# Analysis of community ecology data in R

David Zelený

### Others

Author: David Zelený en:expl_var_r

Section: Ordination analysis

## Explained variation and Monte Carlo permutation test (constrained ordination)

### R functions

• `RsquareAdj` (library `vegan`) - extracts the value of R2 and adjusted R2 from results of ordination (and also regression). For linear constrained ordinations (RDA, tb-RDA), the adjusted R2 is calculated using Ezekiel's formula, while for unimodal constrained ordinations (CCA) the calculation is based on permutation model introduced by Peres-Neto et al. (2006).
• `anova.cca` (library `vegan`) - tests the significance of the variation in species composition explained by explanatory variables in constrained ordination (RDA, CCA), using Monte Carlo permutation test. It can test the significance of
• the global model (default setting), i.e. all variables included in the analysis;
• only the first constrained axis (adding argument `first = TRUE`);
• individual axes (`by = “axis”`), sequentially from the first to the last (this is done by using samples scores on the n-th axis as explanatory variables, while using scores of the axis 1, 2, ... n as covariables);
• individual terms (explanatory variables) added sequentially in the order in which they appear in the formula or data frame (`by = “terms”`; note that this variation depends on the order of variables in which they enter the model);
• variation explained by individual explanatory variables after removing variation of all other variables in the model (`by = “margin”`; here the variation does not depend on the order of variables in the model). 