Dear Ahmad,

The cophenetic correlation test is usually performed between the original genetic distance data set and the one, regenerated from the tree itself (a cophenetic matrix). The two matrixes are then examined using the Mantel test. The cophenetic genetic distance matrix is based on the tree's representation of the original distance data. Thus, the correlation between the cophenetic matrix with the original genetic distance matrix is a measure of how well the tree represents the data of the original genetic distance matrix. If the correlation is high, then the tree is suggested to represent the original data well. If the correlation is low, then the tree does not represent the original data set well and in such case, one would suspect that either a different tree is needed or that no tree is going to represent the data well. Rohlf (1988) suggested a series of judgments (very good fit for r more than 0.9; good fit for 0.8 < r < 0.9; poor fit for 0.7 < r < 0.8 and very poor fit for r < 0.7) as a guide for interpreting cophenetic coefficient values.

I hope this could help.

Nice explanation of cophenetic correlation by Temim. I would like to add that the Mantel test is a quite common statistical test (statistical significance is provided) to test correlation between any two types of matrices (still in the same rank). In studies which include molecular markers, it is usually employed to test correlation between two types of markers (genetic distances or similarities are the input), between the distances obtained from measured or discription (morphological or any other) characters and molecular markers, or between geographic and genetic distances.

Thanks a lot to Temim Deli and Branislav Šiler  for their explanation.

it was usefull.

good luck.