# Plot of MEM eigenvalues vs Moran's I
plot(attributes(mite.invdist.MEM)$values,
mite.MEM.Moran$obs,
ylab = "Moran's I",
xlab = "Eigenvalues"
)
text(0, 0.55,
paste("Correlation = ",
cor(mite.MEM.Moran$obs,
attributes(mite.invdist.MEM)$values
)
)
)
As in the case of the automatic model selection presented before, these MEM
variables can now be used as explanatory variables in RDA or multiple regression, in
the same way as dbMEM variables were.
These are only a few examples. We suggest users to explore the manual of the
package adespatial, which presents in great detail the use of many other options
to construct, present, and use various types of connectivity matrices.
7.4.3.4 Controlling for Spatial Correlation Using MEM
Peres-Neto and Legendre (2010) explored the potential use of polynomials and MEM
eigenfunctions to control for spatial correlation in statistical tests. Their main conclusion is that MEM, but not polynomials, can adequately achieve this goal. They
propose the following procedure: (1) Test for the presence of a spatial structure using
all positive MEM variables. (2) If the global test is significant, proceed to forwardselect MEM variables, but (a novelty) do this individually for each species, and retain
the union of the MEM selected, i.e., retain all MEM that have been selected at east
once. (3) Proceed to test the species-environment relationships, controlling for spatial
correlation by placing the retained MEM variables in a matrix of covariables. The
authors demonstrate that this procedure yields correct type I error for tests of
significance in linear models, in the presence of spatial correlation.
7.4.3.5 MEM on Sampling Designs with Nested Spatial Scales
The hierarchical structure of many natural entities (e.g. metapopulations or
metacommunities; landscapes at various scales) sometimes calls for nested sampling
designs. An example is found in Declerck et al. (2011), where the authors studied
cladoceran metacommunities in wetland pools found in several valleys of the High
Andes. The authors analysed the metacommunity spatial structure among- and
within-valleys by means of a two-level spatial model. The among-valley component
was modelled by a set of dummy variables. For the within-valley component, where
several pools had been sampled in each valley, a set of MEM variables was
computed for each valley. All dummy and MEM variables were assembled into a
7.4 Eigenvector-Based Spatial Variables and Spatial Modelling
347
plot(attributes(mite.invdist.MEM)$values,
mite.MEM.Moran$obs,
ylab = "Moran's I",
xlab = "Eigenvalues"
)
text(0, 0.55,
paste("Correlation = ",
cor(mite.MEM.Moran$obs,
attributes(mite.invdist.MEM)$values
)
)
)
As in the case of the automatic model selection presented before, these MEM
variables can now be used as explanatory variables in RDA or multiple regression, in
the same way as dbMEM variables were.
These are only a few examples. We suggest users to explore the manual of the
package adespatial, which presents in great detail the use of many other options
to construct, present, and use various types of connectivity matrices.
7.4.3.4 Controlling for Spatial Correlation Using MEM
Peres-Neto and Legendre (2010) explored the potential use of polynomials and MEM
eigenfunctions to control for spatial correlation in statistical tests. Their main conclusion is that MEM, but not polynomials, can adequately achieve this goal. They
propose the following procedure: (1) Test for the presence of a spatial structure using
all positive MEM variables. (2) If the global test is significant, proceed to forwardselect MEM variables, but (a novelty) do this individually for each species, and retain
the union of the MEM selected, i.e., retain all MEM that have been selected at east
once. (3) Proceed to test the species-environment relationships, controlling for spatial
correlation by placing the retained MEM variables in a matrix of covariables. The
authors demonstrate that this procedure yields correct type I error for tests of
significance in linear models, in the presence of spatial correlation.
7.4.3.5 MEM on Sampling Designs with Nested Spatial Scales
The hierarchical structure of many natural entities (e.g. metapopulations or
metacommunities; landscapes at various scales) sometimes calls for nested sampling
designs. An example is found in Declerck et al. (2011), where the authors studied
cladoceran metacommunities in wetland pools found in several valleys of the High
Andes. The authors analysed the metacommunity spatial structure among- and
within-valleys by means of a two-level spatial model. The among-valley component
was modelled by a set of dummy variables. For the within-valley component, where
several pools had been sampled in each valley, a set of MEM variables was
computed for each valley. All dummy and MEM variables were assembled into a
7.4 Eigenvector-Based Spatial Variables and Spatial Modelling
347