The following is a model for the connectivity of the Hogg I1 cluster.

This cluster currently consists of six lines descending from six different immigrant ancestors. The DNA matches indicates that all six lines descend from a common pre-immigrant ancestor.

Analysis of the DNA data for these six Hogg I1 lines that are a near match, based on the principle of minimum number of mutations (see note 1), suggests the following model for the tree descending from the common ancestor (see note 2):

A. common ancestor of all 5 lines
|  GATAA10=13, GGAAT1B07=11, DYS441=15, DYS461=12, DYS464=(12,14,15,15), DYS520=20, DYS534=16, DYS570=19, DYS572=11, and
|  DYS635=22 or 23 (it is not possible to tell which was the ancestral value for DYS635;
|  i.e. either A1 is the same as A or A2 is the same as A)
|
+- A1. MD1765a: desc. of Alexander Ogg of Maryland, b.ca.1745
|  |   main branch with DYS635=22 (we cannot tell if this is the ancestral line or a mutation, see note 3)
|  |
|  +-- A1a. PA1754a: desc. of Robert Hogg b.1721, Southern Scotland
|  |        branch defined by mutation at DYS464 from (12,14,15,15) to (12,13,15,15)
|  |
|  +-- A1b. RI1798a: desc. of John Hogg b.1680 RI
|  |        branch defined by mutation at DYS461 from 12 to 13 and mutation at GGAAT1B07 from 11 to 12
|  |
|  +-- A1c. PA1825a: desc of James Hogue b.1825, Pennsylvania
|           branch defined by mutation at DYS459a from 8 to 9, mutation at DYS464 from (12,14,15,15) to (14,14,15,15),
|           mutation at CDYb from 36 to 35, and mutation at DYS481 from 25 to 24
|
+- A2. main branch with DYS635=23 (we cannot tell if this is the ancestral line or a mutation, see note 4)
   |
   +-- A2a. NH1703b: desc. of William Hogg of Londonderry NH, b.1703
   |        branch defined by mutation at DYS570 from 19 to 18
   |
   +-- A2b. NH1703a: desc. of William W. Church b.bf.1829 Montpelier VT and
   |        NH1703c: desc. of Enoch Church b.1791 Sullivan Co. NH
   |        branch defined by mutation at GATAA10 from 13 to 12
   |
   +-- A2c. a branch for which we have no data defined by the mutation of DYS534 from 16 to 17
       |
       +--- A2c1. GA1770a/b: desc. of James Hogg Sr. of Savannah GA, b.1740
       |          branch defined by mutation at DYS441 from 15 to 16
       |
       +--- A2c2. line leading to RD Cromer
                  branch defined by mutation at DYS520 from 20 to 19 and mutation at DYS572 from 11 to 10

note 1: Mutations are rare events. If there are two possible sequences of events that lead to the same observation, the one with the smallest number of mutations is more likely than the one that requires a larger number of mutations. In the world of mathematics, this is known as the maximum likelihood approach. Specifically, we are making the assumption that all mutations are "simple" mutations, that is, a single mutation that occurs only once in one single father-to-son DNA transmission. This means we are assuming there are no complex mutation sequences such as back mutations or parallel mutations.

note 2: A tree of this sort is intended to show the sequence of mutations and gives an indication of which lines descend from a common ancestor more recent than the ancestor who was the common ancestor of all of them. It does not give an accurate representation of the actual family tree because we have no way of knowing whether any given motation was within the most recent generation of the DNA donor or was many generations ago. In some cases, we actually know more about the family tree than we can perceive from the DNA mutations. For example we know that the structure or the tree leading to NH1792a,b, and c is like this:

1 William Hogg of Londonderry NH, b.1703 (DYS570=19, GATAA10=13)
  2 Alexander Hogg b.17_Jun_1732, Londonderry NH
    3 Alexander Hogg Church b.1758, Deering NH, d.3_Feb_1849, Chateaugay, Franklin Co. NY (Name change documented in VT)
    . 4 Joseph Church b.1808, Orange Co. VT, d.14_Apr_1897, South Bend, Pacific Co. WA
    .   5 Azro B. Church b.2_Apr_1830, Orange Co. VT, d.12_Apr_1906, North Mount Tabor Co. OR
    .     6 William Azro Church b.Oct_1855, Oregon
    .       7 George Dewey Church b.3_May_1898, Ilwaco, Pacific Co. WA, d.27_Feb_1981, Long Beach, Pacific Co. WA
    .         8 ________ Church
    .           9 NH1703b: desc of William Hogg of Londonderry NH b.1703 (DYS570=18, GATAA10=13)
    3 John Hogg Church b.25_Feb_1760, Dunbarton NH, d.1842
      4 Enoch Hogg Church b.24_Jul_1791, Lempster twp., Sullivan Co. NH, d.10_Jan_1843, W. Topsham VT
        5 William Perkins Church b.24_Mar_1821, Orange VT, d.11_Dec_1860, Moretown VT (DYS570=19, GATAA10=12)
          6 Charles Albert Church b.15_Feb_1850, Topsham VT, d.27_Apr_1928, Moretown VT
          . 7 Frederick Leon Church b.26_Mar_1909, E. Montpelier VT, d.5_Mar_1973, Fullerton CA
          .   8 NH1703c: desc of Enoch Church b.1791 Sullivan Co. NH (DYS570=19, GATAA10=12)
          6 William Wilber Church b.15_Apr_1855, Montpeliar VT d.18_Feb_1942, Portland OR
            7 Albert Arthur Church b.10_Aug_1880, Minneapolis MN d.4_Jul_1966, Portland OR
              8 Harold Church b.1924, Oregon
                9 NH1703a: desc of William W. Church b.1855 Montpelier VT (DYS570=?, GATAA10=12)

