an automated Coeficient of relationship calculation?

[Charlie Hoffpauir]

The coefficient is explained at this site:

http://www.genetic-genealogy.co.uk/Toc115570135.html

What I'm looking for is some software that will perform this
calculation, instead of laborously doing the math by hand. What would
be ideal is to find a genealogy program that would have this
calculation embedded (I asked RootsMagic to add it years ago, but
either it's too difficult to code or they just don't think it's
needed). Hopefully some other program has it already, if not perhaps
some kind of stand-alone program?

The reason I'd like an automated process is because the calculation
gets very tricky when you have multiple relationships, like this:

(actual relationships for me and a cousin)
1. Fifth cousin once removed (common ancestor: Thomas Hoffpauir &
Marie Charlotte Périllard)
2. Fourth cousin twice removed (common ancestor: Thomas Hoffpauir &
Marie Charlotte Périllard)
3. Fifth cousin once removed (common ancestor: Edward Foreman II &
Nancy Anna Perry)
4. Fifth cousin once removed (common ancestor: Edward Foreman II &
Nancy Anna Perry)
5. Fourth cousin twice removed (common ancestor: Joseph Ephraim
Foreman & Mary Elizabeth Brown)
6. Fifth cousin twice removed (common ancestor: Edward Foreman)
7. Sixth cousin once removed (common ancestor: Edward Foreman)

[Peter J. Seymour]

From a programmer's point of view I can offer the following comment.

One possible difficulty is that a genealogical tree is not necessarily
the same as a genetic relationship tree and people may not be aware that
there is any difference. In such circumstances the coefficient will be
incorrect and pointless. (I hasten to add, I am not implying anything
about the cases you refer to).

Calculating it automatically does not make it more correct, although
some people might assume so.

[Ian Goddard]

On 14/02/15 15:41, Charlie Hoffpauir wrote:
> The coefficient is explained at this site:
>
> http://www.genetic-genealogy.co.uk/Toc115570135.html
>
> What I'm looking for is some software that will perform this
> calculation, instead of laborously doing the math by hand. What would
> be ideal is to find a genealogy program that would have this
> calculation embedded (I asked RootsMagic to add it years ago, but
> either it's too difficult to code or they just don't think it's
> needed). Hopefully some other program has it already, if not perhaps
> some kind of stand-alone program?

1. I wonder if there's a Gramps plugin for it. It's a long time since
I used Gramps & haven't downloaded a recent copy.

2. On a *very* quick look at the link it's an additive thing - you
calculate the individual sets of relationships & add them together.

For a lot of cases all you'd need would be a set of pre-calculated
coefficients for each sort of relationship (e.g. from the link 1C0R =
0.125) in a lookup table. Provided you're prepared to work out the set
of relationships as you've done then that should be straightforward.

The brothers who are children of 1st cousins example as worked out is
less straightforward but as far as I can see this is 1/2 (full siblings)
plus 1/16 for the descents from A & B. And is the latter any different
from any pair of 1st cousins once removed?

--
Ian

The Hotmail address is my spam-bin. Real mail address is iang
at austonley org uk

[Charlie Hoffpauir]

I certainly agree with you, but it's also true that stating my
relationship to that cousin 7 different ways doesn't make it any more
accurate either. What I'd like to see is simply an easy way to achieve
a numerical value that could be used as a comparison. Say person one
to person two are related .0125 whereas one to three are related
.001625.

My ultimate goal is to add this figure to all the Hoffpauir
descendants in my database (now 11480 individuals), showing just how
they each related to the originator of the family.

[Ian Goddard]

It might actually help make it more correct. Given a complex descent
such as Charlie's example it would be quite easy to omit a relationship
working them out by hand.

[Richard Smith]

On 14/02/15 15:41, Charlie Hoffpauir wrote:

> What I'm looking for is some software that will perform this

> calculation, instead of laborously doing the math by hand. [...]

