Horseshoe effect in gmPCA?

[mint...@gmail.com]

In helping a colleague with their analysis, I see that their PCA has a noticeable horseshoe/arch effect in it (see below). I recall learning that such an effect can imply that PC2 is simply a distortion of PC1, and/or non-linearity across whatever gradient is measured. Seeing as these are GPA shape coordinates, I'm not sure how to interpret the issue or go about resolving it. Any help is appreciated.

-Russ 

[Adams, Dean [EEOB]]

Russ,

 

Yes, some ecologists in the earlier literature did claim the horseshoe/arch effect was a ‘distortion’; though to my mind that was largely due to the incorrect expectation that samples obtained along an ecological gradient should result in a linear path in the multivariate space. It was found most common in community composition data, and was best explained as the phasing in and out of different species along the gradient (for those interested, see Legendre and Legendre’s Numerical Ecology textbook for an explanation and simple simulation demonstrating the effect).

As to finding this in shape data, I find this really quite interesting. What I would suggest here for interpreting the pattern is to generate hypothetical shapes along the arch to get a sense of how shapes change along it. This can be done with shape.predictor/plotRefToTarget, or pick.n.plot.shape. I’d also generate a hypothetical shape in empty space of the arch to determine whether or not that is even a biologically-viable shape.

Hope this helps,

 

Dean

 

Dr. Dean C. Adams (he/him)

Distinguished Professor of Evolutionary Biology

Department of Ecology, Evolution, and Organismal Biology

Iowa State University

https://faculty.sites.iastate.edu/dcadams/

phone: 515-294-3834

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