Centrifugal-order distributions in binary topological trees

Statistical properties of topological binary trees are studied on the basis of the distribution of segments in relation to centrifugal order. Special attention is paid to the mean of this distribution in a tree as it will be used as a measure of tree topology. It will be shown how the expectation of the mean centrifugal order depends both on the size of the tree and on the mode of growth in the context of modelling the growth of tree structures. Observed trees can be characterized by their mean orders and procedures are described to find the growth mode that optimally corresponds to these data. The variance structure of the mean-order measure appears to be a crucial factor in these fitting procedures. Examples indicate that mean-order analysis is an accurate alternative to partition analysis that is based on the partitioning of segments over sub-tree pairs at branching points. © 1989 Society for Mathematical Biology.