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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linkfest – 05/29/11

Ugandan Chimpanzees May Be Hunting Red Colobus Monkeys into Extinction

Is Your Religion Your Financial Destiny? – @altright

Prenatal testosterone and sexual jealousy“The evidence keeps pouring out that gender is not a social construction (as if any reasonable person would think it is).” – from the inductivist.

and speaking of gender not being a social construction… Why male motorists are more stressed by traffic jams

Amazonian Tribe Lacks Abstract Concept of Time

Scientists Fight University of California to Study Rare Ancient Skeletons

‘Earliest’ Bronze Age battle site containing 100 bodies found on German river bank

Human Brain Networks Can be Tattle Tales“Greicius and his colleagues have previously shown that the brain operates, at least to some extent, as a composite of separate networks composed a number of distinct but simultaneously active brain regions. They have identified approximately 15 such networks. Different networks are associated with vision, hearing, language, memory, decision-making, emotion and so forth.” @al fin.

Genetic Basis For Prudent Spending Habits – @parapundit

Junk food won’t just make you fat. It could also shrink your brain

Looking for Empathy in a Conflict-Ridden World“The regions in red, he said, represented how subjects responded to others in physical pain; the green areas represented their response to emotional suffering. ‘The second thing you can see is that they’re completely separate from each other. So the brain regions that are responding to physical pain are very different than the brain regions that are responding to emotional suffering,’ he trailed off….”

Misunderstanding heritability – by chuck @occidentalist

bonus: Fiscally I’m A Right-Wing Nutjob, But On Social Issues I’m Fucking Insanely Liberal – heh.

i call b.s.

dennis links to roissy who links to barking up the wrong tree who posts about a study which purportedly shows that human mate selection is more about “market conditions” than assortative mating.

possibly. but the researchers haven’t shown that in this particular study because the people they studied (speed daters) WERE ALREADY SELF-SORTED. see here:

65%+ of them were college graduates versus 20% of the population at large (“bhps” — british household panel survey — column). 83% of the men were in skilled or professional jobs while 86% of the women were — compared to 40% and 52% of the general population respectively.

as bruce said over @dennis’: “Key concept: range restriction.”

yup. these people didn’t have to worry about finding a “like” partner out of this sub-group of the population ’cause they were all already pretty alike. they could just pick the nearest warm body to mate with ’cause they had already self-sorted.

total b.s.

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getting that dynamo to hum

via al fin:

Secrets of the female orgasm revealed: Scientists discover new hope for women who can’t climax

“Scientists have discovered the female orgasm leads to an altered state of conciousness that could help the minority of women who can not climax.

“Researchers at the University of Groningen in the Netherlands unwittingly stumbled across the results after they examined the brain scans of women taken while they orgasmed.

“The team noticed that an area of the brain, known as the orbitofrontal cortex or OFC, switched off when the women climaxed….”

more (of the juicy details) from al fin (here) who has neat charts and pictures and stuff. (no, not THOSE sort of pictures!)

and now for something completely different…

(nsfw or small children. and for god’s sake don’t let your wife or girlfriend hear!)

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new and improved coefficients of relationship

(here we go. me and math again. ruh roh.)

so, just about two months ago i wrote a long and rambling post about calculating the relatedness between various family members. with the generous help of the reluctant apostate, i think i may have finally gotten the math in order. maybe.

before we set off on our magical mathematical journey, let me explain my motivation.

in case you missed it, a couple of researchers took a look at the differential x-chromosome inheritance rates between boys and girls — and then they looked at how this affected how maternal and paternal grandmothers treated their male or female grandkids. they found that the more total dna (autosomal dna + x-chromosomal dna) a grandmother shared with a particular grandkid, the better she treated them. (see my post all grandmas are not created equal. edit: correction – they actually looked at total number of genes shared, not total dna which is what i do here.)

which got me to thinking that this must be true for other familial relationships, too: father -> son or daughter, mother -> son or daughter, sister -> brother, brother -> sister … and, my personal favorite, different cousins -> different cousins.

the coefficients of relationship that are usually used look like this:

0.5 (½) – parent-offspring – exact
0.25 (¼) – grandparent-grandchild – average
0.125 (⅛) – great grandparent-great grandchild – average
1 – identical twins; clones – exact
0.5 (½) – full siblings – average
0.25 (¼) – half siblings – average
0.125 (⅛) – first cousins – average
0.03125 (1/32) – second cousins – average
0.75 (¾) – full hymenopteran sisters (i.e. ants) – average

these are based on the fact that (ignoring the ants) we inherit half of our dna from our fathers and half from our mothers.

