Behold’s Genetic Relationship Notation (BGRN) - Sun, 22 May 2016

Update: August 12, 2018:  This notation has been revised.

See my blog post:  BGRN Revised.

I’m leaving this older post here for historical context.

Yeah, I know. BGRN is a horrible acronym. So if you can get to the end of this post and can think of a better thing to call it, I’ll definitely consider your suggestions.

Almost six months ago, I started thinking about A New Notation for DNA Relationships. I’ve now worked out the bugs, and I’m ready to define the notation more formally, as I prepare to implement it in Behold.

Behold’s Genetic Relationship Notation defines a string of characters that represent how person A connects to person B. With this string, you should be able to:

a) Determine the expected amount of DNA shared by the two people, and
b) Describe the relationship in words.

The notation uses the following characters to make up the string:

• X is a female and is the mother of the previous person in the string.
• Y is a male and is the father of the previous person in the string
• U is a person of unknown sex and is the a parent of the previous person in the string
• A is for a non-genetic parent (e.g. adoptive or step-parent)
• (YX) is for the Most Recent Common Ancestors (MRCA) of person A and person B when the MRCAs are both the father and mother (usual case).
• (Y) is for the MRCA of person A and person B when the MRCA is only the father (half-family on the father’s side).
• (X) is for the MRCA of person A and person B when the MRCA is only the mother (half-family on the mother’s side).
• 2 follows an X, Y, U and represents an identical twin. In this case, the MRCA above is not needed nor shown.   
• x is the daughter of the previous person in the string
• y is the son of the previous person in the string
• u is the child of the previous person in the string
• a is for a non-genetic child (e.g. adopted or step-child) of the previous person in the string
• - (a hyphen) is for the spouse or partner of the previous person in the string.

The core rules, for purely genetic relationships, are:

1. The string starts with 1 or more:  X, Y or U’s, the first of which represent person A.
2. These are followed by at most 1 of:  (YX), (Y), (X), or 2.
3. These are followed by 0 or more:  x, y, or u’s.
4. The last character in the string represents person B.
5. A, a and – (hyphen) specify non-genetic relationships (zero DNA match) and are not part of the core rules.

Examples of the notation for genetic relationships and the relationship in words that can be generated from it:

Y = male person
YXY = male person’s mother’s father
YXY(YX)xy = male person’s mother’s fathers’ sister’s son.
U(Y)xxx = person’s paternal half-sister’s daughter’s daughter’s daughter.
Xyy = female person’s son’s son.
XY2x = female person’s father’s identical twin’s daughter.

Here’s example of some common relationships:

X = female person
XX = mother
XXX = grandmother
XXXX = great-grandmother
XX(YX)x = aunt
XX(YX)xx = 1st cousin
XX(YX)xxx = 1st cousin, once removed
XXX(YX)xx = 1st cousin, once removed (the other way)
XX(YX)xxxx = 1st cousin, twice removed
XXXX(YX)xx = 1st cousin, twice removed (the other way)
XXX(YX)x = great-aunt
XXX(YX)xxx = 2nd cousin
XXX(YX)xxxx = 2nd cousin, once removed
XXXX(YX)xxx = 2nd cousin, once removed (the other way)

(Any of the X’s and x’s (except the last x for the first 4 strings above) can be replaced by Y’s or U’s and y’s or u’s)

Hopefully, you’re getting the idea.

Note that a line up to a direct ancestor will not have a MRCA, and neither will a line down to a direct descendent. When the step is across to an identical twin, the MRCA parents are not shown.

I won’t go into the calculation of how much DNA is shared since it’s worthy of another post, but let me say that the expected values can be easily obtained from strings written in Behold Genetic Relationship Notation, BGRN.

Now I would like to extend this notation to handle more than just Genetic relationships and include all possible genealogical relationships. So let’s define the extended rules as:

1. The string starts with an X, Y or U, which represents person A.
2. These are followed by any number of X, Y, U, A, (YX), (Y), (X), 2, x, y, u, a, and - (hyphens).
3. (YX), (Y) and (X) must be followed by x, y, u or a.  Therefore the string cannot end with (YX), (Y) or (X),
4. 2 must follow X, Y, U, A, x, y, u, a or – (hyphen).
5. The same person is never represented more than once in the string.
6. The last character in the string represents person B.

Examples of the extended notation and the relationship in words that can be generated from it:

Y- = Male person’s spouse
Y-(YX)xaY = Male person’s spouse’s sister’s adopted child’s father.
XXXX–x-X- = Female person’s mother’s mother’s mother’s spouse’s daughter’s spouse’s mother’s spouse.
Y(YX)xy(Y)y-(YX)x- = Male person’s sister’s son’s paternal half-brother’s spouse’s brother’s spouse.

So BGRN can handle any relationship, no matter how complicated.

I am interested in hearing any and all comments, criticisms and suggestions.