[R-sig-eco] Dissimilarity matrix from traits with partial overlap

[Vít Syrovátka]

Dear Jeffrey,
I might be wrong, but I am affraid you will have to define the 
similarity you want by yourself,
calculate it separately and combine with the similarity obtained from 
other traits.
That will not be difficult, since the Gower's coeficient is just a 
(weighted) average of partial similarities.
The definition of your similarity index may be done using the vegan 
package function designdist().

Here is my solution how I would deal with it:

# sample data:
mat<- matrix(c(0,0,1,1,0,0,0,0,0,0,
                1,1,1,1,0,0,0,0,0,0,
                0,0,1,1,1,1,1,1,1,1),
              nrow= 3, byrow=T,
              dimnames= list(paste('sp',1:nrow(mat),sep= ''),
                             paste('fam',1:ncol(mat),sep= '')))

library(vegan)

# for symmetrical similarity calculated as the proportion of families 
shared by ith and jth species within all families of host trees used by 
either (ith and jth) beetle:
designdist(mat, "J/(A+B-J)")

# for asymmetrical similarity calculated as the proportion of families 
that ith species shares with jth species:
mysim<- as.matrix(designdist(mat, "J/A"))
mysim[upper.tri(mysim)]<- designdist(mat, "J/B")

Hope that helps.
Cheers,
Vit

---
Vit Syrovatka
Department of Botany and Zoology
Masaryk University
Kotlarska 2
CZ-611 37 Brno, Czech Republic

Tel.: +420-549498566
E-mail: syrovat at sci.muni.cz




Dne 2015-10-09 02:17, Holland, Jeffrey D napsal:
> Dear Ecologists,
>      A student of mine is using vegan to create a Gower’s
> dissimilarity matrix between species of wood-boring beetles based upon
> ecological traits.  One trait we are using is the Family of host trees
> used as hosts by the larvae.  Most species can use trees from several
> Families, and so the number of trees used can be completely different,
> completely the same, or overlap (i.e., some the same and some
> different).  To accomplish this, we have created a binary variable for
> each tree Family and enter 1 if this is used by the species.  We also
> wish to have the “host trees” variables sum so that they have a total
> weight of 1 in calculating dissimilarity.  Laliberté & Legendre (2010)
> suggest in such cases of partial overlap in variable states to create
> dummy variables as we have and then weight each state-variable (e.g.,
> one tree Family) by 1/n, where n is the number of states.
>      However, this should evaluate to 0 if no hosts are shared and 1
> if there is perfect overlap in hosts.  There is an option in the
> gowdist command in vegan to specify symmetric and asymmetric
> variables, to remove or include double-zeros in the calculation of
> dissimilarity.  If we use an example in which two species each use 2
> of 10 available host tree Families we get the following possible
> scenarios, with each tree Family variable given a weight of 1/10:
> 
> Symmetrical, similarity will range between 0.6 and 1, because even
> with no hosts shared, the double-zeros (6 minimum) will be counted as
> matches.  So, even species with no hosts in common will appear more
> similar than they are.  The total weight will be 1 as required.  The
> obvious solution seem to be to designate the host Families as
> asymmetrical variables.
> 
> Asymmetrical, similarity will range between 0 and 1, because the
> matches and the host Families used by only one of the two species
> compared are properly not counted as matches, and the double zeros do
> not count as similar.  However, the summed weight will now vary
> between 0.2 and 0.4, and never total in such a way to approach the
> desired total weight of 1.
> 
> The result is that we are left choosing between two sub-optimal
> solutions: counting double zeros as similar hosts or greatly
> down-weighting the hosts used in similarity calculation (and doing
> this inconsistently depending on the ranges of hosts for each pair of
> species).  There are many species (~100 beetles) and many hosts (~50
> tree Families).  Does anyone know of a solution to this?
> Sincerely,
> Jeff Holland, Purdue University
> 
> REF: Laliberté, E. and P. Legendre. 2010. A distance-based framework
> for measuring functional diversity from multiple traits. Ecology 91:
> 299-305. Page 301, top of 2nd column.
> 
> 
> Jeffrey D. Holland, PhD
> Associate Professor, Landscape Ecology & Biodiversity
> Dept. of Entomology, Purdue University
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