[R-sig-eco] Species fit in ordination

[syrovat at sci.muni.cz]

My apologies for sending my reply to Jari Oksanen only.
See it below, please.
Vit

Dear Jari Oksanen,

Thank you for your suggestions!

> You really have to define what is a good fit. Having a large change in
> probability is different from explaining a large part of the variation of
> observations. You may have cute, strong response and still large
> residuals.
> In the language of linear models, you may have steep regression slope and
> still large residual variance. Your question sounded like the 'slope'
> component, but most statistics deal with the 'residual' component either
> in
> absolute terms ('residuals') or in relative terms
> ('residuals'/'original').

It was not clear, but I definitely meant good fit in terms of residuals -
the species I am interested in are those, whose abundance (or probability
of presence) significantly change within the 2-dimensional ordination
space and can be predicted well (with reasonable R2) using the two
ordination axes.
For example, in the middle of the ordination diagram, there are gathered
both ubiquitous species and species with their optimum around the middle
of the gradient. I would like to eliminate the ubiquitous ones. Now I see,
it is more complex issue, as the species may be predicted well using the
ordination axes, but may have different niche breath.

> It is not in the Canoco proper (or the code that Cajo ter Braak wrote on
> the
> base of Mark Hill's original), but on its support and wrapper functions.
> These supports were originally a separate program (CanoDraw), but are no
> bundled together. Here the criterion was different: it was the species
> response to the constraints and not to the ordination axes. These may be
> very, very different. Further, constraining uses a linear model so that
> you
> will clearly use here linear goodness of fit to the original environmental
> variables instead of non-linear response to the ordination axes.

Ok, thank you.

Actually, when I asked for the first time, I expected there is some common
practice in calculating the species fit in ordination. Most recently I
have read in a figure legend withou any other explanation that:

"The species displayed ... have a more than average fit and occur five or
more times in the data".

(ter Braak CJF, Schaffers AP, 2004: Co-correspondence analysis: A new
ordination method to relate two community compositions. Ecology 85(3):
834-846.)

I really don't know what fit did they mean. Maybe I should ask them.

> Function goodness() for cca/rda finds the Canoco-like statistics either as
> residual distances or as proportion explained. You may have to set
> choices,
> and set summarize = TRUE. See ?goodness.cca. The text() and points()
> functions for most ordination objects have 'select' argument in vegan so
> that  you can pick up the cases you want to have.
>
> In principle, you can use envfit() for species, but it implies a linear
> species response to the gradients. Function ordisurf() fits a smooth
> surface, and if you set knots = 2, it will fit a quadratic surface, and
> with
> family = binomial it will something similar to Gaussian species response
> on
> the ordination space (with family = quasipoisson it would be the Gaussian
> response, but with binary responses you must use family = binomial). The
> function returns an object of mgcv:::gam and you can use all mgcv:::gam
> methods for further analysis of the results.

The solution seems to me to use the ordisurf method with your suggestions
in case the species response is expected to be unimodal, otherwise (if
linear response expected) the envfit method would do the job.

Last question, should I care about arch effect when estimating the species
fit? (When expecting unimodal species response) In co-correspondence
analysis the arch effect is common.

Thank you very much!

Yours,
Vit