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What is better under what circumstances?
Posted: Posted July 8th
Edited July 8th by chiarizio
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In both some Sikh and some Hindu communities in India, there are restrictions thought of as “consanguinity restrictions”, based on 49 purely patrilineal descent groups presumably from 49 named “sages”.

In one Sikh group I read about, before a young couple can be betrothed, the community’s elders must determine that no grandparent of either party belongs to the same patrilineal descent group (“gotra”) as any grandparent of the other party.
(Technically the fiancé and fiancée could still be quadruple-half-second-cousins; each grandparent of each party could be a uterine half-sibling of some grandparent of the other party. But the odds are against that.)

But in some Hindu group I read about, they make sure the groom, his mother, his father’s mother, and his father’s father’s mother, are none of them from the same gotra as any of the bride, her mother, her father’s mother, and her FFM.
This could allow the fiancé and fiancée to be each other’s half-cousins; their mothers could be uterine half-sisters. (They could at the same time be half-second-cousins, because their father’s mothers could be each other’s uterine half-sisters. And half-third-cousins, because their FFMs could be uterine half-sisters.)

So, for what purposes, or under what circumstances, is it or would it be, better: to keep
the set of {H’s, HM’s, HFM’s, HFFM’s} patriclans (“gotras”) from intersecting
the set of {W’s, WM’s, WFM’s, WFFM’s} gotras, the way the Hindus mentioned above do;
than to keep
the set of {H’s, HM’s, HFM’s, HMM’s} gotras from intersecting
the set of {W’s, WM’s, WFM’s, WMM’s} gotras, the way the Sikhs mentioned above do?

(In case it’s hard to tell; the “Hindu set” includes the father’s paternal grandmother— the FFM— but the “Sikh set” includes the maternal grandmother MM. The Hindu set doesn’t include any ancestress’s ancestress (like MM), and the Sikh set doesn’t include any great-grandparent (like FFM). )

—————






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I think one reason for keeping track of the patrilineal lines but not the matrilineal ones, or mixed ones, is that it's comparatively easy to keep track of who someone's mother is. Even if they don't have an official rule about not marrying your mother's uterine half-sister's child (or grandmother's uterine half-sister's grandchild or great grandmother's uterine half-sister's greatgrandchild), there might be an unofficial "it would be weird" reaction in most people.

Plus, from what you've written, it's not just direct relatives, but people are in the same descent groups. So someone's maternal grandfather could be in descent group A, and their prospective spouse could have one of these specific relatives be 15th cousins so many times removed (as a hypothetical) from that person, but because they both can trace their descent back to the same guy by the paternal lines, the two people can't be married.

That said, there are definitely people who would marry their half-cousins, half-second cousins and especially half-third cousins, if those cousins were otherwise considered ok by their system. This probably wouldn't even be all that problematic genetically. In other marriage systems, cross cousins are not only allowable but the preferred marriage option, and when a cross cousin is not available, often the marriage partner will be someone classed with the would be cross cousin.

Posted July 8th by linguistcat
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@linguistcat:
Thanks for the thoughtful reply!
I will respond to it sometime when I’m not in a doctor’s waiting-room.


Posted July 8th by chiarizio
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@linguistcat:

I think one reason for keeping track of the patrilineal lines but not the matrilineal ones, or mixed ones, is that it's comparatively easy to keep track of who someone's mother is. Even if they don't have an official rule about not marrying your mother's uterine half-sister's child (or grandmother's uterine half-sister's grandchild or great grandmother's uterine half-sister's greatgrandchild), there might be an unofficial "it would be weird" reaction in most people.


