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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father’s brother’s daughter marriage

or fbd marriage (or patrilateral parallel cousin marriage). i mentioned this before (and i’m sure i’ll mention it again).

cousin marriage is pretty common in the world. but most peoples prefer to marry their cross cousins, i.e. (from the point-of-view of a son) father’s sister’s daughter or mother’s brother’s daughter.

however, a few groups of peoples preferentially follow the fbd system. korotayev (2000) convincingly showed that those peoples are mostly to be found in those areas of the world that were a part of the eighth century islamic caliphate. or, here:

he said (in that same article):

“Islamic law does not prohibit FBD marriage, nor does it impose (or even recommend) it (Schacht 1964; al-Jazi:ri: 1990:60-61). But most traditional cultures have a clear perception that marriage between a man and his FBD is incestuous. This is evident in the fact that in most languages a kinship term for FBD (or MSD) would be identical with a kinship term for one’s sister. This normally implies that marriage with a FBD (or MSD) would be perceived as equivalent to marriage with a sister (Korotayev 1999). There appears to be something here that Kronenfeld (pers. comm.) called a ‘cognitive problem’….”

i think fbd marriage is considered incestuous by most peoples because it creates strongly endogamous lineages. look here — here’s fbd marriage versus fzd (father’s sister’s daughter) marriage. look what happens: in fbd marriage, the men and the women all stay within the same clan. that’s hyper-endogamy if you ask me. in fzd marriage, in contrast, the women move between clans. (the straight lines are men, the dotted lines are women, and the big dots are, well, the union of a man and woman.)

continuing with korotayev, where on earth did fbd marriage come from?:

“At the time of its origin, FBD marriage had nothing to do with Islam. The cognitive problem solution seems to have occurred somewhere in the Syro-Palestine region well before the birth of Christ. Rodionov (1999) has recently drawn attention to the fact that this marriage pattern is widespread in the non-Islamic cultures of this area (e.g., Maronites or Druze) and that it has considerable functional value in this non-Islamic context in facilitating the division of property among brothers after their father’s death (Rodionov 1999). Like Rodionov (1999), I believe that this marriage pattern could hardly be attributed to Islamic or Arab influence here. It seems, rather, that this marriage pattern in the Islamic world and the non-Islamic Syro-Palestinian cultures stems from the same source.

“But prior to the time of Islam, the diffusion of the FBD marriage pattern was rather limited. The only adjacent area where it diffused widely was the Arabian Peninsula (Negrja 1981; Kudelin 1994), where its diffusion can be linked with a considerable Jewish influence in the area well before Islam (Crone 1987; Korotayev 1996; Korotayev, Klimenko, and Proussakov 1999). In any case, by the seventh century, preferential parallel-cousin marriage became quite common among several important Arab tribes (Negrja 1981; Kudelin 1994). In the seventh and eighth centuries, an explosive diffusion of this pattern took place when Arab tribes, backed by Islam, spread throughout the whole of the Omayyid Khalifate. Although preferential parallel-cousin marriage diffused (together with Islam and Arabs) later beyond the borders of the Omayyid Khalifate, the extent of this diffusion was very limited. Hence, the present distribution of FBD marriage was essentially created by the Muslim Arab conquests of the seventh and eighth centuries….”

interesting, huh?

i mentioned over here that i thought the practice should really be called father’s brother’s son marriage — not ’cause i’m a raving feminst who wants everything to be considered from the point-of-view of women (you should know me better than that by now!) — but, rather, because it seems to me to be the father-of-the-bride [“C” in chart below] who really wins out here genetically speaking (which is all that matters, right?). the father-of-the-bride gets to “reunite” his y-chromosome (that he shares with his nephew, his brother’s son) with a quarter of his autosomal dna (his daughter carries half of his autosomal dna) in any male grandkids that he has. what other grandfather gets to do that?:

so what?, you say. here’s what, says i (i.e. relatedness matters).

i also think it’s not a coincidence that, in these societies where fbd marriage exists, you also get these extremely paternalistic societies where women are shrouded in burkas or aren’t allowed to drive or whatever. also, the whole honor killing thing. like rs said here, the males in such societies become “super homies” with each other. exactly! why? ’cause they are really closely related genetically.

