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# Science, Math, & Technology

## 961 kinships and how they’re classified

Posted 2 Weeks ago by chiarizio

See https://anthropology.ua.edu/Faculty/murphy/436/kinship.htm
And especially

And the surrounding data and the links and references.

I’m going to consider 961 = 31*31 possible relationships between EGO and ALTER.
There are up to 31 people in a set consisting of
{EGO, EGO’s Parents, EGO’s Grandparents, EGO’s Great-grandparents, and EGO’s GGreat-grandparents}.
Similarly there are up to 31 people in a set consisting of ALTER and ALTER’s ancestors or forebears up to four generations before ALTER.
The kinships I’m planning to classify are those in which EGO or one of EGO’s ancestors up to four generations back, is a sibling of ALTER or one of ALTER’s ancestors up to four generations back.

(If I go back just three generations there’d be 15*15=225 kinship relations to consider. If I go back five there’d be 63*63=3969.)
(I don’t want to consider more than a thousand.)
(Another author already considered the 7*7=49 relations that go back up to two generations.)

The main division the anthropologists referred to or quoted above use, are the following.
1. With the possible exceptions of EGO and/or ALTER themselves, all of the linking relatives are male.
In other words one of
{EGO, EGO’s F, EGO’s FF, EGO’s FFF, EGO’s FFFF}
is siblings with one of
{ALTER, ALTER’s F, ALTER’s FF, ALTER’s FFF, ALTER’s FFFF}.
There are 5*5=25 such kinship relations. They are all patrilineal; they all imply that EGO and ALTER belong to the same patriclan.

2. With the possible exceptions of EGO and/or ALTER themselves, all of the linking relatives are female.
In other words one of
{EGO, EGO’s M, EGO’s MM, EGO’s MMM, EGO’s MMMM}
is siblings with one of
{ALTER, ALTER’s M, ALTER’s MM, ALTER’s MMM, ALTER’s MMMM}.
There are 5*5=25 such kinship relations. They are all matrilineal; they all imply that EGO and ALTER belong to the same matriclan.

Note that there’s an overlap. The relation that EGO and ALTER are each other’s sibling, is in both groups; it implies they are both in the same patriclan and the same matriclan.

3. The set of linking relatives between EGO and ALTER includes both males and females.

.....

Set 3 can be divided into two subsets in two different ways.
3a Either the number of males and the number of females between (but not including) EGO and ALTER are equal, or differ by at most one;
3a’ or else the number of linking relatives of one sex exceeds the number of the other sex by more than one.

3b Either the order in which the sexes occur in the chain of linking relatives is systematic and predictable;
3b’ or else the order in which the sexes occur in the chain of linking relatives is random or unsystematic or unpredictable.

I can think of three different ways for 3b to happen. There may be others but I can’t think of them.
3b1 the sexes alternate.
3b2 the males are all closer to EGO and further from ALTER than any of the females, and the females are all closer to ALTER and further from EGO than any of the males.
3b3 the females are all closer to EGO and further from ALTER than any of the males, and the males are all closer to ALTER and further from EGO than any of the females.

Some things that can happen.

• one of the set {EGO’s F, EGO’s MF, EGO’s FMF, EGO’s MFMF}
is the brother of one of the set {ALTER’s F, ALTER’s MF, ALTER’s FMF, ALTER’s MFMF},
so one of EGO’s parents is in the same Alterclan as one of ALTER’s parents.

• one of the set {EGO’s M, EGO’s FM, EGO’s MFM, EGO’s FMFM}
is the sister of one of the set {ALTER’s M, ALTER’s FM, ALTER’s MFM, ALTER’s FMFM},
so one of EGO’s parents is in the same Alterclan as one of ALTER’s parents.

• The chain of linking relatives (possibly excepting either or both of EGO and ALTER themselves) strictly alternates by sex.
Either one of the set {EGO’s F, EGO’s MF, EGO’s FMF, EGO’s MFMF} and one of the set {ALTER’s M, ALTER’s FM, ALTER’s MFM, ALTER’s FMFM} are brother and sister,
or one of the set {EGO’s M, EGO’s FM, EGO’s MFM, EGO’s FMFM} and one of the set {ALTER’s F, ALTER’s MF, ALTER’s FMF, ALTER’s MFMF} are sister and brother.
That doesn’t imply that they share a clan.

In all of the above, the number of linking males and the number of linking females are probably pretty close, and also the order of females and males are pretty predictable.