“Rule” can mean different things; and it’s my bad that I didn’t say what I meant here by “rule”.
If there’s anything nobody ever does then there’s “effectively” a “virtual rule” against it, in the meaning I had in mind. I think. I might have been a bit ambivalent or ambiguous.

https://www.thehindu.com/opinion/open-page/People-of-the-same-gotra-do-not-necessarily-have-the-same-origin/article16183792.ece
gives several reasons or motives for the rule against marrying within the same gotra in Hinduism.
They also give several reasons they think the rule is out-of-date and unscientific, and the reasons given to conserve the rule are (in their opinions) unconvincing.
I think emphasising patrilineal exogamy over any other kind of exogamy, usually goes with patrilocality and virilocality and patriarchy, especially with the notion that whatever is most valuable, particularly if that happens to be real estate, is inherited father-to-son, not mother-to-daughter. (Nor, for that matter, father-to-daughter nor mother-to-son.)
I don’t know how strong that connection is; the real-life societies I’ve read about where family names were all patrilineal, but real estate was inherited matrilineally and residence was matrilocal and duolocal or uxorilocal, real-estate was not the most valuable thing.
And I can’t really prove anything.

Plus, from what you've written, it's not just direct relatives, but people are in the same descent groups. So someone's maternal grandfather could be in descent group A, and their prospective spouse could have one of these specific relatives be 15th cousins so many times removed (as a hypothetical) from that person, but because they both can trace their descent back to the same guy by the paternal lines, the two people can't be married.


“The Hindu” makes that same objection to the Gotra system.
If you had an ancestor 7 or more generations ago, you average about 3/8 of a chromosome in common with them, unless one of the following two exceptional circumstances obtain:
  • they and all of the intervening ancestors were/are female, in which case you have probably exactly the same mitochondrial DNA in common; or,
  • you and they and all of the intervening ancestors were/are male, in which case you have probably exactly the same Y-chromosome as them.

    If two women share a matrilineal ancestress 7 generations ago, maybe they shouldn’t procreate together. But they’re both women, so that’s not going to be a problem, is it?
    If two men share a patrilineal ancestor 7 generations ago, maybe they shouldn’t procreate together.
    But they’re both men; still not a problem!

    That said, there are definitely people who would marry their half-cousins, half-second cousins and especially half-third cousins, if those cousins were otherwise considered ok by their system. This probably wouldn't even be all that problematic genetically. In other marriage systems, cross cousins are not only allowable but the preferred marriage option, and when a cross cousin is not available, often the marriage partner will be someone classed with the would be cross cousin.


    I am interested in exactly what the index of shared variable autosomal genetic information inherited from recent ancestors should be the limit beyond which people shouldn’t marry. I have a feeling it’s about 1/16 or 6.25%. If so, half-first-cousins or full-first-cousins-once-removed would be right on the edge.
    [edit:]It turns out the accepted genetics definition of consanguineous parents is, at least 1/32 or 3.125% of their variable autosomal genes are shared. (As much as full-second-cousins.) If they share less than that they don’t count as consanguineous. Note that if both parents come from a background wherein most marriages have been consanguineous for generations, they may share more than 1/32 of their variable autosomal genes even if they aren’t as closely related as second-cousins. [/edit]

    One state in the US won’t let full-first-cousins-once-removed marry. I don’t know if they’ll allow half-first-cousins-once-removed, whose index is 1/32 or 3.125% (about one-and-a-half chromosomes-worth) to marry.
    There’s another state that will allow full-first-cousins (whose index is 1/8 or 12.5%) to marry, but will not allow double-full-first-cousins (whose index is 1/4 or 25%) to marry.

    Worldwide the commonest prescriptive marriage system and classificatory kinship system prescribes marriage between a man and his mother’s-side cross-cousin, his mother’s brother’s daughter, or a girl classed as such.
    The second commonest prescribes that a man marry his father’s-side cross-cousin, his father’s sister’s daughter, or a girl classed as such.
    The third commonest prescribes that a man marry his double-cross-cousin, the daughter of his mother’s brother and his father’s sister, or a girl classed as such.

    Clearly the first two systems allow marriages between a couple who already have 1/8 of their variable autosomal genes in common; but it may be very common that they go with the “girl classed with such”, and rarely go with the girl we would call their “actual cousin”.
    The third system would allow marriage between people who have 1/4 of their variable autosomal genes in common — as much as a pair of half-siblings. But it again might be uncommon for them to marry their “actual double-cousins”, and instead be more common to marry their “classificatory double-cousins”.

    Without the classificatory kinship system — or at least without the FB=F and MZ=M classifications — there are preferential marriage systems pretty common where W=FBD is preferred, or W=MZD is preferred, that is marriage to a parallel-cousin is preferred.

