What Null hypothesis does vegan::anova.cca(by = "terms") test against?

Question

I ran a distance-based Redundancy Analysis with the vegan R-package. Statistical significance of axes and explanatory variables can be tested with the anova.cca() function.

Form Legendre et al. 2011, I know that the test of the individual axes tests "The null hypothesis for the test of significance of the jth axis is H0: the linear dependence of the response variables Y on the explanatory variables X is less than j-dimensional". But what is the null hypothesis when testing environmental variables?

--
Legendre, P., Oksanen, J., & ter Braak, C. J. F. (2011). Testing the significance of canonical axes in redundancy analysis. Methods in Ecology and Evolution, 2(3), 269–277.

Answer 1

The null hypothesis changes as the sequence of models is tested. Say we have three terms to be tested A, B, and C and we fit the model as Y ~ C + A + B. We test the following sequence of models

1. Y ~ C
2. Y ~ C + A
3. Y ~ C + A + B

with the corresponding models being the null against which each of those models is tested against

1. Y ~ 1
2. Y ~ C
3. Y ~ C + A

If were turning this into words, then we have variations on:

1. H0 for model 1: the effect of C on Y is equal to 0
2. H0 for model 2: the effect of A on Y after accounting for the effect of C on Y, is equal to 0.
3. ...

and so on.