Dear BioStars Community.

I have done a Procrustes analysis using vegan in R where I compare 3 datasets and I am wondering if my interpretation of the results, and subsequently the conclusions I am drawing, are correct. I have 3 datasets:

- "Performance" (table of continuous variables)
- "Physiology" (table of continuous variables)
- "Phylogeny" (a 6x6 distance matrix)

My aim is to test how well the multivariate datasets are correlated, and in turn perhaps be able to say whether one dataset is able to predict the other. I do PCoA to get their ordination solutions and test the following:

- Physiology VS Performance
- Phylogeny VS Performance

And I get the following output: Note: ("_pc" suffix denotes "principal components", of which I use the first 2 for each dataset)

```
Call:
protest(X = physiology_pc, Y = performance_pc, permutations = how(nperm = 999))
Procrustes Sum of Squares (m12 squared): 0.7936
Correlation in a symmetric Procrustes rotation: 0.4544
Significance: 0.75417
Permutation: free
Number of permutations: 719
Call:
protest(X = phylogeny_pc, Y = performance_pc, scores = "sites", permutations = how(nperm = 999))
Procrustes Sum of Squares (m12 squared): 0.2184
Correlation in a symmetric Procrustes rotation: 0.8841
Significance: 0.020833
Permutation: free
Number of permutations: 719
```

So here we see a positive correlation between my two comparisons, with a better fit for phylogeny vs performance because of the lower m12 value, but most importantly it is also the only significant fit (p-value = 0.02).

I have 2 questions:

First question, from these results, is it correct to conclude: Procrustes analysis indicates there is a significant positive correlation between phylogeny and performance, suggesting that bacteria more similar in phylogeny (i.e. smaller phylogenetic distance) will have more similar performance attributes and vice versa.

Second question, Below are the plots showing individual residuals for each bacteria. I am guessing the m12 value is the overall fit, but there are still some bacteria with high remaining residuals, does it mean that these bacteria do not follow the correlation trend as well as the ones with lower residual?

Any insight into this discussion would be appreciated, I not only found tid-bits of information on Procrustes here and there on the internet.