    These systems institutionalise an increased risk that the couple’s offspring will inherit two copies of some harmful recessive gene. For full-first-cousins I have read that this risk is about 5%, unless they come from a family that regularly practices cousin-marriage. That’s statistically significant, but probably still tolerable, provided neither their parents nor their children practice cousin-marriage.

    If they are half-first-cousins-once removed, or full-second-cousins, they share 1/32 of their variable autosomal genes in common (on average). I wouldn’t say that’s close enough to worry about.

    Wikipedia says if they share just one greatgreatgreatgrandparent, that is they are half-fourth-cousins, they are no closer than any two members of the same landrace. So there’s no improvement in diversity if they’d be proscribed to each other but they practice racial endogamy.

    —————

    I get the impression that prohibiting people with a common patrilineal ancestor and/or a common matrilineal ancestress, has motives other than promoting genetic diversity and avoiding offspring inheriting a double dose of some harmful recessive gene.
    The Basque justification for not allowing first-cousins to marry is that they’d both inherit (property) from the same grandfather.
    If the couple were seven degrees apart or more — say the greatgreatgrandparent of one were the greatgrandparent of the other — then I think the amount of shared variable autosomal genes in common would be negligible.

    —————

    So, I think, if the proscriptions are for the purpose of avoiding inbreeding, it would be more important to make sure the mother’s mothers are not the same, than to make sure the father’s father’s mothers are different.
    (And more important to make sure the FFs are different than to make sure the MMFs are different).

    But there are circumstances in which that’s not the main purpose of the consanguinity restrictions, even if the prevailingly-believed myth is that it is. (Or, at least, so it appears; at least, to me.)
    It may be to make sure bridewealth and dowries and prestations circulate; or to make sure bequests circulate.
    Or it might be some of the ideas expressed in that “The Hindu” article are correct.

    I don’t really know.

    ———

    If you have any ideas they’ll probably help me!


  • Edited July 12th by chiarizio
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    I wrote:
    I am interested in exactly what the index of shared variable autosomal genetic information inherited from recent ancestors should be the limit beyond which people shouldn’t marry. I have a feeling it’s about 1/16 or 6.25%.


    I found https://en.m.wikipedia.org/wiki/Consanguinity#Genetic_definitions says:
    Genetic consanguinity is expressed as defined 1922 by Wright<ref>{{cite journal |last1=Wright |first1=Sewall |authorlink=Sewall Wright |year=1922 |title=Coefficients of inbreeding and relationship |url= https://zenodo.org/record/1431365|journal=[[American Naturalist]] |volume=56 |issue=645 |pages=330–338 |doi=10.1086/279872}}</ref> with the [[coefficient of relationship]] ''r'', where ''r'' is defined as the fraction of [[zygosity|homozygous]] due to the consanguinity under discussion. Thus, a parent and child pair has a value of ''r''=0.5 (sharing 50% of genes), siblings have a value of ''r''=0.5, a parent's sibling has ''r''=0.25 (25% of genes), and first cousins have ''r''=0.125 (12,5% of genes). These are often expressed in terms of a percentage of shared DNA.

    As a working definition, unions contracted between persons biologically related as second cousins or closer (''r'' ≥ 0.03125) are categorized as consanguineous. This arbitrary limit has been chosen because the genetic influence in marriages between couples related to a lesser degree would usually be expected to differ only slightly from that observed in the general population. Globally it is estimated that at least 8.5% of children have consanguineous parents.<ref>{{Cite web|title=Consanguineous Marriage and Inherited Disorders|url=https://www.bradford.gov.uk/media/1901/hgsg-briefing-paper-consanguineous-marriage.pdf|first=Aamra|last=Darr|publisher=City of Bradford|accessdate=31 August 2016 |location=University of Bradforddate=14 October 2010}}</ref>

    In clinical genetics, consanguinity is defined as a union between two individuals who are related as second cousins or closer, with the inbreeding coefficient (F) equal or higher than 0.0156.where (F) represents the proportion of genetic loci at which the child of a consanguineous couple might inherit identical gene copies from both parents.<ref name=hamamy>Hanan Hamamy. [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3419292/pdf/12687_2011_Article_72.pdf Consanguineous marriages. Preconception consultation in primary health care settings.] J Community Genet (2012) 3:185–192 DOI 10.1007/s12687-011-0072-y.</ref>


    So it looks like the accepted limit is about 1/32 or 3.125%.

