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Archiver > GENEALOGY-DNA > 2008-04 > 1207679054


From: "Ken Nordtvedt" <>
Subject: Re: [DNA] underestimating variance
Date: Tue, 8 Apr 2008 12:24:14 -0600
References: <40037.65124.qm@web28303.mail.ukl.yahoo.com><007d01c8997b$2a314bc0$6400a8c0@Ken1><000001c8997e$cbc3b970$0201a8c0@owner8151f88a9><01a101c899a4$b05fbe10$6400a8c0@Ken1>


I forgot to add; you can see some of these distributions at the powerpoint
file ASD.distribution.ppt at my website

http://knordtvedt.home.bresnan.net


----- Original Message -----
From: "Ken Nordtvedt" <>
To: <>
Sent: Tuesday, April 08, 2008 12:16 PM
Subject: Re: [DNA] underestimating variance


> Suppose you took a fixed tree from a single founder to a present-day
> population (either the entire population of descendants or a good sample
> of
> that population, doesn't make any difference). For this fixed tree you
> let
> the computer generate random mutations for the marker each father/son
> generational transition in the tree, with 1 - m being chance of no
> mutation, m/2 being chance of up mutation, and m/2 being chance of down
> mutation. When reaching the present you evaluate the marker's variance
> over
> the population for that simulation of mutational history.
>
> Repeat this thousands of times with the same fixed tree. You will have
> thousands of variances from the various runs. Plot a bar graph of the
> number of runs whose variance falls between V and V + dV with dV being
> some
> small increment. For instance; V starts at 0 and each bin has width of
> .05,
> so there are 20 bins to get up to V = 1, and so on as high as you have
> appreciable variances from your many runs.
>
> You will produce a distribution of the variances from the very small on up
> to the very large. This distribution peaks at some value V(ML). That's
> the
> most likely variance. You can take an average of the distribution. That
> will give you some expected value or average V(AVG). You will find that
> the
> V(ML) is substantially below V(AVG), with a long tail in the distribution
> toward high values compensating for that bulge in the distribution below
> V(AVG)
>
>
>
>
>
>
>
> ----- Original Message -----
> From: "Sandy Paterson" <>
> To: <>
> Sent: Tuesday, April 08, 2008 7:45 AM
> Subject: Re: [DNA] underestimating variance
>
>
>> Hi Ken
>>
>>>
>> If you stick to a single marker, the most likely variance will be
>> substantially smaller than the expected (average) variance over many
>> reruns
>> of the population history.
>>>
>>
>> Can you elaborate on this by giving an example?
>>
>>
>> Sandy Paterson
>>
>>
>>
>>
>>
>>
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>
>
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