i suspect that both the degree and type of genetic relatedness in a society affect all sorts of behaviors of its members (especially those related to reproduction) as well as societal norms and even ideologies (again, especially those related to reproduction).

emmanuel todd seems to have gotten close to this idea as well, although i don’t think he got the genetic side of it (i haven’t actually gotten my hands on a copy of this book yet — gosh-d*rnit!). here’s a blurb about his book, “The Explanation of Ideology: Family Structure and Social Systems (Family, Sexuality and Social Relations in Past Times)”:

“Some parts of the world are dominated by communism, others by Catholicism or by Islam and yet others by liberal doctrines. Why should this be? And why has communism triumphed in Russia, China and Cuba, yet failed in Poland, Cambodia and Indonesia? No one knows. Certainly no clear answer lies in variation of climate, environment, race or, even, economic development. The argument of this book is that world variations in social ideology and belief are conditioned by family structure. The author analyzes the distribution of family forms throughout the world, and examines the relations between particular structures, and (for example) communism, totalitarianism and individualism, as well as the links between these forms and a variety of social phenomena – illegitimacy, suicide, infanticide, marital stability and inheritance laws. He offers evidence to support the belief that family structures and kinship patterns lie behind the ideologies that have shaped the history of the 20th century.”

yes, kinship patterns. and what do kinship patterns reflect? mating patterns.

here’s a little hint at what todd had to say about kinship patterns in the once-part-of-the-caliphate muslim world from a helpful reviewer:

“Endogamous Community Family:
a. Spouse selection: Custom, frequent marriage between the children of brothers.
b. Inheritance: Egalitarian – equality between brothers.
c. Family Home: cohabitation of married sons with their parents.
d. Representative Nations, Peoples, Regions: Arab world, Turkey, Iran, Afghanistan, Pakistan, Azerbaijan, Turkmenistan, Uzbekistan, Tadzhikistan.
e. Representative Ideology: Islam.”

it’s not the family structure that matters, it’s the mating patterns i say.

relatedness matters. a LOT, i think.

previously: cousin marriage conundrum addendum and all cousins are not created equal

edit – a nifty diagram of father’s sister’s daughter (fzd) marriage:

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jewish inbreeding

an israeli water engineer writes: “Consanguineous marriage is almost unknown among Israeli Jews but prevalent among Palestinians.”

that’s probably pretty correct re. ashkenazi israeli jews, but i’m not so sure about other jews in israel.

i couldn’t find any recent data, but has the data from two studies on inbreeding amongst israeli jews, one from the mid-50s and one from the late-60s.

in the mid-50s, 1.4% of ashkenazis were married to either a first-cousin or were part of an uncle-niece marriage. on the other hand, 8.8% of sephardi jews were married to a first-cousin or were in an uncle-niece marriage.

then, in the late-60s, a study done in Petah Tiqwa found that 1.3% of ashkenazis were in a consanguineous marriage, while 14.3% of non-ashkenazi jews were in a consanguineous marriage.

unfortunately, no idea what the israeli rates for more recent years might be.

a study published in 1991 (also on found that jews living in iran had a whopping 25.4% consanguinity rate. they’ve got first- and second-cousin plus uncle-niece marriages. so, look out israelis if you’ve got a lot of immigration from iran!

of course, jews have long been very endogamous. a study published last year looking at the genetics of different jewish populations found that:

“Individuals within each Jewish group had high levels of IBD [identical by descent], roughly equivalent to that of fourth or fifth cousins.”

so, ashkenazis are all related to each other like they are fourth or fifth cousins, iranian jews are all related to each other like they are fourth or fifth cousins, italian jews are all related to each other like they are fourth or fifth cousins, and so on. (comparable to icelanders.)

i would also guess that orthodox jews who observe all those tzniut laws are more inbred than other jewish groups. my favorite, the sheitel, is obviously a direct parallel to the muslim hijab, a practice which exists because of inbreeding. those jews, like so many muslims, must also be practicing some form of patrilineal marriage like fbd marriage.

an israeli water engineer also writes: “Consanguinity certainly increases defectous individuals but provides social stability and a sense of security.”

yes. one study from iceland showed that the sweet spot** re. cousin-marriage and fertility is third cousins, i.e. marry your third cousin to have the most offspring.

similarly, i think there must be a sweet spot re. cousin-marriage| inbreeding and having a functional society which operates in its members best interests. inbreed too much and you get clans and tribes (not to mention lots o’ genetic diseases) which make a society dysfuntional and divided; outbreed too much and you get too much individualism, another sort of dysfunctionality where each guy is out for himself.