> (actual relationships for me and a cousin)
> 1. Fifth cousin once removed (common ancestor: Thomas Hoffpauir &
> Marie Charlotte Périllard)
> 2. Fourth cousin twice removed (common ancestor: Thomas Hoffpauir &
> Marie Charlotte Périllard)
> 3. Fifth cousin once removed (common ancestor: Edward Foreman II &
> Nancy Anna Perry)
> 4. Fifth cousin once removed (common ancestor: Edward Foreman II &
> Nancy Anna Perry)
> 5. Fourth cousin twice removed (common ancestor: Joseph Ephraim
> Foreman & Mary Elizabeth Brown)
> 6. Fifth cousin twice removed (common ancestor: Edward Foreman)
> 7. Sixth cousin once removed (common ancestor: Edward Foreman)

I assume this is so you can interpret the results of autosomal DNA test?
An nth cousin m times removed contributes 1/2^(2n+m-1) to the
coefficient, assuming the children of the most recent common ancestor
are full siblings but not identical twins. Those seven relationships
give: (1) 1/1024, (2) 1/512, (3) 1/1024, (4) 1/1024, (5) 1/512, (6)
1/2048, and (7) 1/4096 -- assuming the latter two have a pair of common
ancestors. (Halve them if they're only half fifth cousins twice
removed, etc.) These are additive, so the coefficient is 31/4096 or
about 0.8%. As I understand it, that's a little above the limit of what
can be normally be detected. That limit comes from two fairly
fundamental factors.

First, it's very unlikely that you have inherited genetic material from
all of their four-great grandparents. I'm not considering non-paternity
events here: rather the process of DNA replication means its more likely
than not that a given gene will be copied from the same parent as the
neighbouring gene. The norm is long sections copied from a given
ancestor, and before long some ancestors are no longer represented in
your genetic make-up. If either you or your cousin have not inherited
material from the common ancestor, you're out of luck.

Secondly, this degree of relationship is close to the background level
for many cultures. Any two people from the same community will have a
great many common ancestors if you go back far enough. Over twenty
generations they'll typically thousands of common ancestors once
pedigree collapse has been considered (i.e. if you count ancestors
multiple times, once per descent); if you're from an isolated community,
whether geographically isolated or culturally, that number will be
larger. I think these unknown common descents within a community
results in a background level somewhere around 0.1%, to within an order
of magnitude.

These are not principally technological constraints, so are unlikely to
improve if you wait ten years.

Richard

[Ian Goddard]

On 14/02/15 17:12, Charlie Hoffpauir wrote:
> My ultimate goal is to add this figure to all the Hoffpauir
> descendants in my database (now 11480 individuals), showing just how
> they each related to the originator of the family.

That's a different matter. The original reference was to calculate the
relationship between two individuals with one or more common ancestors.
What you seem to be describing here would be the relationship between
ancestor & descendant given more than one line between the two.

As far as I can see the approach would be that for any given line the
number halves with each generation, the ancestor having a coefficient of
1.0 so a child would be 0.5, a grandchild 0.25 etc. You would then have
to calculate this for each line of descent & then add all the results
together. So for a pair of grandchildren would each have a coefficient
of 0.25. If they were to marry their child would have 2 lines of
descent, each line would halve again giving 0.125 for that line and
summing both lines would give 0.25.

[Ian Goddard]

On 14/02/15 21:42, Richard Smith wrote:
> I assume this is so you can interpret the results of autosomal DNA test?
> An nth cousin m times removed contributes 1/2^(2n+m-1) to the
> coefficient, assuming the children of the most recent common ancestor
> are full siblings but not identical twins. Those seven relationships
> give: (1) 1/1024, (2) 1/512, (3) 1/1024, (4) 1/1024, (5) 1/512, (6)
> 1/2048, and (7) 1/4096 -- assuming the latter two have a pair of common
> ancestors. (Halve them if they're only half fifth cousins twice
> removed, etc.) These are additive, so the coefficient is 31/4096 or
> about 0.8%.

