Re: About the Bootstrap...

Gilles Escarguel wrote:

> > iii. A parametric bootstrap generates its pseudoreplicate data sets
> > using an explicit model of evolution abstracted from the data, rather
> > than resampling the actual data as in a non-parametric bootstrap. If,
> > for example, I wanted to get bootstrapped data sets for a set of DNA
> > sequences, I might first estimate a tree using some phylogenetic
> > analysis program, then estimate evolutionary parameters over that tree
> > (transition/transversion ratio, proportion of invariable sites, base
> > composition, etc.), and then plug those parameters and that tree into an
> > evolution simulation program to get a new data set. Repeated many times,
> > I would have a set of pseudoreplicate data sets. Those pseudoreplicates
> > can then be used for all sorts of purposes. See this for example:
> >
> > Huelsenbeck, J. P., D. M. Hillis, and R. Jones. 1996. Parametric
> > bootstrapping in molecular phylogenetics: Applications and performance.
> > Pages 19-45 in  Molecular zoology: Advances, strategies, and protocols
> > (J. D. Ferraris and S. R. Palumbi, eds.). Wiley.
>
> Many thanks for this. The procedure you describe is what I put in the
> solution # i -- sorry: I didn't explain it very well.
>
> That's OK for me, but consequently, how to name -- if a specific name
> exists... -- the parametric (as based on parametric estimates of descriptors
> uncertainties) Monte-Carlo resampling procedure described in (ii)?


I have no suggestion. I only have a vague notion of what you mean by 
this. But is it anything like this?: Marshall, C. R. 1991. Statistical 
tests and bootstrapping: assessing the reliability of phylogenies based 
on distance data. Mol. Biol. Evol. 8:386-391. Or this: Krajewski, C., 
and A. W. Dickerman. 1990. Bootstrap analysis of phylogenetic trees 
derived from DNA hybridization distances. Syst. Zool. 39:383-390. One of 
them (I forget which) fills pseudoreplicate cells by choosing from a 
normal distribution with mean at the real value and standard deviation 
determined by experimental measurements. (The other picks at random from 
among experimental measurements for that cell.)

> Actually,
> in the case of biometrical and/or morphometrical data, the procedure you
> describe seems to me hard to apply, even if an explicit model of biometrical
> and/or morphometrical evolution can be formulated from the data (e.g., taking
> into account the variances and covariances between descriptors by using the
> Mahalanobis generalized distance).


If you want to use between-character covariances you will have to write 
your own program. Otherwise there are a number of programs that can 
evolve characters on a tree using brownian motion models. But all of 
them assume independence among traits.

> The procedure proposed in (ii) is much
> more easy and straightforward, but I currently don't know any paper dealing
> with it on a theoretical basis. For instance, when I apply this procedure on
> real data sets (I have done the programs for this), and I compare estimated
> CL with CL estimates obtained by classical nonparametric bootstrap, it (the
> ii procedure) appears to return significantly higher CL estimates, and thus
> to be significantly less conservative than the nonparametric bootstrap
> technique. But how to interpret such differences?


The standard method is to use simulations to assess the behavior of data 
sets when the true tree is known. That's a lot of work, but I don't see 
another way. So it looks once more as if you need a model of evolution 
and a program to implement it over a tree. How much that model matches 
the behavior of real data is always the problem.