[R-sig-eco] null model selection in functional diversity analysis

[Zoltan Botta-Dukat]

Dear Marc,

Try the permutation of trait values! Such permutation does not change 
any of the patterns that you mentioned and probably wanted to be 
constrained.
On the other hand, it removes the correlation between traits and 
environment, and also correlation between traits and abundance.

Cheers,
Zoltan


2014.10.23. 11:43 keltezéssel, Marc Taylor írta:
> Dear r-sig-ecology listers,
>
> I am involved in a study whose objective is the see if there relationships
> between the functional diversity of the fish community and environmental
> factors of the sample site for a number of sites in a bounded environment.
> Specifically, we are looking at the parameters of functional richness
> ("FRic") and functional diversity ("RaoQ") as calculated by the R package
> "FD". We observe certain trends in these indices as related to the
> environmental factors in question, and would now like to determine if the
> effect of their deviation from a null model is significant or not.
>
> Given the fact that FRic and RaoQ are often correlated with the richness
> and diversity, respectively, of the community, many null models are
> designed to remove these effects by permutating the abundance matrix while
> maintaining the functional trait matrix constant.
>
> Null model descriptions:
>
> 1. Own null model - Our first attempt has been to permutate the site
> association of individual fishes to site (see function "ownNull" below). The
> result of the null model is that abundance values for sites (rows) and
> species (columns) are maintained. The original idea was that we wanted to
> maintain the overall site capacity to sustain a certain number of
> individuals. Also, since certain species are linked with higher abundances,
> these total abundances should be maintained. The rationale was that in the
> absence of site-specific environmental controls on species identity,
> individuals would roam at random over the entire study region and end up
> randomly at the individual sites, each of which has a certain carrying
> capacity determining the number of individuals per site, but not their
> identity.
> Summary of constrained patterns:
>      * site abundance (yes)
>      * site diversity (no)
>      * site richness (no)
>      * global spp abundance (yes)
>      * global spp frequency distribution (no)
>
> 2. Independent swap (Gotelli, 2000) - This model also permutates species
> association to site, but randomizes matrix values (i.e. packets of observed
> individuals), with the additional constraint that accepted permutations
> must maintain site richness (i.e. total number of spp). This model seems in
> line with some of our original assumptions, but differs in that it focuses
> more on site richness and maintains global species frequency distributions,
> i.e. it takes the abundance values of species observed at each site and
> randomly assigns them to new sites. My coauthors worried about this last
> point - since it locks in large abundance values which might have been very
> much a product of site, and therefore abundance at site is not constrained.
> Summary of constrained patterns:
>      * site abundance (no)
>      * site diversity (no)
>      * site richness (yes)
>      * global spp abundance (yes)
>      * global spp frequency distribution (yes)
>
>
> We would ultimately like to quantify the effect of these environmental
> factors on our observed FRic and RaoQ indices, and thus were quantifying
> the standardized effect size (SES) based on the null model distribution. Since
> only the independent swap method maintains richness, this would seem to be
> appropriate for determining FRic. For RaoQ, neither option maintains
> diversity, so are either appropriate? Are more than one null model needed?
>
> So, we have two main questions:
> 1. What would be an appropriate null model given our objectives - One of
> these, or another suggestion?
> 2. Another aspect discussed on this list before (
> https://stat.ethz.ch/pipermail/r-sig-ecology/2010-January/001003.html),
> concerns that of the uniqueness of the permutated null models (especially
> applicable given the constraints of the independent swap algorithm) as well
> as the overall variability in null models. Calculating the number of unique
> permutated matrices is easy enough, but how would one assess whether null
> model variability is of a similar magnitude to that of the original data?
>
> Many thanks in advance for any help on these issues. An example script
> illustrating these issues can be found below.
>
> Cheers,
> Marc
>
Botta-Dukát Zoltán
--------------------------------
Ökológiai és Botanikai Intézet
Magyar Tudományos Akadémia
Ökológiai Kutatóközpont
--------------------------------
2163. Vácrátót, Alkotmány u. 2-4.
tel: +36 28 360122/157
fax: +36 28 360110
botta-dukat.zoltan at okologia.mta.hu
www.okologia.mta.hu


Zoltán BOTTA-Dukát
--------------------------------
Institute of Ecology and Botany
Hungarian Academy of Sciences
Centre for Ecological Research
--------------------------------
H-2163 Vácrátót, Alkomány u. 2-4.
HUNGARY
Phone: +36 28 360122/157
Fax..: +36 28 360110
botta-dukat.zoltan at okologia.mta.hu
www.okologia.mta.hu