# COALESCENCE

Discussion in 'Health and medical' started by Www.Ttdown.Com, Feb 27, 2004.

1. ### Www.Ttdown.Com Guest

Hi

I have a dumb question

Can someone explain me what does 1/2Ne stand for in the expression of

F = 1/2Ne / (1/2Ne + 2u)

They only thing that I though was that 1/2Ne represents 1 allele in the population, and (1/2Ne + 2u)
represents that allele on the next generation with 2u mutations added. since we are estimating whats
the probability of this allele being IBD to the allele of the previous generation if u = 0 then F =
1, and theres a 100% probability that the allele represented by the denominator is IBD to the allele
that the numerator represents.

thnks

hans

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2. ### A A Guest

It is hard to communicate without graphics. The expression isn't correct mathematics since there are
different ways to interpret it. Tip, dwell on coalescence in "Glossary of Genetics".

Mats

3. ### Www.Ttdown.Com Guest

sorry for that...

In Fu and Li, 1999 1/(2N) is defined as

"the probability of coalescence at the previous generation, i.e., the two sequences in the current
genera- tion came from a single ancestral sequence in the previous generation, is 1/(2N), where N is
the effective population size.

Then, for the probability that of identity by descent I have this expression

F = 1/(2N) / (1/2N) + 2u

so I just want to understnd why is the numerator 1/(2N), why the denominator (1/2N) + 2u

cheers

hans

On Fri, 27 Feb 2004 16:40:56 +0000 (UTC), [email protected] wrote:

>It is hard to communicate without graphics. The expression isn't correct mathematics since there
>are different ways to interpret it. Tip, dwell on coalescence in "Glossary of Genetics".
>
>Mats

4. ### A A Guest

Hi Hans,

When there are more than one allele present in each of some loci and the population is small then
random mating may extingush alleles.

You started something. I never saw a formula in sci.bio.evolution before.

Regards Mats Liljedahl

5. ### William L Hunt Guest

On Sat, 28 Feb 2004 18:18:21 +0000 (UTC), "www.ttdown.com"
<[email protected]> wrote:

>sorry for that...
>
>In Fu and Li, 1999 1/(2N) is defined as
>
>"the probability of coalescence at the previous generation, i.e., the two sequences in the current
>genera- tion came from a single ancestral sequence in the previous generation, is 1/(2N), where N
>is the effective population size.
>
>Then, for the probability that of identity by descent I have this expression
>
>F = 1/(2N) / (1/2N) + 2u
>
>so I just want to understnd why is the numerator 1/(2N), why the denominator (1/2N) + 2u
>
1/(2N) is the probability of a coalescent in a given generation. 2u is the probability of a
mutation. It is no longer an "identity" (IBD) if a mutation has occurred. So (1/2N) + 2u is the
probability of coalescent OR mutation. F in this equation is then the probability of a coalescent
(IBD) given that either a coalescent OR mutation occured. Sometimes you would see this from the
other side, the probability of a mutation given that either a coalescent OR mutation occured is H
= 2u/(1/2N + 2u) = 4Nu/(4Nu + 1). William L Hunt

>
>cheers
>
>hans
>
>
>
>On Fri, 27 Feb 2004 16:40:56 +0000 (UTC), [email protected] wrote:
>
>>It is hard to communicate without graphics. The expression isn't correct mathematics since there
>>are different ways to interpret it. Tip, dwell on coalescence in "Glossary of Genetics".
>>
>>Mats