Community composition variance partitioning?

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