Introduction
Theory, Examples & Exercises

 Constrained ordination



Note: variation partitioning is sometimes also called commonality analysis in reference to the common (shared) fraction of variation (Kerlinger & Pedhazur 1973). It is also a synonym to variance partitioning^{1)}.
In case we have two or more explanatory variables, one may be interested in variation in species composition explained by each of them. If some of these explanatory variables are correlated, one must expect that variation explained by the first or the other variable cannot be separated  it will be shared.
The way how to approach this problem is variation partitioning, when variation explained by each variable (or set of variables) independently is partitioned into variation attributable purely to given environmental variable, and shared variation attributable to two or more variables.
Variation can be partitioned by individual variables (e.g. variation explained by soil pH vs variation explained by soil Ca) or by groups of variables (e.g. soil variables vs climatic variables).
Results can be visualized using Venn's diagram (see figure on the right). Meaning of the fractions in Venn's diagram is the following^{2)}:
If the variation is partitioned among groups with the same number of variables (e.g. two soil and two climatic variables), then variation explained by each group is comparable without adjustment. However, if groups contain different numbers of variables, variation explained by not adjusted R^{2} is not comparable since R2 tends to increase with the number of explanatory variables. Here, use of adjusted R2 is recommended.
The library vegan
offers function varpart
, which can partition variation among up to four variables (or groups of variables). Note that varpart
is based on redundancy analysis (rda
) and uses adjusted R^{2} to express explained variation. The reason for using only rda
is that in R, there is still no function available to calculate adjusted R^{2} for unimodal ordination methods (like cca
).