altruism towards cousins

here’s a neat, little paper i came across during my r&r: Altruism towards Cousins [pdf]. sounds like it should be right up my alley! (^_^)

the authors — joonghwan jeon and david m. buss — conducted a study of some “w.e.i.r.d.” students at the univ. of texas (n=195) to see if they might treat and feel about their different cousins differently — the different cousins being (hold on!): father’s brother’s (FB) kids, father’s sister’s (FZ) kids, mother’s brother’s (MB) kids, and mother’s sister’s (MZ) kids. they quizzed their subjects on such things like, “would you run into a burning building to save your father’s brother’s son?” — and so on and so forth.

their hypothesis was that, because of paternity uncertainty, people ought to feel closer to, and be more altruistic towards, their mother’s sister’s kids since the connection between those cousins is via two mothers (mother and mother’s sister) and, therefore, the relatedness pretty certain. on the other hand, people ought to show the least altruism towards their father’s brother’s kids since, in that case, the connection is via two fathers (father and father’s brother) thus a LOT of paternity uncertainty there.

they figured that the pattern of altruism ought to go like this: MZ kids first, FB kids last, MB and FZ kids somewhere in between.

so, what did they find?

well, after tweaking the data a bit — i.e. to include things like residential proximity (or not) — they found that, yes, indeed, people are (or say that they would be) the most altruistic towards their MZ kids, then their MB kids, then their FZ kids, and lastly their FB kids. that seems to fit their hypothesis perfectly! however, the authors do note that, all things considered [pg. 1185]:

It is reasonable to conclude, however, that FaSis children [FZ kids] are the least likely to be helped among all the four cousin categories, because (i) the mean rating of FaSis children was invariably the lowest in the willingness-to-help scores, as well as in all the three psychological variables affecting altruism, (ii) the predicted linear trends proved to be highly significant for all the four dependent measures, and (iii) FaSis children were helped more than FaBro children, as predicted, although it just missed conventional significance. Given that MoSis children were always ranked at the top position with a high statistical significance (p less than or equal to 0.001) for all dependent measures, it remains to be revealed why the degree to which FaBro children are the least likely to be helped appears not to be as robust as expected.”

that would make the pattern — MZ kids, MB kids, FB kids, FZ kids — which doesn’t fit their prediction. not perfectly, anyway.

the raw data really don’t fit their prediction (click on table for LARGER view):

here we see three different patterns. although MZ kids always do come first, in two instances, the FB kids came second — and they should come dead last according to the paternity uncertainty theory — AND the MB kids came last twice, which is not right at all:

– willingness-to-help (i.e. burning building) = MZ kids, FZ kids, FB kids, MB kids
– emotional closeness = MZ kids, FB kids, MB kids, FZ kids
– empathic concern = MZ kids, FB kids, FZ kids, MB kids
_____

what i wondered was: could the fact that the different cousins are, on average, related to each other to different degrees be connected to how altruistic cousins are to one another?

the coefficient of relationship between any two first cousins is 0.125 (give or take a few genes here and there) — but this figure doesn’t take into account the differential inheritance of the x- and y-chromosomes in humans, and that that alters the relatedness between different family members depending on whether they are male or female (for some background on this, see this post — also, see this paper).

a long time ago in you know where…, i sat down and calculated the coefficients of relationship for different family members with the differential inheritance of the x- and y-chromosomes in mind. the plan was to do that for ALL the family members — all the various cousins, etc. — but, the best laid plans of mice and female bloggers….

so, unfortunately, i don’t have any new-and-improved coefficients of relationship for all the various cousins (nor do i feel like working on them today), but i DO have them for brothers and sisters, i.e. FB, FZ, MB and MZ. i think we can use them as a proxy for the cousin coefficients. here they are (assuming no inbreeding):

FB (B-B on the chart if you follow the link) = 0.5050
FZ (B-Z) = 0.4951
MB (Z-B) = 0.4872
MZ (Z-Z) = 0.5128

and, rearranged to be in order of relatedness:

MZ = 0.5128
FB = 0.5050
FZ = 0.4951
MB = 0.4872

so, if I were to predict which type of cousin people would be most altruistic towards, i would pick the MZ kids (score! three points to moi) — the least would the MB kids (two points! according to the raw data) — and then the FB kids second (two more points for me!) — and the FZ kids third (one point). that’s eight points to me and … six points to jeon and buss (using their prediction and the raw data). (~_^)

i kinda like my explanation. (^_^) but i could be wrong, of course (the likelihood is that i am, right?).

see also: genealogical terminology

(note: comments do not require an email. cousins?)

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.

(note: comments do not require an email. or a comptometer. wait. wha?)

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*)

(note: comments do not require an email. but, quite possibly, a pocket protector.)

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

(note: comments do not require an email. or a slide-rule [probably].)

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

(note: comments do not require an email. did you want fries with that?)

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! (^_^)

(note: comments do not require an email. calculator, yes. email, no.)