Environmental Engineering Reference
In-Depth Information
(correspondence analysis), DCA (detrended correspondence analysis), and CCA
(canonical correspondence analysis). McCune and Grace (
2002
) and Kenkel (
2006
)
thoroughly review the options and mathematical background behind each technique.
In general, PCA should be used when there are few primary gradients that relate
broadly-linearly to the scope of plant communities studied. CA is best used on
categorical contingency table data (optimizing both sites and species variation simul-
taneously). DCA should be avoided. McCune and Grace (
2002
) argue that NMS is
currently the method of choice because it makes no assumption of linear relations, and
performs very well with high diversity data sets. However, Kenkel (
2006
)suggests
using NMS as a last resort only after PCA and CA options have been exhausted. CCA
is ordination constrained by environmental variables, and should be used when there
are one to few strong environmental gradients of interest. All of these techniques are
available in the R package vegan (Oksanen et al.
2011
) and in vegetation-specific
software, like PC-ORD (McCune andMefford
2011
). Roberts (
2011
) provides helpful
online tutorials for using R to analyze vegetation data.
Ordination is extremely helpful for initial pattern detection and description of
novel systems. Ordination using different transformations of the same species
dataset (e.g., one using abundance, one using frequency, and one using presence
or absence) can be helpful in differentiating between levels of organization in plant
communities (Allen and Wyleto
1983
). It is critically important to prepare the
species dataset for ordination by removing outliers and performing data
transformations to meet the assumptions of the technique (McCune and Grace
2002
; Kenkel
2006
). One criticism of ordination is that it cannot test hypotheses
using the philosophy of inferential statistics, although the structure of ordinations
themselves can be tested through bootstrapping (testing real data configurations
against multiple randomized variations). However, structural equation modeling
(SEM) provides a new way of statistically testing relations discovered through
ordination (McCune and Grace
2002
).
5.4.6 Classification and Regression Trees (CART)
Another method of analysis that addresses the question of how environmental
variables affect plant populations or communities is CART (McCune and Grace
2002
). Classification trees model which independent variables best differentiate
pre-defined groups from each other (e.g., plant community groups from classifica-
tion or occupied versus unoccupied sites). Classification trees have also been used
to assess wetland condition (Cohen et al.
2005
). Regression trees have continuous
response variables. One advantage of CART is that it is a non-parametric method,
meaning that it does not require the same assumptions of data normality that other
methods require. The output is a predictive model that resembles a dichotomously-
forking tree which separates pre-defined groups based on a threshold value of the
best-differentiating environmental variable at each level. Like in hierarchical clas-
sification, the initial fork separates two relatively heterogeneous groups from each
