[R-sig-eco] Community composition variance partitioning?

[Hanna Tuomisto]

Alexandre,

Both RDA and MRM are useful methods but they address different questions.
The R2 value from RDA quantifies the proportion of the variance in species
abundances that can be explained with environmental or spatial gradients. In
other words, the response variables in the analysis are the species
abundance values in the raw data matrix (the sites by species table). This
targets the ecological question "why are species more abundant in some sites
than in others?".

In contrast, the R2 value from MRM quantifies the proportion of variance in
pairwise dissimilarity values that can be explained with environmental or
spatial distances. In other words, the response variable is the
compositional dissimilarity matrix. This targets the ecological question
"why are species compositions more similar between some sites than between
others?".

Both questions are related, of course, but they are not interchangeable. My
personal opinion is that it's fine to run both kinds of analysis in
parallel, but the results of each method should be interpreted according to
it own null hypothesis, not according to the null hypothesis of the other
method.

Cheers,
Hanna


Alexandre Fadigas de Souza wrote
> Hi Steve,
> 
>   Thank you for your response to my message and for the suggestion.
>  
>   We are also performin RDA-based variance partitioning. Reading the
> literature on community composition variance partition, my impression was
> that there is a turmoil and the field is divided into two main fields in
> disagreement: rda- and partial mantel-based approaches using or not pcnm
> as spatial descriptors (as opposed to polinomials of lat long). Simulation
> comparisons concluded that all approaches are subotimal and have strenghts
> and weakenesses. This without mentioning the danish initiative to use
> mixed models as a comparative means to these two approaches.
> 
>    We decided to all three: rda, mantel, and mixed model approaches, so as
> to be able to compare results and see if congruent patterns emerge.
> 
>    To be more specific, in the mixed model approach ordination axes (e.g.,
> pca on hellinger-transformed species data) are used as dependent variables
> and explanatory environmental factors are used as independent variables.
> Levels of spatial cluster are included as nesting effects. Sequential
> model adjustment shows if space is relevent and if the environment is
> relevant, in which case which environmental variables are relevant are
> also evaluated.
> 
>   Regarding the R2 problem in the multiple regression on distance
> matrices, it seems that indeed the problem was that we were including
> variables as extra columns and not as separate matrices in the formula.
> With change we obtained r2 in the expected order of increase.
> 
>    What do you think of this all-inclusive approach?
> 
>    All the best,
> 
>    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
> 
> _______
> 
> 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
> 
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