envfit

Envfit is a function in the vegan package for the R programming language used to relate environmental variables to an ordination, such as NMDS, PCA, or RDA. It helps interpret patterns in community composition by identifying which measured environmental factors align with the observed gradient and how strongly they do so. The function can fit both continuous variables and categorical factors, providing a visual and statistical link between the environment and the ordination results.

For continuous environmental variables, envfit fits vectors (arrows) in the ordination space. The length and direction of each arrow reflect the strength and orientation of the relationship between the variable and the ordination axes, with longer arrows indicating stronger associations. The squared correlation (r2) quantifies the strength, and a permutation test yields a p-value to assess statistical significance. For categorical variables, envfit fits the centroids of groups in the ordination space and tests whether group differences along the ordination are greater than expected by chance; results can be displayed as points or as fitted vectors, depending on the option chosen.

The output is an envfit object containing results for both vectors and factors, including r2 values and p-values for each variable or factor level, along with coordinates for plotting. The object can be printed or plotted on top of an existing ordination, enabling straightforward interpretation of which environmental factors are most strongly associated with the observed patterns.

Usage typically involves providing an ordination object and a data frame or matrix of environmental variables, with an optional perm argument to control permutation testing. Envfit is widely used in ecology for exploratory analysis to link species data to environmental gradients.