ordination in vegan: what does downweight() do?

kelsmith <kelsmith <at> usgs.gov> writes:

Can anyone point me in the right direction of figuring out what downweight()
is doing?

I am using vegan to perform CCA on diatom assemblage data. I have a lot of
rare species, so I want to reduce the influence of rare species in my CCA. I
have read that some authors reduce rare species by only including species
with an abundance of at least 1% in at least one sample (other authors use
5% as a rule, but this removes at least half my species). If I code it as
follows:

cca(downweight(diatoms, fraction=5) ~ ., env)

It is clearly not removing these species entirely from analysis, as some
authors suggest. So I am wondering: what is downweight() doing exactly? I
assume it is somehow ranking the species and reducing their abundance values
based on their rank, but I'm not entirely sure and can't seem to figure out
how to look at the code (R novice here). Nor can I find a clear description
within the documentation (although I may be looking in all the wrong
places).  

So, my inclination is to remove species that are very rare (max abundance <
1%) prior to the CCA and then use the downweight function (fraction = 5?) in
my CCA (as above). This way, I can include most of my species, but overall
still reduce the impact of rare species. 

Dear "kelsmith",


First a question: how do you *know* that rare species influence the result? I
know many people *believe* that rare species have an unduly high influence in
CCA, but that is only ecological folklore with no empirical basis. You could
have a look at the influence: run ordinations with all species and without rare
species and compare resulting ordinations using procrustes() function in vegan.
If the site/lake/sample/core/river results are very different, then rare species
indeed were influential (use plot() so that you don't get misled by numbers). 

Rare species often are extreme in CA-family results, but that does not mean that
they influenced the results. CA-family methods are weighted ordination methods,
and for species the weights are their total abundances (marginal totals). For
rare species the weights are low. The species are blown to the outskirts of the
ordination after the ordination rotation, and they do not often influence that
rotation very much.

I see that I ignored explaining downweighting in detail in vegan documentation.
You must read the reference cited there (Hill & Gauch): they explain the
procedure (at least vaguely: you must read the code to see how it is actually
implemented). However, the principle is simple: like I wrote above, rare species
have low weights, and downweighting makes these weights even smaller. It does
not remove the species, but it makes them even less influential. 

In vegan, downweighting was implemented for decorana, because it was the part of
Mark Hill's original decorana code. However, it was implemented in R (instead of
the original FORTRAN) and made independent of decorana so that it could be used
with other functions. This was done to serve those people who wanted to use it
outside its original context (greetings to Oslo!).

If you do not know what downweighting does, I suggest you don't use it. I also
suggest that you check the influence of rare species before you remove them from
your data.

Cheers, Jari Oksanen