# Calculation of Time to MRCA Using A. Klyosov's Methodology

[This page was posted in 2013 and is included as a matter of historical interest.] Time to the Most Recent Common Ancestor ("MRCA") for the R1a1a Ashkenazi Levite cluster calculated using Anatoly Klyosov’s methodology and marker values, based upon information compiled on the R1a1a Ashkenazi Levite Sortable Spreadsheet as of November 19, 2013.

Time to an MRCA may be inflated, especially at 37 and 67 markers, by the inclusion of palindromic markers, as to which a single mutation may result in a change of more than one step on a single marker and/or a change in more than one marker value.

Under Klyosov’s methodology, one may determine the time to an MRCA for an identified subclade by: (1) assembling the marker values for men in a subclade; (2) adding together the total number of deviations from the mode for the men in that subclade; (3) dividing the total number of deviations from the mode by the number of men whose marker values are being considered; (4) dividing that result by a constant referring to the frequency of mutation rates over the range of markers being considered (which yields the number of generations to an MRCA); and (5) multiplying that number by an assumed number of years per generation (e.g., 25) to determine the number of years to an MRCA.

Klyosov’s mutation rates per generation are as follows: (1) 0.020 (12 markers); (2) 0.046 (25 markers); (3) 0.090 (37 markers); (4) 0.120 (67 markers); and (5) 0.198 (111 markers).

In mathematical terms, let:

d = total number of deviations from mode for men in subclade

m = number of men in subclades

r = mutation rate for number of markers tested

a = number of years per generation

g = number of generations to MRCA

y = number of years to MRCA

To solve for the number of generations to an MRCA:

g = d / m / r

To solve for the number of years to an MRCA:

y = g * a

To calculate the margin of error, you: (1) determine the square root of 1 divided by the number of deviations from the mode; (2) square that number and add 0.01 to the result; (3) take the square root of that number; and (4) multiply that number by the number of years to an MRCA calculated using the methods set forth above (the result is the margin of error in years).

In mathematical terms, let:

d = total number of deviations from mode for men in subclade

y = number of years to MRCA (calculated above)

e = margin of error in years

X1, X2, X3 = results of calculations to be performed sequentially

X1 = square root of 1 / d

X2 = X12 + 0.01

X3 = square root of X2

e = X3 * y