Estimating the time to the most recent common ancestor (abbreviated TMRCA) between two
living descendants is an important aspect of interpreting DNA matches. This
page is about that aspect.

TMRCA calculations help to focus documentary genealogical research as to
time and place in order to discover that ancestor's identity by name, dates,
places and other characteristics.

Importance of MRCA

It follows logically that, if two people share a most recent common ancestor
(MRCA), they
also share the preceding ancestors -- ancestors of the ancestor. Thus, the most recent common
ancestor is the link to all the preceding generations.

The principle of TMRCA calculators is that the more similar area pair of haplotypes,
the more likely that their donors share a common ancestor within a shorter period of time.
It is assumed that a high degree of similarity is not happenstance.

Conversely, the less similar the haplotypes, the less likely and the longer the time for a
common ancestor.

Bear in mind that -- if one goes back far enough in time -- we all share the same set of
ancestors. Scientists estimate that the world's entire human population
consisted of only a couple of thousand people 70,000 years ago. However, we
aren't really looking for 70,000 year-old ancestors.

Molecular Clock

TMRCA estimates are based on the principle that mutations (on average) happen with
relatively stable frequencies. For Y-STRs, imagine a room full of clocks
(12, 25, 37, 67, or 111), all ticking independently. At some time in
the past, they all showed the same time, even if they now show different
times. If we know their tick-rates and the times they show now, we can work
out when it was they showed the same time.

For a layman's explanation of the molecular clock,
see this article.
It describes, mostly, the "big picture" of evolution but the same sort of
thing also happens at the micro-level. In genetic genealogy, the
tick-rates have been mostly worked out by comparing Y-DNA to well-documented
genealogies.

In essence, TMRCA calculators assess the similarity of a pair of compared haplotypes.
All produce a probability (usually expressed in percentages) that
a pair of people whose DNA is compared share a common ancestor within a
specified number of generations. Usually given as a cumulative probability; it
includes all generations from the present (1) to the specified number in the
past.

For example: A TMRCA calculator indicates that Al & Bob have a 90% chance of
sharing a direct paternal ancestor within 10 generations, but further research
identifies the common ancestor as only 6 generations in the past. Was the
calculation wrong? No; 6 generations falls inside the range of 1 to 10.

If the paper trail showed that the MRCA was 11 generations in the past, this
reflects that a 90% probability is, on average, wrong once in 10 times.

Do not be fooled by apparent precision in TMRCA calculations. All results
derived will be no better than probabilistic estimates, based on the input and
the limitations of the method. They have a level of uncertainty which is
unstated and sometimes unknown.

DNA mutations are, essentially, random events. Whenever randomness is
present, certainty is unattainable and probability governs. Some things
are more likely and others less, but none are either guaranteed or
impossible.

Moreover, all probabilistic estimates -- to be worth their salt -- should
come with confidence intervals. A statement such as "10 generation, 90% CL +/- 2"
would clarify the level of uncertainty but are seldom present. TMRCA
estimates likely have wide -- but undisclosed -- confidence intervals.

Results are often specified in
"generations", but
this isn't necessarily the appropriate time unit for two people with lineages
diverging from a common source. Closer to the mark is transmission events, the number
of times DNA is passed from a parent to a child.

Assume Al is 7 generations removed from the MRCA he shares with Bob and Bob
is 5 generations removed. The total number of transmission events is 11: Al's
7 plus Bob's 5 - 1 to avoid double-counting the MRCA. Sometimes, the calculator
merely halves transmission events to report in generations.

We eventually want to convert the TMRCA into years,
so that we can research by dates. However, generations (times between
transmission events) do not have a uniform length and their actual lengths can
not
be determined until the pedigrees are completed. Usually, a rough estimate for
an average length is substituted.

You will see estimates for average generation lengths from 20 to 35 years. In
general, paternal generations tend to run longer than maternal and those in
economically-developed cultures longer than in less-developed.

TMRCA calculations do not have definable confidence levels.
To decide how much confidence to place in the probabilities, it would be necessary to know, not
only the average mutation rates, but also the variance within the data.

A rough estimate for variance in mutation rate may be the stated average
rate for the marker -- a statistical technique often used for rare
events. We haven't yet calculated the effect on confidence
levels.

Exact matches

Exact matches (where there are no differences between haplotypes) present
a unique calculation problem and require a different algorithm than close
matches with at least one difference. The tools yield a hockey-stick shaped probability curve, which may
or may not model the real world. (Other curves follow a slanted S shape.)

Coincidental Matches:

Certain haplotypes -- especially in the R1b1a2
(R-M269) subclade -- are very common. Those with these haplotypes may have
hundreds of "close matches" at high comparison levels. For them, the assumption
that all matches are causal rather than some accidental may not hold. SNP
testing is recommended to help eliminate non-lineage matches.

There are several types of TMRCA calculators available for Y-DNA.
We classify them by their types of inputs:

Number of Markers

With these calculators, one inputs the number of markers to be compared, the
number of markers which agree (or disagree) and an estimated average
mutation rate.

The Clan McDonald TMRCA Calculator -- yields either a table of
generations and associated cumulative probability or a bar graph of the
data. Two versions are available

October 2014 --
here; this version yields a shorter TMRCA.

2006 version -- here; this version yields a longer TMRCA.

Moses Walker's Most Recent Common Ancestor Calculator -- yields
tables in either of two formats: (1) Generations along the left-hand column or
(2) Probabilities along the left-hand column (from 25% to 95% in increments of 5%).

Pearsall Project TMRCA Calculator — yields a line graph of four probabilities (disagreeing
markers of 0 to 3). Probability in decimal form along the y-axis (vertical scale) and markers
disagreeing along the x-axis (horizontal scale). Unique "slider" input for number of markers tested,
generations, length of generations and average mutation rate.

Time to Most Recent Common Ancestry Calculator Using Genetic Marker
Similarity Between Two Individuals — A
tool provided by Family Tree DNA & published on the University of
Arizona website -- yields number of generations for
probabilities of 50% (break-even), 90% and 95%. Also yields a 95%
confidence interval for number of generations, i.e., the number of
generations encompassing 95% of the probability. {These are very
wide windows.} Inputs include number of markers compared (12, 21, 25
or 37), number with one step of difference and number with two or more
steps of difference.

Specific Marker Values

It really does make a difference which markers disagree and by how much,
rather than merely how many markers disagree. Research since 2001 indicates that
some markers follow a stepwise mutation model as opposed to the infinite
alleles model used by the above calculators.

Another strength of these tools is that markers vary widely in their mutations rates,
from 1:28 transmission events (CDY) to 1:11,111 (DYS426). Any overall average is
a poor substitute.
With marker-by-marker comparison, precision of TMRCA estimates is enhanced.

TiP (Time
Predictor) — A proprietary tool of FTDNA, it calculates TMRCA
cumulative probabilities to 24 generations. It is available to FTDNA
customers to estimate TMRCA between them and reported matches and to project
administrators between any pair of project members. As it utilizes results
from teh FTDNA database, input is limited to selecting the generations
interval and paper-trail adjustment. To use it, log
onto your My
FTDNA pages with your kit number and password; bring up a Y-DNA match
list and click the orange icon to the right of the matching person's name.
(See FAQ.).

Bill Willis is in the process of developing a "Dissimilarity Index"