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From: "Sandy Paterson" <>
Subject: [R-M222] Off-modal matches - simulation
Date: Tue, 27 Jul 2010 13:12:00 +0100


The process by which Y-STR populations are believed to develop lends itself
to simulation using computers. I've done this for 67 marker haplotypes and
have managed to develop a crude naming system that in essence contains the
male pedigrees of the final haplotype population. This in turn makes it
possible to examine the TMRCA's of pairs of simulated haplotypes and analyse
by gd, number of matches and number of off-modal matches, without having to
resort to developing a family tree.

Summary tables for pairs of haplotypes with TMRCA's of 10,15,...30
generations are viewable at


http://dl.dropbox.com/u/2733445/OFFMOD10

http://dl.dropbox.com/u/2733445/OFFMOD15

http://dl.dropbox.com/u/2733445/OFFMOD20

http://dl.dropbox.com/u/2733445/OFFMOD25

http://dl.dropbox.com/u/2733445/OFFMOD30


For convenience, I've reproduced the table for a TMRCA of 10 generations but
before addressing it, a few words about the simulation process may be
helpful.

In all 50 populations of 200-500 67-marker haplotypes were generated for 60
generations, starting with the M222 modal. These are available in .csv
format should anyone be interested. Each population is examined by
considering pairs of haplotypes. So a population of say 350 haplotypes will
have 350 x 349 / 2 = 61075 pairs for comparison, giving a total of the order
of about 3m pairs in all. These will have TMRCA's ranging from 1 to 60.

It may worry some that I started with the M222 modal. That's not important
and I could just as easily have started with the McLaughlin modal or any
other surname modal.

The table below gives an extract from these pairs, specifically those with a
TMRCA of 10 generations. So out of 10345 pairs, 704 had no off-modal
matches, 517 had 1 off-modal match and so on. An end modal is determined
separately for each population, and an off-modal match is a match that is
not on the modal.

Note that the mean number of off-modal matches for TMRCA's of 10 worked out
at 4.72 and that a table comparing the results for TMRCA 10,15,...30 is
given following the table below.

Col 1 Col 2 Col 3

0 704 6.8052
1 517 4.9976
2 846 8.1779
3 1067 10.3142
4 1433 13.8521
5 1817 17.5640
6 1456 14.0744
7 1057 10.2175
8 857 8.2842
9 401 3.8763
10 116 1.1213
11 47 0.4543
12 17 0.1643
13 1 0.0097
14 9 0.0870
15 0 0.0000
16 0 0.0000
17 0 0.0000
18 0 0.0000
19 0 0.0000

10345

TMRCA 10
MEAN NO OF OFF-MODAL MATCHES 4.72

Col 1 is the no of off-modal matches running from 0 to 19
Col 2 is the no in the population with the no of off-modal matches in col 1
Col 3 is the % in the population with the no of off-modal matches in col 1


TMRCAMean no of off-mod matches

104.72
154.17
203.27
251.82
301.38

Two things are important to note. The first is that there is a clear decline
in number of off-modal matches by TMRCA. The second is that even at a TMTCA
of 10, zero off-modal matches is quite common.


Sandy







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