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Community composition variance partitioning?

4 messages · Alexandre Fadigas de Souza, Sarah Goslee, Jari Oksanen +1 more

Original
Alexandre Fadigas de Souza
# 
Dear friends,

   My name is Alexandre and I am trying to analyze a dataset on floristic composition of tropical coastal vegetation by means of variance partition, according to the outlines of a Tuomisto's recent papers, specially

Tuomisto, H., Ruokolainen, L., Ruokolainen, K., 2012. Modelling niche and neutral dynamics : on the ecological interpretation of variation partitioning results. Ecography (Cop.). 35, 961?971.

   I have a doubt, could you please give your opinion on it?

   We are proceeding a variance partition of the bray-curtis floristic distance using as explanatory fractions soil nutrition, topography, canopy openess and geographical distances (all as euclidean distance matrices).

We are using the MRM function of the ecodist package:

mrm <- MRM(dist(species) ~ dist(soil) + dist(topograph) + dist(light) + dist(xy), data=my.data, nperm=10000

The idea is that the overall R2 of this multiple regression should be used to assess the contributions of the spatial and environmental fractions through subtraction :

Three separate multiple regression analyses are needed
to assess the relative explanatory power of geographical
and environmental distances. All of these have the same
response variable (the compositional dissimilarity matrix),
but each analysis uses a diff erent set of the explanatory
variables. In these analyses the explanatory variables are:
(I) the geographical distance matrix only, (II) the environmental
diff erence matrices only, and (III) all the explanatory
variables used in (I) or (II). Comparing the R 2 values
from these three analyses allows partitioning the variance
of the response dissimilarity matrix to four fractions.
Fraction A is explained uniquely by the environmental
diff erence matrices and equals R2 (III) R2 (I). Fraction B
is explained jointly by the environmental and geographical
distances and equals R2 (I) R2 (II) R2 (III). Fraction C
is explained uniquely by geographical distances and
equals R2 (III) R2 (II). Fraction D is unexplained by the
available environmental and geographical dissimilarity
matrices and equals 100% R2 (III) (throughout the present
paper, R2 values are expressed as percentages rather
than proportions). [Tuomisto et al. 2012]

The problem is that the R2 of the overall model (containing all the explanatory variables) is smaller than most of the R2 of models containing each of the explanatory matrices. So it seems not possible to proceed with the approach proposed.

    
    Sincerely,

    Alexandre

Dr. Alexandre F. Souza 
Professor Adjunto II Departamento de Botanica, Ecologia e Zoologia  Universidade Federal do Rio Grande do Norte (UFRN)  http://www.docente.ufrn.br/alexsouza  Curriculo: lattes.cnpq.br/7844758818522706
Sarah Goslee
# 
Hi,

That seems a bit odd: can you provide a reproducible example, off-list
if necessary?

Sarah



On Wed, Dec 4, 2013 at 12:50 PM, Alexandre Fadigas de Souza
<alexsouza at cb.ufrn.br> wrote:

  
    
  


  


      

    

    

      
      

        


  

        

      Jari Oksanen
    

    

      
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Hi,

Not only odd, but impossible. If you have a model y ~ x1, and you *add* a new explanatory variable, you cannot get worse in raw R2. You can get worse in adjusted R2. You can also get worse if you add variables to a matrix for which you calculate distances. So dist(y) ~ dist([x1]) can have higher R2 than dist(y) ~ dist([x1,x2]) -- bioenv is based on this.

Cheers, Jari Oksanen

Sent from my iPad

            

      
      
      
    

        

      
      
    

            
        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Steve Brewer
    

    

      
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Alexandre,

I'll leave it to Sarah to advise you on MRM (and I agree with Jari that
the method you're describing is not going to work). I'll just add that it
is not clear to me why the predictors (even geographic distance) have to
be treated as distances to partition the variance in composition. I'm
assuming the environmental variables were not originally in the form of
euclidean distance matrices and that the raw measurements are available?
As for the geographic distances, if you have lat and long coordinates, why
not treat both lat and long as predictors and do the necessary analyses as
partial distance-based redundancy analyses using capscale? In one analysis
the geographic predictors could be partialled out (with the result
explaining the fraction explained by the environment). In another, the
environmental predictors could be partialled out (with the result
explaining the fraction explained by the geographic distance) and in a
third both geographic and environmental predictors could be considered
with no conditioning covariates (which will give the total variance
explained by both combined).

Best
Steve


J. Stephen Brewer 
Professor 
Department of Biology
PO Box 1848
 University of Mississippi
University, Mississippi 38677-1848
 Brewer web page - http://home.olemiss.edu/~jbrewer/
FAX - 662-915-5144
Phone - 662-915-1077




On 12/4/13 11:50 AM, "Alexandre Fadigas de Souza" <alexsouza at cb.ufrn.br>
wrote: