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since 23 Jan 2002 |

Current Version: ** 16 December 2003**

**Method: ** Walsh, Bruce , 2001. Estimating the time to the MRCA for the Y chromosome or mtDNA for a pair of individuals,
*Genetics* 158: 897--912

**Details: **

- Quick version
- All the very technical details:
- Basic approach
- mutation rates
- mutation models
- generation time
- effective population size
- prior information (i.e. same last name)

- Replies to some FAQ's

### 12 Marker test

- 12 - 0 - 0 : Match exactly at all 12 markers
- 11 - 1 - 0 : 11 exact matches, 1 one-step mismatch
- 11 - 0 - 1 : 11 exact matches, 1 two-step mismatch
- 10- 2 - 0 : 10 exact matches, 2 one-step mismatches
- 10- 1 - 1 : 10 exact matches, 1 one-step mismatch, 1 two-step mismatch
- 10- 0 - 2 : 10 exact matches, 2 two-step mismatches

### 21 Marker test

- 21 - 0- 0 : Match exactly at all 21 markers
- 20 - 1- 0 : 20 exact matches, 1 one-step mismatch
- 20- 0 - 1 : 20 exact matches, 1 two-step mismatch
- 19 - 2- 0 : 19 exact matches, 2 one-step mismatches
- 19- 1 - 1 : 19 exact matches, 1 one-step mismatch, 1 two-step mismatch
- 19 - 0- 2 : 19 exact matches, 2 two-step mismatches

### 25 Marker test

- 25 - 0- 0 : Match exactly at all 25 markers
- 24 - 1- 0 : 24 exact matches, 1 one-step mismatch
- 24- 0 - 1 : 24 exact matches, 1 two-step mismatch
- 23- 2- 0 : 23 exact matches, 2 one-step mismatches
- 23- 1 - 1 : 23 exact matches, 1 one-step mismatch, 1 two-step mismatch
- 23 - 0- 2 : 23 exact matches, 2 two-step mismatches

### 37 Marker test

(Cumulative probabilty plots not yet included, will be soon)- 37 - 0- 0 : Match exactly at all 37 markers
- 36 - 1- 0 : 36 exact matches, 1 one-step mismatch
- 36- 0 - 1 : 36 exact matches, 1 two-step mismatch
- 35- 2- 0 : 35 exact matches, 2 one-step mismatches
- 35- 1 - 1 : 35 exact matches, 1 one-step mismatch, 1 two-step mismatch
- 35 - 0- 2 : 35 exact matches, 2 two-step mismatches

Adding additional markers increases the precision of the test. For example (assuming the standard mutation rate),

- If two individuals match exactly at all loci in a 12 marker test, there is a 50% probability of a MRCA within the last 14 generations (exact value 14.4) .
- If they exactly match at all loci in a 21 marker test, there is a 50% probability of a MRCA within the last 8 generations (exact value 8.3).
- If they exactly match at all loci in a 37 marker test, then the 50% value is 5 generations (exact value 4.6).

While there is a fairly dramatic improvement in going from 12 to 21 markers, a comparable improvement (i.e., having the 50% probability be 4 generations) requires scoring 43 markers. With a 100 markers, the 50% probability corresponds to 2 generations (exact value 1.7).

Under the standard mutation rate (0.002 = 1/500), the number of generations giving 50% probability has a very simple form. If two individuals match at all n markers, then the 50% time is

- 250*ln(2)/n = 173.3/n.

Here's this function plotted for 10 to 50 markers

One can also the effect of adding additional markers by looking at the cumulative probability curves for the time to MRCA for a pair of individuals with a complete match at 12, 25, and 37 markers. The black horizontal lines correspond to 2.5, 50, and 97.5 percent (the 95 percent confidence interval is given by the 2.5 to 97.5 interval).