-------- Original Message --------
Subject: population-level non-independence
Date: Thu, 1 Dec 2011 15:09:27 -0500
From: Dean Adams <[email protected]>
To: [email protected] <[email protected]>
Andrea,
Indeed, the lack of independence among observations needs to be handled
differently at different levels of biological organization. For
comparative analyses across species, the phylogenetic relationships
among taxa best describe the non-independence. Thus methods of
independent contrasts (ala Felsenstein 1985) or PGLS (ala Martins and
Hansen 1996) allow one to assess the association of phenotype vs. some
other variable while accounting for non-independence due to shared
evolutionary history.
When populations across the landscape are of interest, one might
consider using an analog from spatial statistics. Here the
non-independence among observations can be captured by a spatial
covariance matrix, which could be held constant in the analyses in much
the same manner in GLS (see Cressie 1993 for estimating spatial
covariance matrices).
Yet another way of accounting for covariance among populations stems
from population genetics. Here a population-level phylogeny is not
appropriate, because this assumes that all of the non-independence is
captured by a branching pattern as seen in the phylogeny. However,
differential migration among populations may follow more of a network
pattern. As such, non-independence may be better approximated by a
migration matrix among populations. Felsenstein described the initial
approach in a book chapter in 2002 (cited in the Stone et al 2011 paper
you mentioned). However, while logical and rather straightforward, to my
knowledge, no one has implemented this procedure to account for
non-independence among populations.
Best,
Dean
--
Dr. Dean C. Adams
Associate Professor
Department of Ecology, Evolution, and Organismal Biology
Department of Statistics
Iowa State University
Ames, Iowa
50011
www.public.iastate.edu/~dcadams/
phone: 515-294-3834
On 12/1/2011 1:30 PM, morphmet wrote:
-------- Original Message --------
Subject: Re: [Past] cva question
Date: Thu, 1 Dec 2011 05:15:48 -0500
From: andrea cardini<[email protected]>
To: Manabu Sakamoto<[email protected]>
CC: Jordan Mallon<[email protected]>, [email protected],
PAST<[email protected]>
Dear Manabu,
thanks for your message.
I could not yet find time to read it, unfortunately, but this could be
interesting for your question:
2011 Phil. Trans. R. Soc. B 366 1410-1424
Graham N. Stone, Sean Nee and Joseph Felsenstein
Controlling for non-independence in comparative analysis of patterns across
populations within species
I doubt that in many cases a within species (or subspecies) phylogeny would
be really 'star-like'. Using appropriate genetic markers for that level, it
is, I suspect, likely that one finds some kind of hierarchical or network
structure. This is at the end of the day much of what's behind
phylogeographic studies.
Besides, there might be other (extrinsic) sources of autocorrelation that
one might have to consider to adress possible issues of non-independence
among observations. The biogeographical literature and studies of spatial
data might be a good source of references on this.
This is not my field, however, and these are issues that I find truly
difficult in terms of both the theory and the applications.
Others on the lists will make much more competent comments.
Cheers
Andrea
At 09:08 01/12/2011 +0000, Manabu Sakamoto wrote:
Dear Andrea,
This probably veers off from the original question (sorry Jordan) but I am
curious how you and others feel about specimen-level ordination. For
instance, if Jordan (or I) want to test for separation in morphospace of
specimens belonging to subspecies Ai from subspecies Aii, then how would we
take into account the phylogenetic non-independence? Surely a
specimen-level phylogeny would be pretty meaningless (i.e., pretty much a
star-phylogeny with a basal dichotomy)?
Manabu
Manabu Sakamoto, PhD
Postdoctoral Research Associate
School of Earth Sciences
University of Bristol
Bristol, UK, BS8 1RJ
Tel: +44 (0) 117 954 5421
Fax: +44 (0)117 925 3385
Email: [email protected]
On 1 Dec 2011, at 07:55, andrea cardini wrote:
Dear Jordan,
this is not an answer to your specific question. It's more of a general
comment.
The hierarchical nature of variation may have some other consequences: your
observations are not independent because of phylogeny. Comparative methods
try to address this issue in statistical analysis but I've never seen any
application to DA/CVA.
DA/CVA ordinations are done in a statistical space which maximize between
to within group differences. This has some interesting implications and
with small samples and large number of variables you can get a perfect
discrimination of random numbers split in arbitrary groups. I'd be very
careful with interpretations of those plots.
For ordinations, a few people (including a recent paper by Mitteroecker&
Bookstein and another one by Kovarovic, myself et al. - should be in my
webpage and in the paper you'll find the ref. to M&B and other refs) have
suggested between group PCA as an alternative for ordinations which
maximize group differences without distortions of the original morphometric
space of your data.
Good luck.
Cheers
Andrea
At 19:34 30/11/2011 -0700, Jordan Mallon wrote:
Dear all,
I've reached a bit of a dilemma with my morphometrics studies lately,
stemming from the hierarchical nature of variation. I've been studying
ecomorphology and how it varies within and between three dinosaur
families (each family contains two subfamilies). I've been using
canonical variates analysis to examine which variables best
discriminate the various taxa. The three families are perfectly
discriminated in CVA space.
Next, I would like to examine how the subfamilies differ, particularly
those that belong within the same family (i.e., looking at
intra-family variation). As far as I can tell, I have two options:
1) Place all six subfamilies into a single CVA and look for
intra-family clustering. The problem I see here is that most of the
variance captured by the CV axes will comprise inter-family
differences, rather than intra-family differences, because the
families are much more separate in space than sister subfamilies. In
other words, if families A and C are well-separated along axis 2, and
subfamilies Ai and Aii are only slightly separated along the same
axis, the loadings on that axis will tell me more about the separation
of families A and C than about subfamilies Ai and Aii. Right?
Hopefully I'm making myself clear.
2) Just run separate discriminant function analyses on all sister
subfamilies. I suppose this negates the problem above, but it
otherwise involves more work.
Has anyone run into a similar problem before? If so, how have you dealt
with it?
Thanks,
Jordan
Dr. Andrea Cardini
Researcher in Animal Biology
Dipartimento di Biologia, Universitá di Modena e Reggio Emilia, via Campi
213, 41100, Modena, Italy
tel: 0039 059 2055017 ; fax: 0039 059 2055548
Honorary Fellow
Functional Morphology and Evolution Unit, Hull York Medical School
University of Hull, Cottingham Road, Hull, HU6 7RX, UK
University of York, Heslington, York YO10 5DD, UK
Adjunct Associate Professor
Centre for Forensic Science , The University of Western Australia
35 Stirling Highway, Crawley WA 6009, Australia
E-mail address: [email protected], [email protected],
[email protected], [email protected]
Webpage: http://sites.google.com/site/hymsfme/drandreacardini
Datasets:
http://ads.ahds.ac.uk/catalogue/archive/cerco_lt_2007/overview.cfm#metadata
Editorial board for:
Zoomorphology:
http://www.springer.com/life+sciences/animal+sciences/journal/435
Journal of Zoological Systematics and Evolutionary Research:
http://www.wiley.com/bw/journal.asp?ref=0947-5745&site=1
Hystrix, the Italian Journal of Mammalogy:
http://www.italian-journal-of-mammalogy.it/
