These models could now be interpreted by regressing them on environmental
variables. But we will postpone that step until we can implement it in another spatial
modelling framework.
Nowadays, the most useful application of trend-surface analysis is for
detrending. We have seen in Sect. 7.2.6 that data have to be detrended before
spatial correlograms can be tested. We will also see later that most eigenvector-based
spatial analyses are best applied to detrended data. Therefore, a handy procedure is to
test the response data for linear trends and detrend them if the trend surface is
significant. This means to regress all response variables on the X-Y coordinates
and retain the residuals. This can most easily be done using the function lm()
applied directly to the multivariate matrix of response data.
# Is there a linear trend in the mite data?
anova(rda(mite.h, mite.xy)) # Result: significant trend
# Computation of linearly detrended mite data
mite.h.det <- resid(lm(as.matrix(mite.h) ~ ., data = mite.xy))
This detrended data set is now ready for more complex spatial analyses and
modelling.
Finally, trend surfaces can also be used to model the broad among-group structure
of groups of sites that are far from one another on the map. In this case, all sites
belonging to a group receive the same X-Y coordinates (normally those of the
centroid of the group). The within-group structures can then be modelled by one
of the techniques presented below.
7.4 Eigenvector-Based Spatial Variables and Spatial
Modelling
7.4.1 Introduction
Trend-surface analysis is a rather coarse method of spatial modelling. The multiscale
nature of ecological processes and data calls for other approaches that can identify
and model structures at all scales that can be perceived by a sampling design.
Practically, this means methods that could model structures at scales ranging from
the broadest, encompassing the whole sampled area, down to the finest, whose sizes
are of the order of magnitude of the sampling interval. To achieve this in the context
of canonical ordination, we must construct spatial variables representing structures
of all relevant scales. This is what the PCNM method (principal coordinates of
neighbour matrices; Borcard and Legendre 2002; Borcard et al. 2004) and its
offspring the MEM do. These methods will now be studied in detail.
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7 Spatial Analysis of Ecological Data
variables. But we will postpone that step until we can implement it in another spatial
modelling framework.
Nowadays, the most useful application of trend-surface analysis is for
detrending. We have seen in Sect. 7.2.6 that data have to be detrended before
spatial correlograms can be tested. We will also see later that most eigenvector-based
spatial analyses are best applied to detrended data. Therefore, a handy procedure is to
test the response data for linear trends and detrend them if the trend surface is
significant. This means to regress all response variables on the X-Y coordinates
and retain the residuals. This can most easily be done using the function lm()
applied directly to the multivariate matrix of response data.
# Is there a linear trend in the mite data?
anova(rda(mite.h, mite.xy)) # Result: significant trend
# Computation of linearly detrended mite data
mite.h.det <- resid(lm(as.matrix(mite.h) ~ ., data = mite.xy))
This detrended data set is now ready for more complex spatial analyses and
modelling.
Finally, trend surfaces can also be used to model the broad among-group structure
of groups of sites that are far from one another on the map. In this case, all sites
belonging to a group receive the same X-Y coordinates (normally those of the
centroid of the group). The within-group structures can then be modelled by one
of the techniques presented below.
7.4 Eigenvector-Based Spatial Variables and Spatial
Modelling
7.4.1 Introduction
Trend-surface analysis is a rather coarse method of spatial modelling. The multiscale
nature of ecological processes and data calls for other approaches that can identify
and model structures at all scales that can be perceived by a sampling design.
Practically, this means methods that could model structures at scales ranging from
the broadest, encompassing the whole sampled area, down to the finest, whose sizes
are of the order of magnitude of the sampling interval. To achieve this in the context
of canonical ordination, we must construct spatial variables representing structures
of all relevant scales. This is what the PCNM method (principal coordinates of
neighbour matrices; Borcard and Legendre 2002; Borcard et al. 2004) and its
offspring the MEM do. These methods will now be studied in detail.
314
7 Spatial Analysis of Ecological Data