Solved – Doubt with a distance based Redundancy analysis

Question

I conducted a distance based redundancy analysis (dbRDA) to explore the relevance of some environmental variables in explaining the patterns of the distribution (i.e., spatial and temporal) of two organisms. I used a Bray-Curtis resemblance matrix based on the abundance of both organisms and the environmental variables were used as predictors. Results showed that along Axis 1 (along this axis seasons were separated) the "% of fitted" was 81.3% and the "% of total variation" was 38.5%. I do not understand the difference between "% of fitted" versus "% of total variation" in this analysis.

Answer 1

In a constrained ordination such as dbRDA, axes are extracted that are linear combinations of predictor variables that best explain "variance" in the multivariate response matrix. We can explain the "variance" explained by these linear combinations of the predictors in two ways:

1. The first way, which you label as "% of fitted", is simply what proportion of the total "variance" explained by the set of linear combinations (constrained axes) is accounted for by each separate linear combination (or axis). This tells you, of the "variance" explained, which axes account for most of this total.
2. The information in 1. above is restricted to an assessment of the explained variance. But this is not the total "variance" in the multivariate response matrix. How much of the "variance" explained by each constrained axis as a proportion of the total "variance" in the response matrix is what is given by "% of total variation"

You don't say where this information came from, but it may well be that the information is provided in terms of the predictors themselves and not the axes, but the distinction above holds; how much of the explain "variance" is contributed by each axis (variable), and how much of the total "variance" is explained by each axis (variable.