...
Although partial Mantel tests (Smouse et al. 1986) have been
used to perform partial regression analyses for genetic
distances (e.g. Malhotra & Thorpe 2000), there has been recent
debate concerning the validity of such an approach for different
situations (e.g. Legendre 2000; Raufaste & Rousset 2001;
Castellano & Balletto 2002; Rousset 2002). The problem arises
due to the lack of independence of individual distances in a
distance matrix. Although a simple Mantel test overcomes this
issue by the use of permutations, a permutational approach does
not necessarily solve problems introduced by
several uncontrolled nuisance parameters in the case of more than one
regressor (i.e. partial tests). Thus, we do not use a Mantel
approach here, but rather use the distance-based multivariate
approach of McArdle & Anderson (2001). The important point is
that, for dbRDA, the individual distances are not treated as a
single univariate response variable, as in the Mantel test, but
rather the individual sites are the units of observation for
analysis, about which we have calculated distances using an
entire set of genetic variables. The distance matrix is
therefore treated as information regarding multivariate response
data. Taking this multivariate approach avoids the problems
associated with the partial Mantel test.
...
First, the assumption that counts of abundances
of species conform to a multivariate normal distribution
(required by MANOVA) is not generally, or even likely,
to be true.
...
Second, partitioning in traditional
MANOVA implicitly uses Euclidean distances among
sampling units. By partitioning, we mean attributing
additive proportions of the total variability to individual
factors in an experimental design. It is generally
agreed that Euclidean distance measure is not
appropriate for use with ecological data of species
abundances (...).
Finally, there are often more variables
(species) in the system than there are sampling
units (or degree of freedom), which makes the traditional
MANOVA statistics impossible to calculate.
