typically look at the coefficients of inbreeding (here’s an example — see the second-to-the-last column on the right). the usual coefficients of inbreeding look like this:

see first-cousins there? the inbreeding coefficient given is 0.0625. but, that’s not really correct since we are not related to all of our cousins in the same way. for instance, two male paternal cousins share a y-chromosome in common, whereas i don’t share a y-chromosome with any of my cousins since i don’t have one (a y-chromosome, that is — cousins i have a plenty!).

here are the actual inbreeding coefficients for cousins from the point-of-view of a guy (remember, these are probabilities — you might, in reality, be much more related to any given cousin, or not share any genes at all with another, although i think that’s pretty unlikely):

s — FBS = 0.0652
s — FBD = 0.0603
s — MBS = 0.0603
s — MBD = 0.0635
s — FZS = 0.0603
s — FZD = 0.0603
s — MZS = 0.0651
s — MZD = 0.0651

see? they’re not all the same. some are above the 0.0625 figure (which is probably some sort of average i guess) while some are below. so what?

well, if inbreeding does affect our behaviors (especially how we behave towards others), then inbreeding with someone with whom you are more related should accentuate whatever behaviors get affected by inbreeding in the first place. (btw, i think this effect would be stronger the more regular the inbreeding — like in saudi arabia where they’ve been marrying their cousins since before the arrival of islam.)

here’s an example — let’s look at a guy and which of his cousins he can marry. he can marry his father’s brother’s daughter [FBD], his father’s sister’s daughter [FZD], his mother’s brother’s daughter [MBD] or his mother’s sister’s daughter [MZD]. turns out that, from the point-of-view of the guy, he’s most related to his MZD. i would’ve thought that FBD marriage was the most inbred since the types of societies in which you find that sort of marriage seem to be the most clannish and tribal, but that’s not the case from the guy’s point of view. (i’ve included the numbers from the point-of-view of the female cousin|wife, as well. again, when a woman marries a cousin in an FBD arrangement, this is actually one of the least inbred cousin marriages she could enter.):

s — FBD = 0.0603 / d — FBS = 0.0593
s — FZD = 0.0603 / d — MBS = 0.0593
s — MBD = 0.0635 / d — FZS = 0.0625
s — MZD = 0.0651 / d — MZS = 0.0641

however, this is not the only way to consider inbreeding in a society. what happens when we start to look at the relationships of some of the other relatives in these different types of marriage systems? turns out that, from the point-of-view of the uncles or aunts in question, the father’s brother [FB] is the most related to his nephew (the groom):

FB — s = 0.1255
MB — s = 0.1238
MZ — s = 0.1282
FZ — s = 0.1186

that’s because, as i’ve mentioned before, a guy and his FB share a y-chromosome in common (see chart below; the FB = C on the chart) — and when a FB gets his daughter to marry his paternal nephew, he gets to “reunite” his y-chromosome, which his daughter does not carry, with part of his autosomal dna and part of his x-chromosome, which his daughter does carry:

we can even calculate the genetic relatedness of this grandfather (FB, or MGF from the point-of-view of the child) and his grandson. the grandson inherits, via his mother, 1/4 of the maternal grandfather’s autosomal dna plus 1/2 of his x-chromosome. from his father, the grandson inherits his maternal grandfather’s y-chromosome (which is virtually the same as his paternal grandfather’s y-chromosome!). so the calculation is (maths explained in this post):

1/4 autosome + 1/2 x-chromosome + y-chromosome =
(96.42% x 0.25) + (2.60% x 0.5) + 0.99% = 26.395% = 0.2640

without any inbreeding, the genetic relatedness between a MGF and a grandson is 0.2540.

if this is a pattern that holds true for other male relationships in societies where FBD marriage occurs, it may go a ways to explaining why those societies are so paternalistic, i.e. because the males are more related to one another than they are to the females and so, inclusive fitness-wise (if you can say that!), it’d be more in their genetic interests to help out their brothers and nephews and grandsons than their sisters and nieces and granddaughters.

i don’t know if this is true or not. i’m just speculating at this point. i want to run the numbers for different inbreeding scenarios to see what i come up with. might be something. might be nothing at all. stayed tuned….

previously: new and improved coefficients of relationship and all grandmas are not created equal and all cousins are not created equal and father’s brother’s daughter marriage and cousin marriage conundrum addendum

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