4.9 Comparison with Environmental Data
All methods above have been presented with examples on species abundance data.
They can actually be applied to any other type of data as well, particularly environmental data tables. Of course, care must be taken with respect to the choice of the
proper coding and transformation for each variable (Chap. 2) and of the association
measure (Chap. 3).
4.9.1 Comparing a Typology with External Data (ANOVA
Approach)
We have seen that internal criteria, such as silhouette or other clustering quality
indices, which rely on the species data only, were not always sufficient to select the
“best” partition of the sites. The final choice of a typology should be based on the
ecological interpretability of the groups. It could be seen as an external validation of
the site typology.
Confronting clustering results (considered as response data) with external, independent explanatory data could be done by discriminant analysis (Sect. 6.5). From
another point of view, the clusters obtained from the community composition data
can be considered as a factor, or classification criterion, in the ANOVA sense. Here
is a simplified example, showing how to perform quick assessments of the ANOVA
assumptions (normality of residuals and homogeneity of variances) on several
environmental variables separately, followed either by a parametric ANOVA or by
a non-parametric Kruskal-Wallis test. Boxplots of the environmental variables (after
some simple transformations to improve normality) for the four optimized Ward
groups are also provided (Fig. 4.24). Note that, despite the fact that the clustering
result based on the community composition data acts as an explanatory variable
(factor) in the ANOVA, ecologically speaking we really look for an environmental
interpretation of the groups of sites.
# Test of ANOVA assumptions
with(env, {
# Normality of residuals
shapiro.test(resid(aov(sqrt(ele) ~ as.factor(spech.ward.gk))))
shapiro.test(resid(aov(log(slo) ~ as.factor(spech.ward.gk))))
shapiro.test(resid(aov(oxy ~ as.factor(spech.ward.gk))))
shapiro.test(resid(aov(sqrt(amm) ~ as.factor(spech.ward.gk))))
4.9 Comparison with Environmental Data
107
All methods above have been presented with examples on species abundance data.
They can actually be applied to any other type of data as well, particularly environmental data tables. Of course, care must be taken with respect to the choice of the
proper coding and transformation for each variable (Chap. 2) and of the association
measure (Chap. 3).
4.9.1 Comparing a Typology with External Data (ANOVA
Approach)
We have seen that internal criteria, such as silhouette or other clustering quality
indices, which rely on the species data only, were not always sufficient to select the
“best” partition of the sites. The final choice of a typology should be based on the
ecological interpretability of the groups. It could be seen as an external validation of
the site typology.
Confronting clustering results (considered as response data) with external, independent explanatory data could be done by discriminant analysis (Sect. 6.5). From
another point of view, the clusters obtained from the community composition data
can be considered as a factor, or classification criterion, in the ANOVA sense. Here
is a simplified example, showing how to perform quick assessments of the ANOVA
assumptions (normality of residuals and homogeneity of variances) on several
environmental variables separately, followed either by a parametric ANOVA or by
a non-parametric Kruskal-Wallis test. Boxplots of the environmental variables (after
some simple transformations to improve normality) for the four optimized Ward
groups are also provided (Fig. 4.24). Note that, despite the fact that the clustering
result based on the community composition data acts as an explanatory variable
(factor) in the ANOVA, ecologically speaking we really look for an environmental
interpretation of the groups of sites.
# Test of ANOVA assumptions
with(env, {
# Normality of residuals
shapiro.test(resid(aov(sqrt(ele) ~ as.factor(spech.ward.gk))))
shapiro.test(resid(aov(log(slo) ~ as.factor(spech.ward.gk))))
shapiro.test(resid(aov(oxy ~ as.factor(spech.ward.gk))))
shapiro.test(resid(aov(sqrt(amm) ~ as.factor(spech.ward.gk))))
4.9 Comparison with Environmental Data
107