**Introduction**

**Theory, Examples & Exercises**

*Unconstrained ordination**Constrained ordination*

**Data, Links & References**

**Other stuff**

Author: David Zelený

**Introduction**

**Theory, Examples & Exercises**

*Unconstrained ordination**Constrained ordination*

**Data, Links & References**

**Other stuff**

Author: David Zelený

en:varpart

Note: variation partitioning is sometimes also called ** commonality analysis** in reference to the

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)}:

- [a] - variation explained by variable 1 (conditional (or partial) effect of variable 1, i.e. variation this variable would explain if putting variable 2 as covariable);
- [c] - variation explained by variable 2;
- [b] - shared variation explained by both variables (cannot be decided to which of them should be attributed, and is a result of correlation between both variables);
- [a+b] - variation explained by variable 1 (independent simple (or marginal) effect of variable 1, i.e. variation this variable would explain if it is as the only explanatory variable in the model);
- [b+c] - variation explained by variable 2;
- [d] - unexplained variation.

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`

).

en/varpart.txt · Last modified: 2017/02/17 08:01 by David Zelený