I am unclear on how the R2 output from adonis2 is interpreted. Is it that a particular factor "explains" the differences in community composition? And thus, would R2 be interpreted as typically is in univariate analyses?
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The $R^2$ values reported are indeed coefficients of determination, but they are all partial-$R^2$s (of at least the second-type). That is to say, the partial $R^2$ values reported most likely will not sum to 100%. However, each factor can be viewed as explaining (at least) $R^2\times 100\%$ of the variability in the dependent variables.
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$\begingroup$ The type of R-squared depends on the type of requested test (argument
byinadonis2). In marginal tests they indeed are partial, an do not sum up to 100%. However, the default is to use sequential tests that do sum up to 100%, but the R-squared of individual terms will be order-dependent. $\endgroup$ Commented Jul 6, 2023 at 17:45