**NO pun intended! (~_^)

update: i meant (and then forgot) to mention the most famous cousin-marrying jew of all — a. einstein. his second wife was elsa löwenthal (née einstein). that “née einstein” gives ya a clue right there. elsa was albert’s maternal first cousin AND paternal second cousin. but, they had no kids, so it really doesn’t count.

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cousin marriage conundrum addendum

several years ago now, stanley kurtz, steve sailer and parapundit wrote a great bunch of articles/posts about the futility of america trying to secure the oil resources in bring democracy to iraq since the society there is tribal and the tribalism is based on the long-standing iraqi practice of inbreeding (i.e. marrying their cousins).

steve sailer wrote about how cousin marriage leads to “strong nepotistic urges” ’cause, of course, working from the “selfish gene” perspective and bill hamilton’s idea of inclusive fitness, it makes sense to favor your relatives that share a heck of a lot of ur genes over some strangers in the next town.

and the MORE you are related to your relatives (for instance, ’cause ur clan members have been inbreeding for generations), you’d think the MORE you’d favor them. which is exactly what we see in the world.

from cousin marriage conundrum:

“In Iraq, as in much of the region, nearly half of all married couples are first or second cousins to each other. A 1986 study of 4,500 married hospital patients and staff in Baghdad found that 46% were wed to a first or second cousin, while a smaller 1989 survey found 53% were ‘consanguineously’ married. The most prominent example of an Iraqi first cousin marriage is that of Saddam Hussein and his first wife Sajida.

By fostering intense family loyalties and strong nepotistic urges, inbreeding makes the development of civil society more difficult. Many Americans have heard by now that Iraq is composed of three ethnic groups — the Kurds of the north, the Sunnis of the center, and the Shi’ites of the south. Clearly, these ethnic rivalries would complicate the task of ruling reforming Iraq. But that’s just a top-down summary of Iraq’s ethnic make-up. Each of those three ethnic groups is divisible into smaller and smaller tribes, clans, and inbred extended families — each with their own alliances, rivals, and feuds. And the engine at the bottom of these bedeviling social divisions is the oft-ignored institution of cousin marriage.

“The fractiousness and tribalism of Middle Eastern countries have frequently been remarked. In 1931, King Feisal of Iraq described his subjects as ‘devoid of any patriotic idea, connected by no common tie, giving ear to evil; prone to anarchy, and perpetually ready to rise against any government whatever.’ The clannishness, corruption, and coups frequently observed in countries such as Iraq appears to be in tied to the high rates of inbreeding.

“Muslim countries are usually known for warm, devoted extended family relationships, but also for weak patriotism. In the U.S., where individualism is so strong, many assume that ‘family values’ and civic virtues such as sacrificing for the good of society always go together. But, in Islamic countries, loyalty to extended (as opposed to nuclear) families is often at war with loyalty to nation. Civic virtues, military effectiveness, and economic performance all suffer.

“Commentator Randall Parker wrote, ‘Consanguinity [cousin marriage] is the biggest underappreciated factor in Western analyses of Middle Eastern politics. Most Western political theorists seem blind to the importance of pre-ideological kinship-based political bonds in large part because those bonds are not derived from abstract Western ideological models of how societies and political systems should be organized. Extended families that are incredibly tightly bound are really the enemy of civil society because the alliances of family override any consideration of fairness to people in the larger society. Yet, this obvious fact is missing from 99% of the discussions about what is wrong with the Middle East. How can we transform Iraq into a modern liberal democracy if every government worker sees a government job as a route to helping out his clan at the expense of other clans?'”

