# Dissimilarity Cheat Sheet

#### 2017-07-12

Things to do with dissimilarity matrices

(ecodist functions are marked in bold)

(untested ideas marked with ?)

Description Notation Name R function
Relationship between two matrices D1 ~ D2 Mantel test mantel(D1 ~ D2)
Relationship between two matrices given more D1 ~ D2 | D3 … Dn Partial Mantel test mantel(D1 ~ D2 + D3 + …)
Spatial structure in one matrix D1 x S Mantel correlogram mgram(D1, S)
Spatial structure in one matrix given more D1 | D2 … Dn x S Partial Mantel correlogram ?mgram(residuals(lm(D1 ~ D2 + …)), space)
Spatial structuce in one matrix D1 x S Multivariate correlogram pmgram(D1, S)
Spatial structure in one matrix given more D1 | D2 … Dn x S Partial multivariate correlogram pmgram(D1, S, D2)
Spatial structure in the relationship between two matrices D1 ~ D2 x S Mantel cross-correlogram pmgram(cbind(lower(D1), lower(D2)), S)
Spatial structure in the relationship between two matrices given more D1 ~ D2 | D3 … Dn x S Partial Mantel cross-correlogram pmgram(cbind(lower(D1), lower(D2)), S, D3)
Ordination of one matrix (N)MDS nmds(y) or pco(y)
Ordination of one matrix given more (Partial (N)MDS ?nmds(residuals(lm(y ~ z1 + …)))
Grouping of items based on one matrix Cluster analysis hclust(y)
Grouping of items based on one matrix given more Partial cluster analysis ?hclust(residuals(lm(y ~ z1 + …)))
Grouping of items given space Spatially-constrained cluster analysis NA
Multiple regression D1 ~ D2 | D3 … Dn Multiple regression on distance matrices MRM(D1 ~ D2 + D3 + …)

Ways to calculate dissimilarity matrices

Description Result R function
From a site by sample matrix Symmetric matrix with zero diagonals dist(x) or bcdist(x) or distance(x)

Things to do with cross-dissimilarity matrices

Description Notation Name R function
Relationship between two cross-dissimilarity matrices D12 ~ D34 Cross-Mantel test xmantel(D12 ~ D34)
Relationship between two cross-dissimilarity matrices given more D12 ~ D34 | D56 … Dn Partial cross-Mantel test xmantel(D12 ~ D34 + D56 + …)
Spatial structure in one cross-dissimilarity matrix D12 x S Cross-Mantel correlogram xmgram(D12, spaceX)
Spatial structure in one cross-dissimilarity matrix given more D12 | D34 … Dn x S Partial cross-Mantel correlogram ?xmgram(residuals(lm(D12 ~ D34 + …)), spaceX)

Ways to calculate cross-dissimilarity matrices

Source Result R function
From 2 site by sample matrixes for the same sites and samples (e.g. different years) nonsymmetric matrix with nonzero diagonals xdistance(x, y)