I have a set of trees and am using Blomberg's K to detect phylogenetic signal. I am finding that for several of them, my values for K are close to 0 (in the region of K = 0.001 - 0.004) which would suggest no phylogenetic signal. However, the P values are high significant (p = 0.001), which suggests these results are different from a random distribution of traits.
Does this suggest that there is significant signal, but it is extremely weak?