vizachv vizachv 2006-12-01T16:48:24Z 2006-12-01T17:43:34Z Morgan Stanley 11.8107
How Related is "Related"?
To illustrate the way in which the haplotypes of two related men might be revealed by DNA testing, I undertook a computer simulation using latin hypercube sampling.  In short, I established a single 37 marker "founding haplotype" then let two descendant lineages randomly accumulate mutations consistent with observed and published mutation rates (mean rate = 0.00492, standard deviation = 0.00074) over X generations. The genetic distance between the two lineages was logged, and the simulation was repeated 10,000 times.
The following chart summarizes the results.
.
Cumulative Probability Generations to MRCA
2 4 6 8 10 12 14 16 18 20
5% 0 0 0 0 1 1 1 2 2 3
10% 0 0 0 1 1 2 2 3 3 3
20% 0 0 1 1 2 2 3 3 4 4
30% 0 1 1 2 2 3 3 4 5 5
40% 0 1 2 2 3 3 4 5 5 6
50% 1 1 2 3 3 4 5 5 6 6
60% 1 2 2 3 4 4 5 6 6 7
70% 1 2 3 4 4 5 6 6 7 8
80% 1 2 3 4 5 6 7 7 8 9
90% 2 3 4 5 6 7 8 9 9 10
95% 2 4 5 6 7 8 9 10 10 11
97.5% 3 4 5 6 8 9 10 10 11 12
99% 3 5 6 7 9 10 11 11 13 13
99.9% 4 6 8 9 10 12 13 14 16 16
99.99% 5 7 9 11 13 14 15 17 18 21
100.00% 5 9 10 12 14 16 17 18 20 21
   
By matching the number of generations since the MRCA (columns) and a particular observed genetic distance (rows) it is possible to conclude the probability associated with the observed results.  The easiest way to draw a conclusion is to fill in the blanks in the following statement:
When two men who have a MRCA [X] generations ago compare the results of a 37 marker DNA test, there is a probability of [Y] that the computed genetic distance will be [Z] or less.
To read the chart, X is the column headings, Y is the is row headings, and Z is the result of the lookup.
Example:  When two men who have a MRCA 10 generations ago compare the results of a 37 marker DNA test, there is a probability of 90% that the computed genetic distance will be six or less.
Another way to read the chart:  When two men who have a MRCA 10 generations ago compare the results of a 37 marker DNA test, there is a probability of 10% that the computed genetic distance will be greater than six.
The genetic distance rules propogated by Family Tree DNA suggest that a genetic distance of six or greater should be interpreted as meaning that  two men are "Not Related".  With a MRCA ten generations ago, people strictly following this rule will be wrong approximately 10% of the time. In other words, they will conclude that the two men are not related when (in fact) they are.  The chart above shows genetic distances of six or greater in red/pink.
Source:  http://www.familytreedna.com/GDRules_37.html
Caution:  this analysis is not informative about the probability that two "random" genetic matches are actually related.  Rather, it reveals the probability that two related people will have a given genetic distance.  This is an important distinction, and the results of this analysis are applicable to well-designed surname or lineage projects.
Questions or comments?  Vincent Vizachero (dna@vizachero.com)
Modified:  1 December 2006