HAM Surname DNA Project
HAM Surname DNA Project
by Dave Hamm
I received an email from Laverne Piatt of Ontario, OH regarding how
many mutations she should expect to see for an ancestor that was born
in the 1670's. Good question. Aside from the normal
probability curves, can we answer that with something more direct, and
easy to calculate?
One question that remains in the back of my mind is how will I be
able to tell if or when one of the HAM groups might match the DNA of
one of our famous European cousins?
I have been working along the lines of DNA reconstruction, just in the
event that some day some genetic genius figures out a way to extract
enough DNA from the body of Odon's crystallized bones.
that at least one branch of our HAM lines descend from him, for
example, how will we know if any of our HAM groups would descend from
if the data was good enough, then we would be looking for things like
haplotype group, and the number of matching markers. But, if the data
is not good enough, then my question becomes, how can we reconstruct
what his DNA should have looked like?
those lines, I took a stab at answering the question of how many
mutating markers should we expect among any of his descendants that
might be living today?
the number of generations ago, and the number of markers tested, how
would we calculate the expected number of mutations for Odon, or say
perhaps Jerome HAM, given the birth date and the number of markers
tested? O.K., in the event that you are not so much interested in
either of them, but just want to figure out how many mutations you
might expect to see from your newly discovered-long-lost DNA
we have a general procedure for this (that might be easy to use)?
should be an equation somewhere that does this, but where?
For the heck of it, I grabbed Ken Nordtvedt's equation, and
pretty much butchered his intent, but it does give me an easy to
calculate "estimate" of mutating markers out of the number of total
probably would have flunked Nordtvedt's pop quiz, but this is what I
which is briefly explained here:
and tried to reduce it to give me a simple equation to give me an
estimation of the expected number of mutating markers.
has, roughly the change in Average Squared Difference (dASD) is
proportional to roughly 2 times the mutation rate (m)
the change in generations (dG):
dASD/dG ~= 2m
the purposes of illustration, Nordtvedt uses dASD to be about 1, and
mutation rate at about 1/400.
then all we need to solve for is the number of changing markers,
di, or roughly proportional to dASD.
di ~= N*[SQRT(dG*2*m)] (in very
di = number of changing markers
N = number of markers tested
dG = the number of Generations to MRCA, or TMRCA in generations
m = mutation rate of 1/400
we have a TMRCA of 1670, then the number of generations from the 1670
date: G = (2006 - 1670 )/25 = 13
say that the number of markers has been given at 67 markers.
67*[SQRT(2*13/400)] ~= 17 mutating markers (out
37*[SQRT(2*13/400)] ~= 9 mutating
25*[SQRT(2*13/400)] ~= 6 mutating
Aside from me not fully expanding Nordtvedt's equations, any experts
that may be reviewing my crude interpretation (of Nordtvedt's
equations) can easily see that my interpretation self implodes after
some 400 generations, or some 10,000 years in the past (400*25).
Perhaps this may be an indication of an implied limit within the
equations pertaining to the haplotype group, and this limit is of
course, proportional to known mutation rates.
to get on with it, let's do a few estimated mutations that we might
that I have the equations roughly correct, Odon would have been born in
(I don't have the exact date handy). That gives the number of
= (2006 - 1150)/25 = 34 generations
the equations below, descents that have been DNA tested today should
show this many mutating markers:
67*[SQRT(2*34/400)] ~= 28 mutating markers
37*[SQRT(2*34/400)] ~= 15 mutating markers
25*[SQRT(2*34/400)] ~= 10 mutating markers
is, descendants of Odon IV living today would show 15/25, 22/37, or
39/67 markers that match.
another example, estimating that Jerome HAM was born in about 1630, the
= (2006 - 1630)/25 = 15 generations
67*[SQRT(2*15/400)] ~= 18 mutating markers
37*[SQRT(2*15/400)] ~= 10 mutating markers
25*[SQRT(2*15/400)] ~= 7 mutating markers
I would expect descendants of Jerome HAM living today to share 18/25,
27/37, or 49/67 matching markers.
I would like to thank Laverne Piatt of Ontario, Ohio for asking the
I would like to thank Ken Nordtvedt for posting his theory to the
internet, and for not taking me to the woodshed for pretty much
butchering his equations.