only we don’t.

we inherit half of our chromosomes from each parent, but chromosomes come in different sizes, and — for instance — the y-chromosome is a lot smaller than the x-chromosome.

so, i looked up the sizes of the chromosomes on the vega genome brower and worked out the sizes of a man and a woman’s genomes:

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%)

moving on from there, we can work out some new and improved coefficients of relationship based on the facts that:

– a son inherits half of his father’s autosomal dna + his full y-chromosome (virtually) unrecombined
– a daughter inherits half of her father’s autosomal dna + his full x-chromsome (virtually) unrecombined
– both sons and daughters inherit half their mother’s autosomal dna + one x-chromosome (recombined)
– etc., etc. (for more details on the other familial genetic relationships, see the previous post, esp. all the comments — if you can stand it.)

so, here we go. i don’t have all the calculations made yet, but here’s a start (figures rounded to four decimals; key at the bottom):

0.4920 F — s 0.4920
0.5081 F — d 0.5000
0.5000 M — s 0.4951 0.5081
0.5000 M — d 0.5000

and now for other family members (these numbers are probabilities, not exact percentages as between parents and children):

0.5050 B — B 0.5050
0.4951 B — Z 0.4872
0.5127 Z — Z 0.5127

(oops. fogot to calculate the grandfathers. that’ll have to wait ’til tomorrow. or sunday.)

0.2509 PGF — s 0.2509
0.2410 PGF — d 0.2372
0.2540 MGF — s 0.2540
0.2540 MGF — d 0.2500
0.2372 PGM — s 0.2411
0.2628 PGM — d 0.2628
0.2500 MGM — s 0.2476 0.2540
0.2500 MGM — d 0.2500

0.2510 FB — s 0.2510
0.2541 FB — d 0.2500
0.2372 FZ — s 0.2411
0.2500 FZ — d 0.2500
0.2541 0.2476 MB — s 0.2541 0.2476
0.2476 MB — d 0.2436
0.2756 0.2564 MZ — s 0.2606
0.2564 MZ — d 0.2564

FBD – s 0.1205
FBS – s 0.1304
FZD – s 0.1205
FZS – s 0.1205
MBD – s 0.1270
MBS – s 0.1205
MZD – s 0.1303
MZS – s 0.1303

FBD – d 0.1314
FBS – d 0.1186
FZD – d 0.1250
FZS – d 0.1250
MBD – d 0.1250
MBS – d 0.1186
MZD – d 0.1282
MZS – d 0.1282

(another oops! don’t have calculations yet for the cousins→sons OR for cousins→daughters and aunts, uncles or cousins, either. jeez, i’m such a slacker!)

well, there you have (some of) it.

i’m not going to make a lot of comments about this tonight (esp. since i don’t have all the calculations finished), but here are some interesting notes: 1) out of all his cousins, a son is most closely related to his FBS — that’s ’cause they share a full y-chromsome; 2) out of all his female cousins, a son is most closely related to his MZD — that’s kinda interesting ’cause, i think, the most common form of cousin marriage is MBD — and then we have FBD marriage in the formerly-part-of-the-caliphate world and, yet, that’s one of the cousins a guy is least related to — but he’s really related to her brother.

ok. that’s it for now. more on this anon.

– key –
F = father
M = mother
s = son
d = daughter
B = brother
Z = sister
PGM = paternal grandmother
MGM = maternal grandmother
FB = paternal uncle
FZ = paternal aunt
MB = maternal uncle
MZ = maternal aunt
FBD = father’s brother’s daughter
FBS = father’s brother’s son
FZD = father’s sister’s daughter
FZS = father’s sister’s son
MBD = mother’s brother’s daughter
MBS = mother’s brother’s son
MZD = mother’s sister’s daughter
MZS = mother’s sister’s son

previously: all cousins are not created equal and all grandmas are not created equal and the apple of his eye.

edit: oh — if anyone (is a glutton for punishment and) wants to check my math, feel free. please! (pretty please?)

update 05/29: corrections have been made, numbers have been added (grandfathers, daughters, but not yet cousins→sons OR for cousins→daughters — those will have to wait for another day.) many, many thanks to the AWEsome, albeit reluctant, apostate for his help. he’s really cool! (^_^)

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