As I posted elsewhere Charlie's answer to Peter seems to imply that what
he was actually looking for was something different, a measure of
descent from a particular ancestor given multiple lines of descent.

This thread, however, has set me thinking about a measure of pedigree
collapse. One measure would be the ratio of distinct ancestors in the
generation where the common ancestor occurs to the number expected if
there were no collapse. This measure fails by not making allowance for
the fact that there may be more generations in one line than another.
It also makes no allowance for further pedigree collapse in earlier
generations.

[Charlie Hoffpauir]

That's exactly right! And when you're looking at 6 or 7 generations
back to our family originator, it's a formidable problem. But it seems
to be the kind of a problem that computers are excellent at.

[Charlie Hoffpauir]

But the coefficient of relationship calculation accounts for multiple
lines back (common ancestors in the pedigree) as well as different
numbers of generations in the different paths.... but the problem is
it's laborous to do the calc by hand. Not difficult... just sum the
coefficients for each path and calculate each path coefficient by
(1/2)**n where n is the number of "steps" in the path. It seems to me
to be something that should be easily included in a genealogy program
in which all the possible paths back are already "known" (they must be
in RM since RM was able to state all the ways two individuals are
related).

[Tony Proctor]

"Ian Goddard" <godd...@hotmail.co.uk> wrote in message
news:cka74u...@mid.individual.net...

I would argue that the contributions from ancestors appearing multiple times
are not really additive. Even if the percentage of DNA was fixed (see
Richard's post) then the actual DNA would be different for each pathway.

Tony Proctor

[Ian Goddard]

On 15/02/15 11:18, Tony Proctor wrote:
>
> I would argue that the contributions from ancestors appearing multiple times
> are not really additive. Even if the percentage of DNA was fixed (see
> Richard's post) then the actual DNA would be different for each pathway.

It seems to be a standard measure. From the site in Charlie's original
link:
"The standard procedure for measuring degrees of relationship
quantitatively uses Sewall Wright's method of path coefficients (Wright,
1922)."

There are two interpretations of the figure, however, genealogical and
genetic. If we are solely interested in the genealogical interpretation
then the DNA considerations don't matter.

[Ian Goddard]

As you say, it should be easy to incorporate. Presumably nobody has
chosen to do so but no doubt if one vendor were to do it the others
would follow suit. Why not send a feature request to your preferred S/W
vendor?

[Henry Soszynski]

http://opensource.geneanet.org/projects/geneweb/wiki/En_Geneweb#Relationship-and-Consanguinity-Calculator
is that the sort of thing you are looking for?

Cheers,
Henry Soszynski

[Richard Smith]

On 15/02/15 23:56, Henry Soszynski wrote:

> http://opensource.geneanet.org/projects/geneweb/wiki/En_Geneweb#Relationship-and-Consanguinity-Calculator
> is that the sort of thing you are looking for?

The consanguinity rate isn't quite the same as the relationship
coefficient. According to Wikipedia "consanguinity, as commonly
defined, does not depend on the amount of shared DNA within two people's
genome. It rather counts the number of meioses separating two
individuals." In simple cases, the consanguinity rate is half the
relationship coefficient, as shown by the examples on that page: e.g.
full siblings have a consanguinity rate of 25% but a relationship
coefficient of 50%. But I cannot find any discussion of how the
consanguinity handles pedigree collapse, and it may not be additive in
the way that the relationship coefficient is. If it's not, you cannot
simply take the consanguinity rate and double it.

Richard

[Charlie Hoffpauir]

On Sun, 15 Feb 2015 12:02:56 +0000, Ian Goddard

good idea! (did that a year ago)

[Charlie Hoffpauir]

Henry,

Yes, from a reading of the info on the site you gave, it looks like it
does exactly that! I'll definitely check this out.