7.5.3 Application to the Detrended Mite
and Environmental Data
Let us apply an MSO analysis to the detrended mite and environmental data, as an
effort to meet the conditions of application of the calculation of the variogram
confidence intervals. Preliminary computations (not shown) revealed that the goal
of completely eliminating spatial autocorrelation in the residuals could be reached by
modelling the trend by means of the Y coordinate only. We shall therefore detrend
the mite and environmental data on the Y coordinate before running the RDA.
# Detrend mite data on Y coordinate
mite.h.det2 <- resid(lm(as.matrix(mite.h) ~ mite.xy[ ,2]))
# Detrend environmental data on Y coordinate
env2.det <- resid(lm(as.matrix(mite.env2) ~ mite.xy[ ,2]))
# RDA and MSO
mitedet.envdet.rda <- rda(mite.h.det2 ~., env2.det)
(miteenvdet.rda.mso
grain = dmin,
perm = 999))
msoplot(miteenvdet.rda.mso, alpha = 0.05/7, ylim = c(0, 0.006))
The result (Fig. 7.15) tells us the same story as our first MSO analysis, less the
broad-scale gradient that has been removed prior to the analysis by detrending. The
residual variance shows no spatial correlation, and the second, fourth and fifth
classes of the variogram of explained plus residual data fall outside the confidence
intervals. So the overall variogram shows no trend, but some regional spatial
variance is present. Can the MEM control successfully for this spatial variance?
## MSO of the detrended mite data vs detrended environment RDA,
## controlling for MEM
mite.det.env.MEM
as.data.frame(MEM.select))
(mite.env.MEM.mso
grain = dmin,
perm = 999))
msoplot(mite.env.MEM.mso, alpha = 0.05/7, ylim = c(0, 0.005))
The answer is “yes” (Fig. 7.16). As in the undetrended example, one can see no
spatial variance in the residuals or in the data. Compare with Fig. 7.14: the
variograms are very similar. The MEM variables have successfully controlled for
the spatial variance unexplained by the environmental data.
7.5 Another Way to Look at Spatial Structures: Multiscale Ordination (MSO)
359
and Environmental Data
Let us apply an MSO analysis to the detrended mite and environmental data, as an
effort to meet the conditions of application of the calculation of the variogram
confidence intervals. Preliminary computations (not shown) revealed that the goal
of completely eliminating spatial autocorrelation in the residuals could be reached by
modelling the trend by means of the Y coordinate only. We shall therefore detrend
the mite and environmental data on the Y coordinate before running the RDA.
# Detrend mite data on Y coordinate
mite.h.det2 <- resid(lm(as.matrix(mite.h) ~ mite.xy[ ,2]))
# Detrend environmental data on Y coordinate
env2.det <- resid(lm(as.matrix(mite.env2) ~ mite.xy[ ,2]))
# RDA and MSO
mitedet.envdet.rda <- rda(mite.h.det2 ~., env2.det)
(miteenvdet.rda.mso
grain = dmin,
perm = 999))
msoplot(miteenvdet.rda.mso, alpha = 0.05/7, ylim = c(0, 0.006))
The result (Fig. 7.15) tells us the same story as our first MSO analysis, less the
broad-scale gradient that has been removed prior to the analysis by detrending. The
residual variance shows no spatial correlation, and the second, fourth and fifth
classes of the variogram of explained plus residual data fall outside the confidence
intervals. So the overall variogram shows no trend, but some regional spatial
variance is present. Can the MEM control successfully for this spatial variance?
## MSO of the detrended mite data vs detrended environment RDA,
## controlling for MEM
mite.det.env.MEM
as.data.frame(MEM.select))
(mite.env.MEM.mso
grain = dmin,
perm = 999))
msoplot(mite.env.MEM.mso, alpha = 0.05/7, ylim = c(0, 0.005))
The answer is “yes” (Fig. 7.16). As in the undetrended example, one can see no
spatial variance in the residuals or in the data. Compare with Fig. 7.14: the
variograms are very similar. The MEM variables have successfully controlled for
the spatial variance unexplained by the environmental data.
7.5 Another Way to Look at Spatial Structures: Multiscale Ordination (MSO)
359