FREQUENCY DISTRIBUTIONS OF LENGTHS OF POSSIBLE NETWORKS FROM A DATA MATRIX

Abstract- It is common practice to attempt to find the minimum length tree (also known as the Wagner tree) for a given data matrix on a group of OTUs (taxa). However, little study has been made of the pattern of frequency distributions when the lengths of all possible networks (unrooted trees) are taken into consideration. A published real data matrix with eight OTUs was compared with randomly generated data, when the former showed a much larger variance and very marked skewness. A number of published data matrices with a larger number of OTUs were studied by random selection of 10240 out of the possible trees: these were compared with 32 randomly generated data sets with 13 OTUs, using the same program. An algorithm has been found for calculation of the expected mean, variance and skewness for random binary data with up to 13 OTUs, based on the number of characters representing each type of partition of the OTUs. The calculation requires listing of the possible topologies and their relative weighting, which are tabulated.