# 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….

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