# Genetic Distance to Generations Calculation for Y-STR DNA tests

As a follow-up to the Q&A on Generational Loss of Data with DNA Testing, which described generational detail loss really well for Autosomal, I am now looking for a calculation or some basic formula to estimate generational relationship based on genetic distance for the different levels of DNA testing, and with some sort of probability perhaps related as well.

I know Family Tree DNA has explanation tables for 37, 67, and 111, but the way they display the information is different and I would like to have or build an 'all-in-one chart' for each of the levels 12-111, similar to the highlighted section below as well as the following graphic. (which the lower levels do not contain in the linked FAQ pages)

As well as combined the following information in an easy to display reference table for all levels from 12-111 Y-STR DNA tests. (Missing 111)

The above image from a 2010 FamilyTreeDNA Presentation which they described the calculation as complex (with an unrelated whiteboard calculation as a joke).

I have also looked at ISOGG's website and haven't found a good reference chart nor anything digestable to make my own.

The have some other good information on their site in different places and that referenced presentation is one of the best consolidated places, but so far I have not found a nice all in one table.

Part of what I am trying to determine is with different test levels what is reasonable with an assigned confidence level, but also when looking at approaching someone for testing are they close enough of a level to get the answer I am looking for at the time. This comes up as recently I've had some unexpected surprises with a Y-Str testing that has opened new mysteries..

Has anyone found a nice consolidated reference chart for all levels 12-111 that has the information above at all testing levels or can point me to a more digestable formula for me to build my own?

• The maths slide is a just a joke and has nothing to do with genetics or genealogy! The point being made is: it's complicated. – Harry V. May 14 '15 at 17:40

First, it is important to note that all the probabilities provided in these charts are estimations. Different formulas have been proposed and used to give us an idea of what a relationship might be based on a given genetic distance, but they are nothing more than estimates.

Fundamental to these charts is the concept of Time to Most Recent Common Ancestor (TMRCA). This refers to the likely number of generations within which two individuals are related, based on their genetic distance. Genetic distance, in simple terms, is the number of alleles at which two individuals differ. For example, matches at 111/111 markers have a genetic distance of 0, while matches at 21/25 have a genetic distance of 4. These calculations can be performed at various levels of confidence. For example, at 90% confidence, we can be conclude that for a given genetic distance and number of markers, we can be 90% confident that the relationship is within x generations.

The calculations are complicated. A glance at Walsh's paper titled Estimating the Time to the Most Recent Common Ancestor for the Y chromosome or Mitochondrial DNA for a Pair of Individuals may be enough to convince you that you don't really want to understand exactly how these numbers are calculated. Nordtvedt proposes an even more sophisticated method in More Realistic TMRCA Calculations. The bottom line is you don't want to be doing these calculations yourself.

That's where online calculator come in handy. There are a variety of tools available to calculate TMRCA for you. I like to use J. D. McDonald's TMRCA Calculator, but there are many others listed on the ISOGG website.

The reason why you may have been unable to find any chart with all the data is because it quickly gets complex and confusing to include everything on one page. You can use the TMRCA calculators to make your own charts, and I have included an example below.

To generate this, I used McDonald's calculator to obtain the data, then organized it in Microsoft Excel. You will note it is for TMRCA at 90% confidence. The TMRCA numbers would differ for other levels of confidence, but the trend is the same. Note that McDonald's calculator uses Walsh's formula for standard infinite alleles, which is why the numbers may differ from those given on the Family Tree DNA charts (these numbers tend to be more conservative estimates than FTDNA). To be clear how to read the chart, say you took a 67-marker test and matched with someone at 64/67 markers, then you would look at the 67-marker row, go across to a genetic distance of 3 (because 67-64=3), and could conclude with 90% confidence that you were related within the last 17 generations.

• I built one of these over the weekend at different confidence levels as well as compared it to what ftDNA had it on their site. Where do you get your definition of "very tightly related" to "probably not related" you used in your coloring for each test, as it varies by test. I couldn't find that. – CRSouser Jun 1 '15 at 14:59
• The categories in my chart just came from the data you posted in the question. FTDNA does provide a chart with data for all Y-DNA tests that mostly matches up what is on the other data you posted. I'm not certain what methods were used to define which category covered which level, but it is a bit arbitrary and may change with further research. It's all a matter of probability, so while it is most likely a certain match falls in the category described on the chart, there is a small chance it may not. – Harry V. Jun 2 '15 at 8:34

For 37 markers, I co-author a paper that can be find at http://tracingroots.nova.org/SS-WEHGDPaper.pdf that we used to estimate when STR mutations took place. If you date when a common mutation take place, you have the earliest that you are related. Note: at the time we wrote it, we only had mutation rates of only 37 markers.