This family is a good example of how the combination of an accurate pedigree and DNA data provides more information than either alone. For example, since NH1793c has the ancestral value DYS570=19, we know that the mutation for DYS570 from 19 to 18 occurred in the line leading to NH1703b after the 3rd generation. We cannot at this time determine the value of DYS570 for NH1793a (the data is from SMGF and we do not know the identity of the donor), but based on the model, we would expect it to be 19. If it is a value other than 19, that would be due to a separate mutation somewhere between generations 6 and 9. If it is 18, that would be a parallel mutation.

note 3: If thu ancestral value of DYS635 is 22, then A1 (above) is the ancestral line and the tree would be revised to look like this:

A. MD1765a: desc. of Alexander Ogg of Maryland, b.ca.1745
|  ancestral line with GATAA10=13, GGAAT1B07=11, DYS441=16, DYS461=12, DYS464=(12,14,15,15), DYS520=20, DYS534=16,
|  DYS570=19, DYS572=11, and DYS635=22
|
+- A1. PA1754a: desc. of Robert Hogg b.1721, Southern Scotland
|      branch defined by mutation at DYS464 from (12,14,15,15) to (12,13,15,15)
|
+- A2. RI1798a: desc. of John Hogg b.1580 RI
|      branch defined by mutation at DYS461 from 12 to 13 and mutation at GGAAT1B07 from 11 to 12
|
+- A3. PA1825a: desc of James Hogue b.1825, Pennsylvania
|           branch defined by mutation at DYS459a from 8 to 9, mutation at DYS464 from (12,14,15,15) to (14,14,15,15),
|           mutation at CDYb from 36 to 35, and mutation at DYS481 from 25 to 24
|
+- A4. a branch for which we have no data defined by the mutation of DYS635 from 22 to 23
   |
   +-- A4a. NH1703b: desc. of William Hogg of Londonderry NH, b.1703
   |        branch defined by mutation at DYS570 from 19 to 18
   |
   +-- A4b. NH1703a: desc. of William W. Church b.bf.1829 Montpelier VT and
   |        NH1703c: desc. of Enoch Church b.1791 Sullivan Co. NH
   |        branch defined by mutation at GATAA10 from 13 to 12
   |
   +-- A4c. a branch for which we have no data defined by the mutation of DYS534 from 16 to 17
       |
       +--- A4c1. GA1770a/b: desc. of James Hogg Sr. of Savannah GA, b.1740
       |    branch defined by mutation at DYS441 from 15 to 16
       |
       +--- A4c2. line leading to RD Cromer
            branch defined by mutation at DYS520 from 20 to 19 and mutation at DYS572 from 11 to 10

note 4: If the ancestral value of DYS635 is 23, then A2 (above) is the ancestral line and the tree would be revised to look like this:

A. common ancestor of all 5 lines with GATAA10=13, GGAAT1B07=11, DYS441=16, DYS461=12, DYS464=(12,14,15,15),
|  DYS520=20, DYS534=16, DYS570=19, DYS572=11, and DYS635=23 (we have no data case with these values)
|
+- A1. MD1765a: desc. of Alexander Ogg of Maryland, b.ca.1745
|  |   branch defined by mutation at DYS635 from 22 to 23
|  |
|  +-- A1a. PA1754a: desc. of Robert Hogg b.1721, Southern Scotland
|  |        branch defined by mutation at DYS464 from (12,14,15,15) to (12,13,15,15)
|  |
|  +-- A1b. RI1798a: desc. of John Hogg b.1580 RI
|  |        branch defined by mutation at DYS461 from 12 to 13 and mutation at GGAAT1B07 from 11 to 12
|  |
|  +-- A1c. PA1825a: desc of James Hogue b.1825, Pennsylvania
|           branch defined by mutation at DYS459a from 8 to 9, mutation at DYS464 from (12,14,15,15) to (14,14,15,15),
|           mutation at CDYb from 36 to 35, and mutation at DYS481 from 25 to 24
|
+- A2. NH1703b: desc. of William Hogg of Londonderry NH, b.1703
|      branch defined by mutation at DYS570 from 19 to 18
|
+- A3. NH1703a: desc. of William W. Church b.bf.1829 Montpelier VT and
|      NH1703c: desc. of Enoch Church b.1791 Sullivan Co. NH
|      branch defined by mutation at GATAA10 from 13 to 12
|
+- A4. a branch for which we have no data defined by the mutation of DYS534 from 16 to 17
   |
   +-- A4a. GA1770a/b: desc. of James Hogg Sr. of Savannah GA, b.1740
   |        branch defined by mutation at DYS441 from 15 to 16
   |
   +-- A4b. line leading to RD Cromer
            branch defined by mutation at DYS520 from 20 to 19 and mutation at DYS572 from 11 to 10