Re: Triangulated DNA matches and Pile-up Areas #dna


Eva Lawrence
 

 

Like Lee, I've got really interested in the theory of triangulation. Ive been trying to think if it in the abstract as a mathematical problem.

.In the abstract. it just depends on two lines of ancestors meeting in a single point, another ancestor  - but there's no such thing as single ancestor. It takes two to make a baby.  Each point on your tree is a node,  A person's DNA is just the track of one line of their enormous tree,  going back to 'Adam' or a Neanderthal man but also to  Eve or Neanderthal woman..

Triangulation can only find a node from their ancestral line which also lies on someone else's ancestral line if the line is reflected in their DNA -or in their paper records..

Geometrically a line is defined by two points. Lee put the (very partial) back history of 11 people, A to G who share one segment of DNA into a black box - the algorithm used - and it searched the rest of their DNA to find a second piece (a series of numbers representing  chromosomes)  that existed on one of the other sets of DNA.. . ie a second point where the lines cross.  But it's no surprise if the algorithm doesn't find one, because its existence is almost independent of the first piece - like the second throw of a dice theoretically doesn't depend on the previous throw

The further back you go, the more widely the net of ancestors has spread,  but only a small proportion of  lines is recorded as leading  back to each of the initial list of matches (who were people on a database, but nodes in the abstract)  and provides the information on which the triangulation algorithm reports.

My second  thought was that it was not just a single line, but as Adam Cherson pointed out, at some nodes two lines back are possible because both parents have inherited that piece of DNA. But unless they were identical twins (!)  there must be some difference in their make-up that takes the DNA line back unequivocally to another node. 

It is only because communities were limited in size  that triangulation has any success.

Eva Lawrence

St Albans, UK

 
 

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Eva Lawrence
St Albans, UK.

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