[adegenet-forum] Using PCA of SPCA in linear models with environmental data.

[Jombart, Thibaut]

Hello, 

I'll give the useless opinion of someone on holiday. As long as you are not using a weighting scheme based on the inverse spatial distance, you should be fine. Some graphs deal poorly with duplicated locations though  (Delaunay, Gabriel). Neighbourhood based on a distance threshold, or K nearest neighbours are probably better options. 

As for your analysis using 35 vs 68 sites, well, yes the PCNM will be different as these are different data. If you have a few highly sampled locations then Valeria's suggestion is worth trying too.

Cheers

Thibaut
________________________________________
From: valeria montano [mirainoshojo at gmail.com]
Sent: 20 July 2012 20:07
To: Hanan Sela
Cc: Jombart, Thibaut; adegenet-forum at lists.r-forge.r-project.org
Subject: Re: [adegenet-forum] Using PCA of SPCA in linear models with environmental data.

Dear Hanan,

I will give you the useless opinion of someone working at 9pm on a Friday night. I guess the difference here could be made by the spatial matrix you are using. If it's a connectivity matrix, the binary code will consider the inds from the same locations as neighbours and won't really mind about them having the same coordinates. If you are otherwise using a weighted matrix, I suppose that having the same weights associated to different quantitative variables may be a confusing information, more than redundant. In this second case I would probably calculate the gene frequencies for all the inds at each site as they were pops and perform the spatial analysis on it...that's all that comes to my mind.

Have a nice weekend too

Valeria

On 20 July 2012 08:56, Hanan Sela <hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il>> wrote:
Hello
One more question about PCNM.  I have 68 wild wheat genotypes collected from 35 sites. This means that some sample pairs have zero spatial distance. How  should  I calculate the PCNM?    1. Use the coordinates of the 68 samples even tough there is redundancy.
2. Use the coordinates of the 35 sites.
I have done both calculations and the results are some what different.
Have a nice weekend
Hanan


On Mon, Jul 16, 2012 at 3:29 PM, Jombart, Thibaut <t.jombart at imperial.ac.uk<mailto:t.jombart at imperial.ac.uk>> wrote:

Hello,

in fact this is a trivial result, and there is nothing wrong in your data. CCA is a Correspondence Analysis on predicted variables; in your case, you have exactly 2 predictors (the 2 PCNM), which are already uncorrelated (by construction). This the best plane in 2D is exactly that of your 2 PCNMs.

Cheers

Thibaut

________________________________________
From: adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org> [adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org>] on behalf of Hanan Sela [hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il>]
Sent: 14 July 2012 14:57
To: adegenet-forum at lists.r-forge.r-project.org<mailto:adegenet-forum at lists.r-forge.r-project.org>
Subject: Re: [adegenet-forum] Using PCA of SPCA in linear models with environmental data.

Hello list
I have done what Thibaut suggested using the "pcnm" function in "vegan" (with no wights).  I have used the first two  pcnm PC's in canonical correspondence analysis (CCA) between SNP matrix as dependent matrix and the pcnm's PC's as perdictors. I have used the "cca" function in "vegan". The results are in the attached PDF file.  The results show that the fist two PC's fits exactly the first two cca PC's.  To remind you, the pcnm PC's are derived from spatial data and the cca PC's are derived from genetic SNP data.  My explanation to this is that I have a bias in the sampling that may results artifacts. In my data there are 1-5 genotypes from the same site (spatial distance=0)
average 1.9 genotypes per site.  I suspect that the structure of the sampling which is not spatially uniform may contribute to the high correlation of the PC's.  When I choose one genotype per site, the correlation is lower but still very high. I would like to hear your opinion.
Hanan

On Thu, Jul 12, 2012 at 3:35 PM, Jombart, Thibaut <t.jombart at imperial.ac.uk<mailto:t.jombart at imperial.ac.uk><mailto:t.jombart at imperial.ac.uk<mailto:t.jombart at imperial.ac.uk>>> wrote:

Yes, there has been quite a few methods developed since. A starting point would be:

Dray, S.; Legendre, P. & Peres-Neto, P. Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM) Ecological Modelling, 2006, 196, 483-493

Cheers

Thibaut

________________________________________
From: Hanan Sela [dooshra at gmail.com<mailto:dooshra at gmail.com><mailto:dooshra at gmail.com<mailto:dooshra at gmail.com>>]
Sent: 12 July 2012 12:44
To: Jombart, Thibaut
Cc: adegenet-forum at lists.r-forge.r-project.org<mailto:adegenet-forum at lists.r-forge.r-project.org><mailto:adegenet-forum at lists.r-forge.r-project.org<mailto:adegenet-forum at lists.r-forge.r-project.org>>
Subject: Re: [adegenet-forum] Using PCA of SPCA in linear models with environmental data.

