Identifying highly influential species in CCA

[Arthur APA]

Bruce and others;

In the "Multivariate analysis for community ecologists..." publication
by Jerilynn Peck (Pc-ORD guidebook) on p.70 a technique is suggested for
assessing compliance with an important assumption of CCA. The linearity
of explanatory variables with the ordination scores "can be somewhat
assessed using scatterplots of highly influential species abundances
against explanatory variables." This, I think, parallels something
I do with CCA ordinations in a post-hoc manner. After a CCA, I examine
overlays of the main matrix variables (species abundance).

1. What grabbed in what she said was to use "highly influential species"
for these assessments. How were these identified?

To date I have been able frequently to use an Indicator Species Analysis
because many of the CCA have included gradients correspondent to some
categorical variable(s). The species thus identified I take to be
influential in the CCA as well.

2. The difference also in that these overlays plot against axes versus
the suggested explanatory variables I take to be less important.

To reiterate, the question would be how to identify the highly influential
species in order to do the CCA performance assessment?

Thanks again,

Art

[Bruce McCune]

I'm just guessing at what Jeri meant -- that the highly influential species would be those that are at least moderately abundant. This is debatable with CCA, however, in that the chi-square distance implicit in the CA family gives more weight to rare species, at least to the extent that they are graphed on the periphery in the ordination. However a couple of recent papers (see Greenacre 2013. The contributions of rare objects in correspondence analysis. Ecology 94:241–249.) make the opposite point.

But in general, what Jeri suggests is similar to my suggestion to an earlier post -- plot species against environmental or ordination axes. You can use a scatterplot or nonparametric regression (i.e. smoother).

-Bruce McCune

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[Arthur APA]

Bruce,

 

Thank you for this response.

 

The reference provided also was very helpful (and looks to lead to more).

 

As noted, I am looking at one kind of scatterplot in using the main matrix overlays on the ordination graphs.

Would the 'nonparametric regression' be a reference to the blue curves in those side plots?

 

Thanks again,

 

Art

[Bruce McCune]

Yes, "nonparametric regression" is a generic term for using smoothers to determine curve shape as well as degree of fit. That includes things like GAMs, splines, and kernel smoothers (as in NPMR and HyperNiche). PC-ORD uses nonparametric regression along with linear regression in its "side scatterplots" for ordination overlays (the blue lines by default). However, PC-ORD calls those "envelopes" because by default they are placed x local standard deviations above the expected value, so that they enclose most of the points rather than bisecting them. If, however, you select the standard deviation parameter in the side scatterplots to zero, then these are traditional univariate kernel smoothers.
-Bruce McCune

[Arthur APA]

Bruce,

 

Thanks again!

 

Art