[btw – i highly recommend reading steve’s “cousin marriage conundrum” and all of parapundit’s posts on the topic.]

this is why i was babbling about the levels of cousin marriage in egypt (38.9% in 2000) the other day. egyptians are inbred like the iraqis — so there’s a lot of nepotism and corruption and generally not getting along with other, not-so-related egyptians. egypt has probably functioned as well as it has over the last few decades precisely because they haven’t had a free democracy and, as meng b pointed out, the military has basically been running the place (which a majority of egyptians don’t actually mind!).

what stanley kurtz absolutely nailed, tho, is the fact that not only do a lot of middle easterners and south asians inbreed a lot, they also do it in a very special way.

a very common form of marriage in that part of the world — which tends to be avoided by most other human populations, btw — is called “father’s brother’s daughter” (fbd) marriage or patrilateral parallel cousin marriage, which sounds like a bunch of gobbledygook but just means that the typical form of marriage is that of brothers’ children (i.e. cousins who share a common paternal grandfather -or- cousins whose fathers are brothers).

what difference does that make? a LOT. for one thing, it means that pretty much all of the men in an extended family share (virtually) the same y-chromosome. the genes that make them men? — they have pretty much the same exact ones.

to my mind, the practice should really be called “father’s brother’s son” marriage because, in terms of the y-chromosome anyway, the advantage in this arrangement goes to the father-of-the-bride since he gets to have (virutally) his y-chromsome inherited by any grandsons his daughter bears since she will be married to his paternal nephew [click on chart for LARGER version – adapted from here]:

somehow, some way — and i haven’t thought it through fully yet — fbd marriage makes the males in an extended, inbred family — like the ones in the middle east/south asia — very paternalistic.

again, stanley kurtz nailed it in “veil of fears” [read that, too]:

“The ‘family’ to which a Muslim Middle Easterner is loyal, however, is not like our family. It is a ‘patrilineage’ — a group of brothers and other male relatives, descended from a line of men that can ultimately be traced back to the founder of a particular tribe. Traditionally, lineage brothers will live near one another and will share the family’s property. This willingness of a ‘band of brothers’ to pool their labor and wealth is the key to the strength of the lineage.

“But the centrality of men to the Muslim kinship system sets up a problem. The women who marry into a lineage pose a serious threat to the unity of the band of brothers. If a husband’s tie to his wife should become more important than his solidarity with his brothers, the couple might take their share of the property and leave the larger group, thus weakening the strength of the lineage.

“There is a solution to this problem, however — a solution that marks out the kinship system of the Muslim Middle East as unique in the world. In the Middle East, the preferred form of marriage is between a man and his cousin (his father’s brother’s daughter). Cousin marriage solves the problem of lineage solidarity. If, instead of marrying a woman from a strange lineage, a man marries his cousin, then his wife will not be an alien, but a trusted member of his own kin group. Not only will this reduce a man’s likelihood of being pulled away from his brothers by his wife, a woman of the lineage is less likely to be divorced by her husband, and more likely to be protected by her own extended kin in case of a rupture in the marriage. Somewhere around a third of all marriages in the Muslim Middle East are between members of the same lineage, and in some places the figure can reach as high as 80 percent. It is this system of ‘patrilateral parallel cousin marriage’ that ex plains the persistence of veiling, even in the face of modernity.

“By veiling, women are shielded from the possibility of a dishonoring premarital affair. But above all, when Muslim women veil, they are saving themselves for marriage to the men of their own kin group. In an important sense, this need to protect family honor and preserve oneself for an advantageous marriage to a man of the lineage is a key to the rise of Islamic revivalism.”

the particular sort of clannishness that we see in the middle east and parts of south asia that steve sailer talked about in “cousin marriage conundrum” is based on: 1) inbreeding, AND 2) the type of inbreeding.

the societies in that part of the world are split into a myriad of extended families and clans and tribes that will never get along so long as they continue their current marriage practices.

previously: on the origins of the multicultacracy, aígyptos, assimilation interrupted, kissin’ cousins.

update 03/09: see also all cousins are not created equal


double bonus:

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