Thank you for the answer
I want to test whether space (lat+lon) has significant effect on the genetic structure. Therefore I would like to use spatial variables in the right side of the model. Can you suggest a better representation of the spatial structures than lat-lon?
Thank you
Hanan

On Thu, Jul 12, 2012 at 1:58 PM, Jombart, Thibaut <t.jombart at imperial.ac.uk<mailto:t.jombart at imperial.ac.uk><mailto:t.jombart at imperial.ac.uk<mailto:t.jombart at imperial.ac.uk>><mailto:t.jombart at imperial.ac.uk<mailto:t.jombart at imperial.ac.uk><mailto:t.jombart at imperial.ac.uk<mailto:t.jombart at imperial.ac.uk>>>> wrote:
Dear Hanan,

this is a tricky question, and I don't think there is a single universal answer. Technically speaking, the only requirement is that your residuals are independent, so you need to make sure there is no spatial autocorrelation left there. Otherwise minimizing the sum of squared residuals is no longer the ML solution.

The real problem relates to the interpretation, and the assumption implicitly made by the model. There is several reasons why spatial genetic patterns can occur. Your model has the form:
genetic pattern = lat+lon + environment + residuals

Which means that beyond linear trends, genetic patterns are due to the environment. It makes sense to treat spatial autocorrelation as a confounding factor first removed from the analysis. But lat+lon is often not enough to capture all spatial structures. In this respect, using PCs from PCA on the left side is probably better than sPCA (no need to seek spatial structures to remove them afterwards).

Cheers

Thibaut

________________________________________
From: adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org><mailto:adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org>><mailto:adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org><mailto:adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org>>> [adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org><mailto:adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org>><mailto:adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org><mailto:adegenet-forum-bounces at lists.r-forge.r-project.org<mailto:adegenet-forum-bounces at lists.r-forge.r-project.org>>>] on behalf of Hanan Sela [dooshra at gmail.com<mailto:dooshra at gmail.com><mailto:dooshra at gmail.com<mailto:dooshra at gmail.com>><mailto:dooshra at gmail.com<mailto:dooshra at gmail.com><mailto:dooshra at gmail.com<mailto:dooshra at gmail.com>>>]
Sent: 12 July 2012 07:34
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Subject: [adegenet-forum] Using PCA of SPCA in linear models with       environmental data.

Hello all
I am trying to estimate the major factors affecting the spatial distribution of wild wheat genotypes.  I am using a linear model where the PCA or the SPCA   first and second axis are the dependent variables and the environmental variables are the predictors. Additionally I am using the longitude and the latitude as predictors.   Since there is a spatial reference on the left side of the formula, I was wondering if using SPCA on the right side will not be a problem.
Thank you
Hanan



--
Hanan Sela Ph.D.
Curator of the Lieberman Cereal Germplasm Bank
The Institute for Cereal Crops Improvement
Tel-Aviv University
P.O. Box 39040
Tel Aviv 69978
Israel

hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il><mailto:hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il>><mailto:hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il><mailto:hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il>>>
Phone: 972-3-6405773
Cell: 972-50-5727458
Fax: 972-3-6407857




--
Hanan Sela Ph.D.
Curator of the Lieberman Cereal Germplasm Bank
The Institute for Cereal Crops Improvement
Tel-Aviv University
P.O. Box 39040
Tel Aviv 69978
Israel

hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il><mailto:hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il>>
Phone: 972-3-6405773
Cell: 972-50-5727458
Fax: 972-3-6407857




--
Hanan Sela Ph.D.
Curator of the Lieberman Cereal Germplasm Bank
The Institute for Cereal Crops Improvement
Tel-Aviv University
P.O. Box 39040
Tel Aviv 69978
Israel

hans at tauex.tau.ac.il<mailto:hans at tauex.tau.ac.il>
Phone: 972-3-6405773
Cell: 972-50-5727458
Fax: 972-3-6407857


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