GENEALOGY-DNA-L Archives

Archiver > GENEALOGY-DNA > 2011-06 > 1307746568


From: "Kenneth Nordtvedt" <>
Subject: Re: [DNA] Asymptotic Distributions for General Mutation Models
Date: Fri, 10 Jun 2011 16:56:08 -0600
References: <972D673E3D084E2DBBD515DD90077C82@kenPC> <000001cc2606$b16669c0$14333d40$@com> <4DEFBCFF.6040501@gmail.com> <000001cc2610$d0ce1240$726a36c0$@com> <4DEFD211.60207@gmail.com> <000001cc26db$a4d9eb20$ee8dc160$@com> <4DF16E65.9050205@gmail.com><000001cc2745$06e43eb0$14acbc10$@com> <4DF27CFB.10503@gmail.com><152353867B34425387AF3752E2F28D06@kenPC><4DF290E9.3040700@gmail.com>
In-Reply-To: <4DF290E9.3040700@gmail.com>


-----Original Message-----
From: David Johnston

On 6/10/11 3:53 PM, Kenneth Nordtvedt wrote:
> [[You can get most likely solution of the mutation outcome properties for
> a
> given tree. To go further you have to introduce very subjective and
> speculative assumptions from demographics about the relative probabilities
> of all the different possible tree shapes. Every possible tree is
> certainly
> not equally likely a-priori. So your problem is now a hybrid
> investigation
> of mutations and demographics. ]]
>
I am not sure I understand. Let's say you have three people. There is
only one topologically distinct tree to make and three ways to assign
the people to that tree. So three trees in total. Why would any of those
trees be more likely a priori than any other? None of the people have
anything special about them so all should have same prior.

[[You stacked the deck by picking a degenerate case where as you say, you
still have just a single tree structure with only multiple ways to assign
the people to the branch ends. As population increases beyond three, you
will soon have extremely many distinct tree structures logically possible
and have to assign now relative weights to those different tree structures,
even before you consider the multiple ways to assign haplotypes to the
branch ends of each structure.

The liklihood function in general will have a great number of local maxima
in it. One could say I'll focus on the maximum of the local maxima; but the
total probability in the vicinity of that maximum of the maxima will
probably represent just a tiny piece of the whole. We can only infer useful
attributes of this global liklihood function if they are pretty immune to
the details. Certain TMRCA estimates are robust in that sense; while others
are not.

And surely different branch lengths between nodes have no equality of
probability a priori. Those branch segment lengths determine the node
density as function of time. Node density is a measure of population growth
rate. Population growth rate varies with time, location, culture.....
Compare after industrial revolution with before. After agriculture comes to
a population to before. After a group moves from old world to new world,
etc.

Let's take your tree leading to three.

a______________________
b______________________|_________
c___________|

You have three known haplotypes today. For each assignment of one of those
haplotypes to the top branch, you can find a probability function for the
two nodes being at time depths G and G* for each choice of node haplotypes h
and h* respectively producing those hap outcomes: Prob(a,bc|G,G*,h,h*) =
calculable probability of getting haps a,b,c given node ancestors h and h*
at times G and G*

What Bayesian procedure will you now enact to bring at least G* to the left
side of the conditional --- P(G....|abc) = Prob(a,bc|G,G*,h,h*) times some
priors and perhaps summed over unwanted variables or unseen distinctions?
And what assumption about reality are you introducing with any priors
introduced.

This is an analytically soluble model until the priors stuff (which
simulations can't escape from either) are faced. I went through it some
time in the past. KN ]]









Then there is the issue of about the prior on the ratio of leg length. I
suppose that is sort of a demographic issue. Not sure what the best
prior would be on that. Would the uniform prior, 0 to 1 be so bad?
Dave

-------------------------------
To unsubscribe from the list, please send an email to
with the word 'unsubscribe' without the
quotes in the subject and the body of the message

This thread: