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Estimating the central TMRCA using the ASD method


The formula above shows the Average Squared Difference approach used in this application to calculate the
central TMRCA estimate for a given set of YDNA STR haplotypes. It draws its computational inspiration
from the statistical analysis section of the Behar et al. (2003) paper and its derivative Matlab/Octave program
Ytime, but with some differences/modifications:

  1. Computing the unbiased estimate T (seen in square brackets above), by partitioning the ASD
    over each locus using the specific mutation rate for that particular locus(m), and then finding
    the mean across all the partitions, versus using a single mean mutation rate across all loci to
    divide into an overall ASD that was computed across all markers. Note that these two methods
    would have identical outcomes if all locus specific mutation rates were set to be equivalent
    (for instance when using the Zhivotovsky rates).

  2. Simultaneous calculation of TMRCA estimates from 6 different sources of mutation rate
    estimates. (see below for specifics).

  3. The use of both Median and Modal repeats to represent the ancestral haplotype.

  4. The ability to explicitly specify any marker combination from the full marker set and the
    automatic extraction, and computation with these specified markers on the given haplotype
    dataset.

  5. The absence of confidence interval calculations.



Mutation Rate Sources

Theoretically, any published mutation rate sets could be used in the application, but since it is also necessary
to maximize the number of markers available for analysis, a tradeoff has to be made between maximizing the
number of mutation rate sources and the total markers made available, since most mutation rate estimates come
for only a limited set of markers. Therefore, the application uses marker specific mutation rates* compiled
only from the following sources:

  1. Ballantyne Mutation Rates: - Download

  2. Burgarella & Navascués Mutation Rates: - Download

  3. Chandler Mutation Rates:- Download

  4. Marko Heinila Mutation Rates: Developed by a genealogical community member, see this thread - Download

  5. Stafford Bayesian Mutation Rates: Essentially a compilation of other mutation rates - Download

  6. The effective mutation rate estimate of Zhivotovsky: - Download *Note, Markers not found in the publication
    were normalized using the pedigree relative rates, see procedure here .



Pre-defined Marker Lists

While any marker combination drawn from the full marker list can be used with this application, listed below
are the Pre-defined marker lists included in the application, these lists come from different publications and
are a convenient way to conduct TMRCA estimates for comparison:


Where,
L = Average Branch Length (SNPs)
M = Substitution Mutation Rate (Per Site Per Generation)
G = Years Per Generation
S = Total Sequence Length (Base Pairs)

The simple linear formula above is used to estimate the TMRCA for any node on the Y chromosome
phylogenetic tree. Given a total sequence length, S, of the Y Chromosome, the average branch length,
L, can be estimated by counting the total number of SNPs below the node of interest and dividing by the
total number branches under the node. The years per generation, G , is an assumption that usually varies
between 20 and 40 Years, while the substitution mutation rate, M, can be derived by using several
different methodologies, many times with different outcomes. This application uses mutation rates from
the sources shown below and will look to expand on them as more sources arise.
Publication Method Substitution Rate (per site per generation)
Central 95% CI
Lower Upper
Kuroki et al. (2006) Chimp Comparison 4.50 X 10-8 2.30 X 10-8 6.30 X 10-8
Xue et al. (2009) Deep-rooting Pedigree 3.00 X 10-8 8.90 X 10-9 7.00 X 10-8
Poznick et al. (2013)* Founding Migrations 2.46 X 10-8 2.16 X 10-8 2.76 X 10-8
Francalacci et al. (2013)* Founding Migrations 1.59 X 10-8 1.26 X 10-8 2.10 X 10-8
Mendez et al. (2013)** Autosomal Adjustment 1.85 X 10-8 8.78 X 10-9 2.83 X 10-8
Scozzari et al. (2013)* Autosomal Adjustment 1.92 X 10-8 1.41 X 10-8 2.46 X 10-8
Fu et al. (2014)* Ancient DNA 2.40 X 10-8 2.10 X 10-8 2.70 X 10-8
Karmin et al. (2015)* Ancient DNA 2.22 X 10-8 1.89 X 10-8 2.85 X 10-8
Trombetta et al. (2015)* Ancient DNA 2.148 X 10-8 N/A N/A
* Used 30 Years/Generation to convert from per site per year
** Used 30,20 and 40 Years/Generation respectively to convert Central, Lower and Upper rate estimates.