phylogenetically corrected PCA in geomorph

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Chris Law

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Jan 9, 2018, 2:42:33 PM1/9/18
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Hi all,

I wish to plot skull shapes from 65 species in tangent space. Does one usually perform a phylogenetically corrected PCA to plot species from a geometric morphometric analysis in tangent space? 

I've played around with the plotGMPhyloMorphoSpace function but it doesn't seem to perform a phylogenetically corrected PCA. Is there a way to do so in geomorph?

Thanks!
Chris


Chris Law
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Adams, Dean [EEOBS]

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Jan 9, 2018, 2:56:43 PM1/9/18
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Chris, both PCA with the phylogeny superimposed (so-called phylomorphospaces), and phylogenetic PCA (PPCA) have been used to view tangent space.  Presently, geomorph only allows for the former, though PPCA is on our list of future updates.

 

For a more thorough understanding of the differences between the two and what PPCA actually does, and does not do, I recommend a careful read of Polly et al. 2013 in Hystrix. It shows clearly what PPCA actually is and how it is related to PCA. 

 

From my perspective, PPCA is not strictly ‘necessary’ as a procedure. Unlike PGLS where non-independence must be accounted for during the statistical evaluation of regression or anova, PCA has no such issues (there is no hypotheses test in PCA containing an assumption of independence, and so accounting for it is not necessary).

 

Dean

 

Dr. Dean C. Adams

Professor

Department of Ecology, Evolution, and Organismal Biology

       Department of Statistics

Iowa State University

www.public.iastate.edu/~dcadams/

phone: 515-294-3834

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Mike Collyer

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Jan 9, 2018, 3:08:32 PM1/9/18
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Dean kind of beat me to the point I wanted to make, but I’ll add more to his perspective.  The term, "phylogenetically corrected PCA” is a bit dangerous, in my opinion.  PCA is nothing more than finding the major axes of variation in a data space, given a covariance matrix.  The phylogenetic “correction” is less precise to me than recognizing that a phylogenetically-informed covariance matrix is what is used to obtain the principal components.  The difference between a standard PCA with phylogeny superimposed and a phylogenetic PCA is merely a shift in origin from the data centroid to the estimated phylogenetic mean, and rotation based on the phylogeny rather than just the data covariance.  The geometric relationships of all points in this space remain unchanged.  I suppose with phylogenetic PCA, the covariance matrix has been “corrected”, but the PCA itself, has not been changed in any way.

Cheers!
Mike

Chris Law

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Jan 9, 2018, 6:35:35 PM1/9/18
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Great; thanks for the insight!

Chris Law


Cheers!
Mike


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