Fergus(s)on DNA Project

Robert FERGUSON and Martha BAUGH

Times to Most Recent Common Ancestor

The numbers in red show how many generations removed each participant is from the family's most recent common ancestor. One of the difficulties in the computations to follow is comparing participants who are not of the same generation. Ignoring the difference and using a Family TMRCA based on the most distant tested generation is a reasonable approximation. It is equivalent to assuming that the haplotypes of persons whose generation does match the Family TMRCA are unchanged for the difference in generations being ignored. The approximation is reasonable because the probability of a haplotype changing from father to son is known to be low. Compared with other choices one might make, the choice of a most distant generation results in the largest Family TMRCA and presents a more severe test when compared with the 95% TMRCA. Finally, the numbers in blue are the resultant TMRCA.

TMRCA

The tables below compare the actual pairwise TMRCA as deduced from the above diagram with theoretical computations of the 95% TMRCA.

Actual TMRCA

A
n
o
n
y
m
o
u
s

J
o
h
n

M
u
r
r
a
y

F
r
a
n
k
l
i
n

D
o
n
a
l
d

R
o
g
e
r

J
o
h
n

M
a
r
t
i
n

J
o
h
n

D

Anonymous_SMGF

John_Murray_Ferguson

Franklin_George_Ferguson

Donald_Cameron_Fergusson

Roger_George_Ferguson

John_Martin_Ferguson

John_D_Ferguson

95% TMRCA

SMGF_Ira_Ferguson

John_Murray_Ferguson

Franklin_George_Ferguson

Donald_Cameron_Fergusson

Roger_George_Ferguson

John_Martin_Ferguson

John_D_Ferguson

0-9 Generations

10-19 Generations

20-29 Generations

30-39 Generations

- Infinite allele mutation model is used
- Average mutation rate varies: 0.0028 to 0.0033
- Mutation rates from Chandler, Little & Hutchison
- Values on the diagonal indicate number of markers tested
- Probability is 95% that the TMRCA is no longer than indicated

Twenty of twenty-one or 95.2% of actual TMRCA are less than the 95% numbers as they probably should be. The one case wherein the TMRCA is greater than the 95% number is highlighted in red. If the computations are repeated at 98% one obtains 98%-TMRCA = 9 and the exception goes away. In the context of trying to discover if the genealogy and DNA results are consistent this exception is somewhat equivocal because the calculations are not accurate enough nor the sample size large enough to say with the requisite confidence that 95% of the actual TMRCA are falling in line.

Exclusion of CDYa, b

Many researchers believe that CDYa,b is too volatile a marker to include in a TMRCA analysis. Its mutation rate is on the order of ten times that of other markers and can mutate up or down in relatively short times. The table repeats the 95% TMRCA computations excluding CDYa,b, The effect is dramatic and now all the TMRCA are less than the 95% numbers. It is concluded the resultant set of pairwise actual TMRCA defined by the genealogical structure is consistent with the corresponding set of pairwise TMRCA computed from the DNA mismatches.

Time to Most Recent Common Ancestor (Generations)

S
M
G
F

I
r
a

F
e
r
g
u
s
o
n

J
o
h
n

M
u
r
r
a
y

F
e
r
g
u
s
o
n

F
r
a
n
k
l
i
n

G
e
o
r
g
e

F
e
r
g
u
s
o
n

D
o
n
a
l
d

C
a
m
e
r
o
n

F
e
r
g
u
s
s
o
n

R
o
g
e
r

G
e
o
r
g
e

F
e
r
g
u
s
o
n

J
o
h
n

M
a
r
t
i
n

F
e
r
g
u
s
o
n

J
o
h
n

D
.

F
e
r
g
u
s
o
n

SMGF_Ira_Ferguson

John_Murray_Ferguson

Franklin_George_Ferguson

Donald_Cameron_Fergusson

Roger_George_Ferguson

John_Martin_Ferguson

John_D_Ferguson

0-9 Generations

10-19 Generations

20-29 Generations

30-39 Generations

- Infinite allele mutation model is used
- Average mutation rate varies: 0.0024 to 0.0028
- Mutation rates from Chandler, Little & Hutchison
- Values on the diagonal indicate number of markers tested
- Probability is 95% that the TMRCA is no longer than indicated

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