Re: Date for Last Common Ancestor?
Stephen Barnard (firstname.lastname@example.org)
Fri, 16 Aug 1996 19:30:12 -0800
John Hawks wrote:
> CHESSONP wrote:
> > The point of the example is to illustrate the fault in your logic. A
> > decreasing sequence of numbers may not converge to anything. A decreasing
> > sequence of numbers that is bounded will converge to its greatest lower
> > bound which need not be zero. A decreasing sequence of positive whole
> > numbers will converge to zero, but any finite segment of this sequence
> > will not. A non-increasing sequence of positive whole numbers will
> > converge to its greatest lower bound, which may not be zero.
> > You cannot claim that the size of your set of great .... grand mothers
> > reaches one at some point simply because each set (going backward by
> > generation) is not larger than the previous one. On logical grounds alone
> > the number of females in this "lca founding population" could be any
> > number no larger than the smallest known human population size at some
> > time.
> You are right about Steve's proof. In fact, to be accurate, Steve's proof must be
> expressed in terms of probability. In each generation, each mother will, with a
> certain probability, have one daughter, more than one daughter, or no daughters. The
> use of probability is what introduces *stochasticity* (of which you will probably
> have heard) into the proof. It cannot be demonstrated in this way that there *must*
> be a single mitochondrial ancestor. However, it can be demonstrated with
> *overwhelming* likelihood that such an ancestor existed.
Now just a darn minute, John. I *did* make a probabilistic argument.
Go back and read it again. I admit that the *original* argument
wasn't probabilistic and it was flawed, but I fixed it up. I think
we're saying exactly the same thing.