[R-sig-eco] Quantifying functional trait diversity through Gowerdistance and pcoa

Wed Nov 17 11:38:26 CET 2010

Dear Chris,

Given that your study is multi-faceted, and given the numerous
'purpose-specific' FD metric that exist, my humble advice would be to
use consistent ways to measure PD and FD.

I guess that for PD you are using a tree .... and that you are summing
branch lengths to calculate PD in your (discrete ~ grid cells)
communities. So why not use the same strategy for FD, building a
Functional tree and summing branch lengths ? But do not forget to
standardise by species richness (PD and FD are not independent of
species richness).

I would recommend you to read the following paper which is analysing
similar things at a more restricted scale :

Devictor V, Mouillot D, Meynard CN, Jiguet F, Thuiller W, and &
Mouquet N. (2010). Spatial mismatch and congruence between taxonomic,
phylogenetic and functional diversity: the need for integrative
conservation strategies in a changing world. Ecology Letters, 13,
1030-1040

you can find the pdf here :
http://nicolasmouquet.free.fr/publications/Devictor_et_al_2010_EcoLett.pdf

To get the best tree you can follow the strategy of Mouchet et al. :

Mouchet M., Guilhaumon F., Villéger S., Mason N., Tomasini J. A.,
Mouillot D. 2008. Towards a consensus for calculating dendrogram-based
functional diversity indices. Oikos 117 (5) : 794-800.

For which we have developed a piece of code :

http://www.ecolag.univ-montp2.fr/index.php?option=com_content&task=view&id=174&Itemid=117

You may also want to have a look at this paper and associated R code
on the PLos ONE site :

Cadotte, M. W., J. Cavender-Bares, D. Tilman and T.H. Oakley. 2009.
Using phylogenetic, functional and trait diversity to understand
patterns of plant community productivity. PLoS ONE 4(5): e5695.

link to paper :
http://www.utsc.utoronto.ca/~mcadotte/pubs/Cadotte%20et%20al.%202009%20PLoSONE.pdf

Hope this help in the 'cruel' world of Functional diversity.

Cheers,

François.

