[R-sig-eco] vegan RDA triplot species arrows

[Jari Oksanen]

On 4/05/11 22:44 PM, "Tyler Smith" <tyler.smith at eku.edu> wrote:
> 
> Why does vegan not plot species as arrows in plot? I know how to use
> scores() and arrows() to create my own arrows, but it seems odd that
> this feature is not built in. Is there ever a situation where species
> *should* be plotted as points rather than arrows?
> 
> I checked ?plot.cca, vegan-decision, and google, but I didn't find
> anything, (excepting the possibility of using biplot.rda, but only for
> unconstrained analyses).

Tyler,

Not using arrows for species is a design decision, and it is mainly for
practical reasons. Ordination graphics are usually very messy with points,
and if you add arrows they get messier beyond grasp. The arrows are readable
only for a small number of species. Try them, say, in the BCI data and
describe what you see: it is pretty close to a Rorschach test. CanoDraw and
GUI wrappers around Canoco get around this by secretly dropping out most
species and showing only a selection (you can overrule their decision by
navigating in the GUI if you know how to do it). Having arrows for species
and arrows for constraints is the mess squared. Actually, when Gavin
implemented biplot.cca, we discussed about having a triplot, but decided
that having two kind of arrows is a mess nobody wants to see. It is doable,
of course, but is this really something you want to get.

Here is my previous example in the constrained ordination framework:

m <- rda(dune ~ A1 + Management, dune.env)
plot(m, dis=c("si","cn"))
plot(envfit(m ~ ., dune, display="lc"), add = TRUE, col="red")

To test that this gives the correct kind of arrows, you can add species
scores which should lay on the arrows or their continuations.

I agree that the use of arrows is justified in PCA & RDA. They are linear
methods, and the arrows show the linear trends. There is also one advantage
in arrows: logically, the *absolute* location of the arrow head is
irrelevant. The only things that matter are the directions and *relative*
lengths of arrows. In this way you get over the tricky issue of scaling
species and site scores against each other in absolute units. This is really
tricky in PCA/RDA and I really do not know a real good solution. We have
tried several in vegan, and the one we use works sometimes nicely, but not
always.

Gav is correct about my aversion to arrows. However, I think they are
appropriate for strictly linear and Euclidean methods (PCA, RDA). They may
not be adequate for metric scaling with non-Euclidean dissimilarities
(cmdscale, capscale) but may not be entirely bad either. Certainly they are
dubious for CA and related methods and NMDS, but can be easily added in
vegan using envfit like above (but, please, please, please...). However,
there are worse aversions in this area than mine: Dave Roberts once told me
that he doesn't see species as *points* (or arrows), but "fields" or
response surfaces in n-dimensional space. I agree, but I don't know how to
display that to, say, 225 species in the BCI data.

Cheers, Jari Oksanen