Hi all,
I have trouble understanding some recent observations. The scenario is like this; I have a cophenetic matrix C (inferred using a given non-binary tree). Then I have n distance matrices D{1..n} (defined over same set of leaf nodes as the given tree). I want to choose a distance matrix that is a good fit to the cophenetic matrix. So I ranked the D{1..n} according to their Spearman correlation with C. My intuition says the if I pick the D with highest correlation the resulting trees should be more similar than if I pick a D with lower correlation. To check for this I calculated quartet distance between the tree generated from C (reference) and trees generated using D{1..n}. To a bit of my surprise in many cases higher correlation did not mean lower quartet distance. Is this expected? Is there any explanation for this?
As note I should mention two details; 1. The trees were generated using either NJ or UPGMA and similar behavior was observed. 2. I also checked for ultrametricity of the D{1..n} using the function defined in http://www.springerlink.com/content/wn376681315788n3/ and only chose the ones with low values for this function and high Spearman correlation and observations above didnt change.
I will appreciate any insights into this.
Best regards
