Depth scaling of protein phylogenies. Mean depth scaling for all protein families in the PANDIT database (solid circles, where each point represents a subtree) and the corresponding averaged binned depth (empty circles). Where the error bars are not visible we have that the standard error for the mean depth is smaller than the symbol size. The discontinuous and continuous lines correspond to the two extreme binary trees: fully imbalanced and fully balanced trees, respectively. The scales of the axes are chosen so that a behavior of the type d ~ (ln A)2 appears as a straight line. Note that the values below the fully balanced tree scaling correspond to polytomic subtrees.