2010/11/17 Chris Mcowen <chrismcowen at gmail.com>:
> Dear all;
>
> Thanks very much for all of this, it has been very helpful. As previously mentioned i am relatively new to this area, and before reading around the subject a bit more i have little to add to the, very useful, but slightly over my head comments.
>
> To the aims of my study and the context are as follows:
>
> I have a dataset of 1500 species for which i have 14 life history traits - mainly dichotomous i.e woody / not woody, fleshy fruit / dry fruit but i also have some factors with more levels such as breeding system (which has 3 etc)
>
> I have detailed GIS information for the distribution of these species allowing the identification of biodiversity hotspots i have made a phylogenetic tree of the species and calculated phylogenetic diversity and isolated phylogentic diversity hotspots. My plan was to calculate functional diversity and plot all the diversity indices on a map and look for patterns and understand the underlying processes.
>
> I shall have a read around the areas discussed in these comments, and choose the best metric to use; i was wondering if given my scenario my approach was sensible and if there is any metric that would capture my data?
>
> Thanks again,
>
> Chris
> On 17 Nov 2010, at 07:27, Etienne Laliberte wrote:
>
> Following up on Jari's comments:
>
> From my perspective, getting the right metric depends on the ecological
> question asked. Some are better than others for particular questions -- and
> some are not that useful regardless of the question.
>
> That said, irrespective of the merits of different metrics that express
> different individual/independent facets of FD, my limited previous
> experience tells me that people are often looking for a single, "synthetic"
> metric that expresses the concept of dispersion not unlike what the sample
> variance does (but with more than one variable, and using weights, where
> weights are species relative abundances). This is pretty much what Rao's
> quadratic entropy (Q) does - a multivariate analogue of a weighted variance.
>
> Functional dispersion (FDis) is basically just a weighted version of Marti
> Anderson's multivariate dispersion, and is therefore a multivariate analogue
> of the weighted mean absolute deviation (MAD). Both Rao's Q and FDis are
> closely related (like the MAD and variance are), but the MAD (and FDis) is
> less sensitive than the variance (and Rao's Q) to extreme values (which can
> be either good or bad).
>
> The analogy is shown here:
>
> # get FD library
> library(FD)
>
> # get traits and abundances
> trait <- runif(30) # trait with uniform values
> abun <- rlnorm(30) # lognormal abundance distribution
>
> # get names for both vectors
> names(trait) <- paste("sp", 1:30, sep = "")
> names(abun) <- paste("sp", 1:30, sep = "")
>
> # get Euclidean distance matrix from traits
> trait.dist <- dist(trait)
>
> # get Rao's Q and FDis using the dbFD function in the FD library
> test1 <- dbFD(trait.dist, abun, calc.FRic = F, calc.CWM = F, calc.FDiv = F)
> rao <- test1$RaoQ
> fdis <- test1$FDis
>
> # weighted sum function
> wsum <- function(x, w) {
>  w2 <- w / mean(w)
>  x2 <- sum(x * w2)
>  return(x2)
> }
>
> # weighted variance function
> wvar <- function(x, w) {
>  x.mean <- weighted.mean(x, w)
>  x2 <- (x - x.mean)^2
>  x2.wvar <- wsum(x2, w) / length(x)
>  return(x2.wvar)
> }
>
> # weighted mean absolute deviation
> wdev <- function(x, w) {
>  x.mean <- weighted.mean(x, w)
>  x2 <- abs(x - x.mean)
>  x2.wdev <- wsum(x2, w) / length(x)
>  return(x2.wdev)
> }
>
> # get weighted variance and weighted mean absolute deviation
> trait.var <- wvar(trait, abun)
> trait.dev <- wdev(trait, abun)
>
> # show that Rao's Q is a weighted variance
> # while FDis is the weigthed mean absolute deviation
> # rao = trait.var?
> # fdis = trait.dev?
> round(rao, digits = 6) == round(trait.var, digits = 6) # TRUE
> round(fdis, digits = 6) == round(trait.dev, digits = 6) # TRUE
>
> I personally feel that FD metrics that have clear univariate analogues are
> easier to grasp, and justify. I must admit that I'm not so keen on
> tree-based metrics, unless one can finally explain to me why it would be
> useful to first cluster species (and thus to distort trait space) when one
> is not actually interested in forming functional groups in the first place.
> If someone has an answer to this, I'd greatly appreciate you sharing it,
> because I never quite understood it.
>
>
>
> -----Original Message-----
> From: r-sig-ecology-bounces at r-project.org
> [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of Jari Oksanen
> Sent: Wednesday, 17 November 2010 2:38 PM
> To: chris mcowen; r-sig-ecology at r-project.org
> Subject: Re: [R-sig-eco] Quantifying functional trait diversity through
> Gowerdistance and pcoa
>
> Chris,
>
> Here some random exegeses:
>
> You should be aware that functional diversity seems to be dangerous field
> where you cannot do the right thing: there are different schools of thought,
> and you can always get a "wrong referee" what ever you do. Be warned. The
> major difference seems to be between tree-based and ordination-based
> (distance based) approaches. Some other, perhaps even more dangerous fields,
> are distance decay (Mantel) vs. variation partition (RDA) where you will be
> shot down by a "wrong referee" what ever you do. Even after you change your
> manuscript following one referee, the other referee burns you because you
> did so. Beta diversity is still one dangerous example that is hot to touch.
> You better read the literature very carefully.
>
> I find it curious that the same things have been invented in a bit different
> disguise in several fields of ecology s.lat. Aquatic and marine ecologists
> have taxonomic diversity which seems to be exactly the same thing except it
> uses taxonomy instead of traits. Mycologists and microbiologist have
> phylogenetic diversity since they don't have traits and don't know the
> "species", but they only have OTUs, sequences and phylogenies. Terrestrial,
> aquatic and microbial ecologists do not read the same journals and so they
> reinvent parallel variants of similar things and use different words and
> names.
>
> Finally, if you make your traits into distances (dissimilarities), it is
> best to see what Marti Anderson tells you to do with them. She has ideas for
> full space analysis of differences (like adonis in vegan), for full space
> analysis of dispersion (like betadisper in vegan), and for reduced space
> analysis (like db-RDA as in capscale in vegan). All these use the geometry
> of PCoA/ classic MDS/ metric MDS, although this is not always visible to the
> surface:. The full space analyses by Marti Anderson even handle the
> imaginary dimensions (associated with negative eigenvalues in metric MDS)
> within the function which may be very hard to handle with explicit PCoA.
>
> Cheers, Jari Oksanen
>
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