First: Jane, if it's OK for you to reveal it, I'd be interested
to know more about the case where 'fitting a normal distribution
to a time series (ie ignoring time order) was taken as evidence
that the data were "random".'! I've known arguments like this to
come up in inquries and courts of law, and they can seem convincing
to the uninitiated (especially when emanating from an Authority
such as Excel ... ).

As to the general question:

Some insight into the approach (I haven't got access at the moment
to the original article) can be found in the Supplementary Material
at:

http://www.nature.com/nature/journal/v463/n7279/suppinfo/nature08630.html

As I understand it, they have essentially postulated 5 mechanisms
for speciation, each leading to a specific distribution for the
evolutionary branch-legths ion the phylogeny:

1: Constant net speciation rate ==> Exponential distribution
2: Variable bet-speciation rate (Gamma mixture of exponentials)
   ==> f(x) = a*b/((1 + b*x)^(1+a)) [no name known to me]
3: Net speciation rate dependent on time from ancestral species
   (i.e. on time since split) ==> Weibull distribution
4: Net speciation rate is cumulative effect of additive factors
   ==> Normal distribution
5: Net speciation rate is cumulative effect of multiplicative
   factors ==> LogNormal distribution

They would therefore be using distribution type as an index to
discriminate between these explicitly postulated mechanisms:
the best-fitting type would correspond to the most plausible
mechanism amongst those postulated.

As to applicability of such things in social sciences, it would
depend on context, of course. But a google search on

  "Gamma mixture of exponentials"

(including quotes) gave many hits mentioning a social-science
context. A good number of these refer to "duration data", and
mention alternative models (e.g. Weibull). So length of time
unemployed (or employed), duration of a social state, etc.,
could be processes for which such models could be postulated,
and such methods be used for appraising which of a number of
competing models might be the best fit to the data, and therefore
indicate which underyling mechanism might be most plausible
as an explanation.

Ted.

On 08-May-10 18:11:53, Jane Galbraith wrote:
> I haven't read the articles. It sounds suspicious to me, especially
> if applied to social science.
> 
> I recently came across an example where fitting a normal distribution
> to a time series (ie ignoring time order) was taken as evidence that
> the data were "random".
> 
> If a distribution does not fit that might suggest that the theoretical
> model giving rise to the distribution might not hold (or it might be
> that there are extra complications, for example observational error).
> 
> If the distribution does fit that means very little ... if there is
> good theoretical justification for the model then finding it "fits"
> could be reassuring.
> 
> Jane Galbraith
> 
>> After it was covered in New Scientist, I've been struggling to
>> understand the principles behind an article in Nature (C Venditti
>> et al, Phylogenies reveal new interpretation of speciation and
>> the Red Queen, Nature 463, 349-352 (21 January 2010).  As New
>> Scientist explained it, Pagel and others had been trying to track
>> evolutionary histories by looking at the fit between evidence
>> and four statistical distributions (exponential, variable rates,
>> lognormal and normal).  Looking at the paper, it's rather more
>> complex:  the fit is being determined by Bayesian methods, five
>> distributions are reviewed rather than four, and the second-best
>> performing distribution is a Weibull distribution.
>>
>> Can anyone point me to some illustrations of  work in social
>> science which has approached the problem in the same way - fitting
>> distributions, not as a description of patterns, but as a method
>> of identifying causalinfluences?
>>
>> I've seen the Weibull distribution used in some work to describe
>> the likelihood of escaping from poverty, but I'd assumed this was
>> descriptive, and I'm now having to reexamine that assumption.
>> What are the theoretical implications of assuming a Weibull
>> distribution?  Is there any guide to its application in social
>> science that someone can point me to?
>>
>>  Paul Spicker

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Date: 08-May-10                                       Time: 23:09:27
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