    Anyone less closely related than full-second-cousins would be considered “unrelated” for purposes of estimating the risk to offspring of inheriting two copies of the same harmful recessive allele at the same locus.

    That would include half-second-cousins, and full second-cousins-once-removed, for whom the “coefficient of relationship” r=1.5625% or 1/64; or a couple who share three different ancestors each of whom is a greatgreatgrandparent of one of them and a greatgrandparent of the other, for whom the coefficient r=2.34375% or 3/128; and various other blood-relations, for instance triple-third-cousins, with a coefficient of relationship below 1/32 or 3.125%. (For triple-third-cousins it’s 3/128, about 2.3438%.)

    For instance, 15-tuple fourth-cousins would have a coefficient of relationship r=15/512 or 2.9296875%, or let’s just say roughly 2.9297%. They’d also be considered effectively unrelated, or at least negligibly related, for this purpose.

    (In such a case, of each party’s 16 greatgreatgrandparents, 15 would be full-siblings to one of the other party’s greatgreatgrandparents. There are clearly 16! (that is, “16 factorial”) different ways that could happen. Don’t worry, I will never post 16! of anything. I’ll probably never post 32 of anything!.)

    63-tuple 5th-cousins would have r=63/2048 = about 3.0762%.
    That’s also less than 1/32 = 3.125%.



    Edited July 10th by chiarizio
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    This post kind of blew my mind, so I made a chart for my own use.

    Hindu Layout

    Looking at the group of 8 great-grandparents, they could intersect on any of the following:

  • FFF

  • FMM or FMF (MF doesn't match so only one of these can intersect)

  • 3/4 of MMM, MMF, MFM, MFF

    At most, they could intersect at 5/8 points, which makes them slightly more closely-related than first-cousins.

    Sikh Layout

    The great-grandparents that could intersect are:

  • FFM and FFF

  • Either FMM or FMF

  • Either MMM or MMF

  • MFM and MFF

    At most, they could intersect at 6/8 points, which is equivalent to sharing 3/4 grandparents (though they can't share that many actual grandparents in practice).

  • Posted July 10th by Xhin
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    Xhin
    Sky's the limit

    Thank you, @Xhin:

    I can’t quite understand your last post.

    Here’s what I calculate; maybe you can get explicit and explanatory, in clarifying how my —- let’s call it an “analysis” —- differs from yours?

    ———————————————————

    In what I called “the Hindu System”;

    H, HF, HFF, HFFF, HFFFF, (H and his patrilineal ancestors),
    HMF, HMFF, HMFFF, (HM’s patrilineal ancestors),
    HFMF, HFMFF, (HFM’s patrilineal ancestors),
    HFFMF, (HFFM’s patrilineal ancestor),
    WF, WFF, WFFF, WFFFF, (W’s patrilineal ancestors),
    WMF, WMFF, WMFFF, (WM’s patrilineal ancestors),
    WFMF, WFMFF, (WFM’s patrilineal ancestors),
    WFFMF, (WFFM’s patrilineal ancestor),
    all have to be 21 different guys,

    and
    HM, HFM, HFFM,
    W, WM, WFM, WFFM,
    all have to be 7 different women.

    But we could have any matchup of
    HMM, HFMM, HFFMM, HFFFM,
    with any of
    WMM, WFMM, WFFMM, WFFFM,
    be the same woman.

  • The husband’s mother HM and the wife’s mother WM can be enate half-sisters, because they have the same mother (HMM=WMM).
    That makes H and W half-cousins, and adds 1/(2^4) to their coefficient of relatedness.
    It also means they have the same MMM and the same MMF (ie HMMF=WMMF and HMMM=WMMM), but that adds nothing new to the coefficient, because we already have accounted for HMM=WMM.

