Re: Korean/Japanese/Inupiaq/Aleut/Yupik/Samenoid(sp)

> Date:         Sun, 20 Aug 2000 23:40:17 -0700
> From:         Marcus Smith <smithma@...>
> Cavali-Svorza (I believe that's the spelling) has worked at a
> genetic family tree of all the races. There is lots of interesting
> stuff related to Native Americans, but since genetics is not
> something I understand really well, I can't recall most of it.
> Unusually large groupings around a small number of alleles,
> suggestive that there was a small number of original settlers who
> were closely related. Can't recall anything else.
At the time this came out, Cavalli-Sforza was criticized for not
taking into consideration (or even understanding) the limitations of
the technique he used. The computer will always spit out a nice tree,
but in some cases the branch structure may be very sensitive to small
changes in the input data.

For instance, if we have three genomes

        A xxNxxNxxNxxNxxNxx
        B xxNxxNxxOxxOxxOxx
        C xxPxxPxxPxxPxxPxx

then the distance between A and B is 2, and both A and B are at
distance 5 from C; the correct tree will clearly group A and B
together:

        A   B     C
         \ /     /
          Y     /
           \   /
            \ /
             Y

But what about this case:

        A xxNxxNxxNxxNxxNxx
        B xxNxxNxxNxxOxxOxx
        C xxOxxOxxOxxOxxOxx

The distance between A and B is again 2, and 5 between A and C. But B
is now only 3 away from C, and there's no way of making a tree that
correctly represents all three distances. The program has to choose
which one to get wrong:

        A   B     C     A   B     C     B   A C
         \ /     /       \   \   /       \ / /
          Y     /         \   \ /         Y /
           \   /           \   Y           Y
            \ /             \ /
             Y               Y

IIRC, the program will output the first tree, not only making B seem
much farther away from C than it really is, but also hiding the fact
that changing just gene in B from N to O would change the branch
structure at the 5 deep level.

(If the program is written properly, it will of course output warnings
when this sort of ambiguity is found, as well as sensitivity analyses
on the input data --- but the user has to understand the mathematics
to be able to interpret all that).

I don't know if C-S ever put up a defense against these critics (apart
from the classical "I plugged it into the chi-square table/a computer
program, and this is what I got, so of course it's right." Cf. Ruhlen
and the "I multiplied a lot of numbers, so there" argument).

Lars Mathiesen (U of Copenhagen CS Dep) <thorinn@...> (Humour NOT marked)