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

valeria montano mirainoshojo at gmail.com
Fri Jul 20 21:07:20 CEST 2012

```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> 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> 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 [
>> adegenet-forum-bounces at lists.r-forge.r-project.org] on behalf of Hanan
>> Sela [hans at tauex.tau.ac.il]
>> Sent: 14 July 2012 14:57
>> To: 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>> 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>]
>> 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>
>> 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>>> 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>> [
>> 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>>]
>> Sent: 12 July 2012 07:34
>> To: 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: [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>>
>> 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
>>
>>
>
>
> --
> 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
> Phone: 972-3-6405773
> Cell: 972-50-5727458
> Fax: 972-3-6407857
>
>
> _______________________________________________
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