  • The husband’s father’s mother HFM can be the enate half-sister of the wife’s father’s mother WFM.
    In other words it may be that HFMM=WFMM.
    But in this system they can’t have HFMF=WFMF, because if that were true, then HFM and WFM would belong to the same patriclan.
    So since HFMM=WFMM, HFM and WFM are enate half-sisters, so HF and WF are half-cousins, and H and W are half-second-cousins.
    That adds an additional 1/(2^6) to their coefficient. 1/16 + 1/64 = 5/64 is what it is so far.

  • But HFFM and WFFM can also be enate half-sisters.
    They can’t be full sisters nor agnate half-sisters, because they don’t belong to the same patriclan.
    So HFFMF and WFFMF have to be different, but HFFMM and WFFMM can be the same.
    So H and W can be half-third-cousins; which adds an extra 1/256 to their coefficient, making the running total so far be 21/256.

  • And HFFF and WFFF can be enate half-brothers; there’s no rule that HFFFM and WFFFM can’t be the same woman,
    but HFFF and WFFF can’t be in the same patriclan,
    because HFFF’s patriclan is HFF’s patriclan is HF’s patriclan is H’s patriclan,
    and that has to be different from W’s and WF’s and WFF’s and WFFF’s patriclan.
    HFFFF and WFFFF can’t be the same guy; but HFFFM and WFFFM can be the same woman.
    So H and W can actually be double-half-third-cousins.
    This adds an additional 1/256 to their coefficient.
    Their coefficient is now 1/16 + 1/64 + 1/256 +1/256 = 22/256 = 11/128.

    If I’d assumed HMM=WMM, HFMM=WFMM, HFFMM=WFFFM, HFFFM=WFFMM,
    instead of HMM=WMM, HFMM=WFMM, HFFMM=WFFMM, HFFFM=WFFFM,
    the coefficient of relatedness would have turned out the same.

    ——————————————————

    In what I’d called “the Sikh system”:

    H, HF, HFF, HFFF, HFFFF, (H and his patrilineal ancestors),
    HMF, HMFF, HMFFF, (HM’s patrilineal ancestors),
    HFMF, HFMFF, (HFM’s patrilineal ancestors),
    HMMF, HMMFF, (HMM’s patrilineal ancestors),
    WF, WFF, WFFF, WFFFF, (W’s patrilineal ancestors),
    WMF, WMFF, WMFFF, (WM’s patrilineal ancestors),
    WFMF, WFMFF, (WFM’s patrilineal ancestors),
    WMMF, WMMFF, (WMM’s patrilineal ancestors),
    have to be 23 different guys,

    and
    HM, HFM, HMM,
    W, WM, WFM, WMM,
    have to be 7 different women.

    But there can be any matchup of
    HFFM, HFMM, HMFM, HMMM,
    with any of
    WFFM, WFMM, WMFM, WMMM,
    to be the same woman.

    Any grandparent of H can be an enate half-sibling of any grandparent of W.

    There are 4*3*2*1=24 ways to match each grandparent of either party to exactly one grandparent of the other party,
    and have them be enate half-siblings.

    So H and W can be quadruple-half-second-cousins.

    Their coefficient of relationship could go as high as 1/64 + 1/64 + 1/64 + 1/64 = 1/16.

    ————————————————

    1/16 is 8/128, 3/128 less than 11/128.
    In the “Hindu” system, husband and wife can be more consanguineous, from a genetics POV, than they can be in the “Sikh” system.

    In the “Sikh” system, any great-grandmother of either party can be also some great-grandmother of the other party.
    That’s not exactly what happens in the Hindu system.

    —————

    I’d like to make a table.



  • Edited July 10th by chiarizio
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    @linguistcat:
    From commentaries on the proscriptions on sex and marriage in the Hebrew bible (aka “Old Testament”), people seem to think that a lot of the proscriptions that concentrated on patrilineal relationships as opposed to matrilineal or mixed ones, were there to prevent arguments or fights or bad feeling or bad blood, between patrilineal relatives.
    Because men were patrilocal and women were virilocal, there seemed to be no such risk of friction between matrilineal relatives: so the only proscription necessary on the matrilineal side, was, that a man who was already married, shouldn’t marry a close matrilineal relative of one of his current wives.
    I don’t know how reliable or accurate that is.


    Posted July 10th by chiarizio
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