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Re: Date for Last Common Ancestor?
Geoffrey Norman Watson (gwat@cs.uq.oz.au)
Thu, 22 Aug 1996 17:31:32 +1000
On Wed, 21 Aug 1996, Stephen Barnard wrote:
>
> Your definition is fine, as far as it goes. Like you say, you need further
> assumptions to get the size to converge to one.
>
> The assumption that I made, which seems perfectly reasonable to me, is that the
> probability that every mother in M_k-1 produces *exactly* one mother in M_k is
> less than one.
>
> Steve Barnard
>
Your assumption is reasonable, but how to justify it? One defect of this analysis
is that it is difficult to see how it could be used for simulations. The
generation of the sets M_k is in the opposite direction to time, and a lot of
what is happening depends on the rest of the population, which is not modelled
here.
Forwards simulations from a small base population show that female-line-lineages
die out randomly. To eliminate them rapidly you need a small population, and
obviously the probability of losing one falls as the number of lineages left
reduces. This supports your requirement that the probability is less than one
but I can't see how you would derive it rigorously.
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Geoffrey Watson gwat@cs.uq.edu.au
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