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?)

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7 Comments

  1. In terms of the MZD and FBD systems it seems there is more relatedness at all levels with the MZD system so the band of brothers theory doesn’t work out as a specific driver for FBD marriage unless there is an additional factor like a compounding effect across generations.

    Of course if the driver of FBD was herd inheritance then greater relatedness might result simply from inter-marrying within a smaller total pool due to the lower population density of pastoralism.

    Shame if so. A marriage system selected for specifically maximizing male relatedness is a fun theory. However the same end result of males being more related to each other in some groups rather than others might simply come about from the smaller pool effect (i think?) so you still get the differential toughness factor of low-density populations (nomads and mountain people) versus higher-density people.

    Reply

  2. @g.w. – “…so the band of brothers theory doesn’t work out as a specific driver for FBD marriage unless there is an additional factor like a compounding effect across generations.”

    the one thing that’s unique about the fbd system is that all the men wind up having (virtually) the same y-chromosome. i don’t know what difference(s) that should make, but it does carry the genes that make men men. -??-

    also, the fbd system keeps the lineage closed unlike, as you’ve seen, the mbd system which can create alliances across many, many lineages.

    Reply

  3. “the one thing that’s unique about the fbd system is that all the men wind up having (virtually) the same y-chromosome”

    yes, more related in general terms in the MZD pattern but more related in the y chromosome in FBD. maybe

    the other thing i realised was if you had two pieces of terriotory with the same surface area but one was steppe/mountains that could only support twelve little villages of 200 people each whereas the other was a river valley that could support twelve villages of 600 people each then, even if both peoples followed the same female circulating pattern between each of their twelve settelements the mountain dwellers would be circulating around a total pool of 1200 people and the valley dwellers a toal pool of 7200. Which i think would mean the mountain dwellers would always be more inter-related?

    If so then all environments that forced lower population density would get the stronger band of brothers effect?

    i still wonder about the FBD thing though. my gut feel is it would be a benefit in low-level violence (and a disbenefit in large-scale teamwork violence)

    what would be great would be a computer program where you could set the size of your original population and a specific marriage pattern and run it over multiple generations to see what you up with – with options to throw in polygamy effects etc

    Reply

  4. @g.w. – “what would be great would be a computer program where you could set the size of your original population and a specific marriage pattern and run it over multiple generations to see what you up with – with options to throw in polygamy effects etc.’

    now you’re talkin’! “sim mating patterns.” (^_^)

    Reply

  5. @g.w. – “In terms of the MZD and FBD systems it seems there is more relatedness at all levels with the MZD system so the band of brothers theory doesn’t work out as a specific driver for FBD marriage unless there is an additional factor like a compounding effect across generations.”

    i thought of something late last night that might alter the scenario a bit, but i’m not sure how much.

    in societies where they practice fbd marriage, there is often a certain amount double first-cousin marriage. genetically, double first-cousins are like half-siblings. this, obviously, changes the relatedness levels.

    in afghanistan, for example, 7% of consanguineous marriages are to double-first cousins (46.2% of marriages were consanguineous).

    could double first-cousin marriages have been more prevelant in the past in times when it was less easy to travel? dunno.

    anyway, one day, when i’m not so tired, i’ll have to do the math for double first-cousin marriages. not tonight, tho. yaaaaaaaaaaawn. (~_^)

    Reply

  6. “could double first-cousin marriages have been more prevelant in the past in times when it was less easy to travel? dunno.”

    ah yes, compound interest type effects

    .
    “anyway, one day, when i’m not so tired, i’ll have to do the math for double first-cousin marriages. not tonight, tho. yaaaaaaaaaaawn. (~_^)”

    :)

    .
    A thought i had, of all the times in history where a King or other ruler had a brother who tried to usurp the crown, i wonder if that ever happened with a twin?

    It’s like that expression “i’ve got your back!” to mean i’m guarding your back, with twins the expression is literally true.

    Reply

  7. @g.w. – “A thought i had, of all the times in history where a King or other ruler had a brother who tried to usurp the crown, i wonder if that ever happened with a twin?”

    i dunno! something else to research. (^_^)

    you know, identical twins are clearly the most genetically related to each other (until we can manage to clone ourselves (~_^) ), but they are, surprisingly, not absolutely identical genetically. who knew?!

    so, when push comes to shove, even an identical twin may give a push.

    Reply

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