Other things that can happen:
• One of {EGO’s F, EGO’s FF, EGO’s FFF, EGO’s FFFF} and one of {ALTER’s M, ALTER’s MM, ALTER’s MMM, ALTER’s MMMM} could be brother and sister. (Here all of the males are closer to EGO and all of the females are closer to ALTER.)
Or
• one of {EGO’s M, EGO’s MM, EGO’s MMM, EGO’s MMMM} and one of {ALTER’s F, ALTER’s FF, ALTER’s FFF, ALTER’s FFFF} could be sister and brother. (Here all of the females are closer to EGO and all of the males are closer to ALTER.)

So there are 4*4=16 + 4*4=16, totaling 32, kinships putting a parent of EGO in the same Alterclan as a parent of ALTER;
Another 32 kinships wherein the chain of linking relatives strictly alternate by sex but not implying a parent of EGO shares a clan with a parent of ALTER;
And 32 kinships implying a patrilineal ancestor of one of them, and a matrilineal ancestress of the other, are brother-and-sister.

That’s <=145 of these kinships classified so far. (If EGO or either of EGO’s parents is a sibling of ALTER or one of ALTER’s parents I might have double-counted that kinship.)

....

There are other such kinships-by-descent satisfying 3b2 and 3b3. But I don’t know a good way to talk about them.

Anyway there are still at least 961-145 = 816 kinships in this group I haven’t even talked about yet.
For most of them the chain of linking relatives will be of mixed sex in no particular order and in unequal numbers.

....

If there are six or more linking relatives other than EGO and ALTER themselves, the odds they inherit a variable gene from a recent common ancestor will be below 3/8 of a chromosome (maybe more like 11/32 of a chromosome): unless it’s the Y chromosome (because both EGO and ALTER and all the linking relatives are male), or some mitochondrial DNA (because all the linking relatives, possibly excepting EGO and/or ALTER themselves, are all female).
If they are as closely related as second-cousins-once-removed or closer, they probably have a better-than-even chance of having inherited a copy of the same chromosome from a recent common ancestor, even if that’s not the Y chromosome nor a mitochondrial gene. Otherwise they might be no closer, genetically, than strangers-in-blood.

• ## There are 1 Replies

Suppose I classify ancestors and ancestresses into the following seven groups,
For illustration purposes I’ll use the 63-member family tree for five or fewer generations.

First there is the individual themself; EGO or ALTER. This “group” has only one member.

Then there are all their patrilineal male ancestors; back to five generations those will be F, FF, FFF, FFFF, FFFFF, ...

Then there are all their matrilineal female ancestresses; back to five generations these are M, MM, MMM, MMMM, MMMMM, ...

Then there are the alternating ancestors and ancestresses of their father; e.g. FM, FMF, FMFM, FMFMF, ...

And the alternating forebears of their mother; MF, MFM, MFMF, MFMFM, ...

Then all the matrilineal ancestresses of their patrilineal ancestors:
FMM, FMMM, FMMMM;
FFM, FFMM, FFMMM;
FFFM, FFFMM;
FFFFM; ...

And all the patrilineal ancestors of their matrilineal ancestresses:
MFF, MFFF, MFFFF;
MMF, MMFF, MMFFF;
MMMF, MMMFF;
MMMMF; ...

Note all parents and grandparents and greatgrandparents are included.
Greatgreatgrandparents are not all included. FFMF and FMFF and FMMF and MMFM and MFMM and MFFM are excluded. Maybe some of them should be included but I just haven’t thought of a way.

==== ..... ===== ..... ===== ..... ===== ..... =====

We can classify “kinship relations by descent” in 49 groups, saying a forebear of EGO in one of these classes, is a sibling of a forebear of ALTER in one of these classes.

..... ——— ...... ——— ...... ——— ...... ——— ...... ——— ......

Going back five or fewer generations these seven classes cover 37 of the forebear-types in each family tree.
There are 1*1=1 relation in which ALTER and EGO are siblings;
1*36=36 in which ALTER is a collateral descendant of EGO;
36*1=36 in which ALTER is a collateral ancestor of EGO;
And 36*36=1296 cousin-type relations.
For a total of 37*37 = 1369 relations classified this way.

I doubt this is the only way to do this.

....

On top of this there’s still the cross-versus-parallel classification for the cousin-like kinship relations.
If the sibling-pair of apical ancestors are the same sex it’s a parallel relation; if they’re opposite sex it’s a cross relation.

1 Week ago
chiarizio