Thursday, February 1, 2018

Autosomal DNA Half Life Equation

Autosomal DNA Half Life Equation

Feb 1, 2018


In the previous article, I had talked about creating a phylogenetic tree for autosomal data.
 
Andrew Millard suggested that because the Genetic Distance value of 1/cMs is not linear, I might try an exponential equation of the form -ln(cm/7200).

That formula suggestion was tried that, and I was not real happy with the results. The Genetic Distance did not correspond well to cousin level, and the upper limit for data greater than 1 cM appeared to be about 8 (generations), even for the results for Lauren Shutt (M804xxx), who was not even a match to the group.

Andrew had also suggested that I do not use kitsch, but I have not yet found different program that works with Genetic Distance.

So, here, I have used the equation for the half life decay rate, typically used in radioactive decay under the presumption that we are looking at Half Identical Regions (HIRs). The results mostly returned the expected cousin level (or number of generations).


Hypothetical Genetic Distance derived from half life decay rate: 

Nt = No*e^kt

Solvng for t, Hypothetical Genetic Distance given as: 

t = -1*ln(cMs*.0035524)/0.693147

where 'ln' is the natural log function. 

For a spreadsheet, the equation should be something like this:

=-LN(F1234*0.0035524)/0.693147






where 'F1234" would be the location in cMs on line (row) 1234.

The largest segment (i.e., most obvious) for mother/child or parental half life calculations (for size is initially at 281.5 cMs):

a = 1/281.5 cMs = 0.0035524

and for parent/child half life decay:


k = ln(N0/Nt) = ln(1/2) = 0.693147


Below is the link to the data and phylogenetic tree resulting from the use of the half life decay rate calculations. Basically, an update to the previous article by applying the autosomal half life decay equation.

Article:  Autosomal Half Life Equation

 


Updated 02/17/2018 to add spreadsheet version of the equation.




References:


HAM Group #1 Information

HAM Y-DNA Project Phylogenetic Tree

HAM Group #1 Initial Tiny Autosomal Segment Triad Study

HAM DNA Project Dean McGee's Utility output

HAM DNA Project Y-DNA Results at HAM Country

HAM DNA Project at FTDNA

How to Read HAM DNA Phylograms
    (video)