Hadamard conjugation: A versatile tool for modelling nucleotide sequence evolution

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Abstract
Hadamard conjugation has proved to be a useful tool in examining some of the properties of the patterns of nucleotide sequences arising from the evolution of the taxa they represent. It has a considerable advantage in that the formulae are independent of the phylogenetic structure under consideration, and can be given for any number of taxa. Hadamard conjugation is outlined and four applications are introduced. The applications are the theoretical examination of tree building methods, the generation of sample sequences under various models for simulation studies, the identification of some phylogenetic invariants, and the closest tree method for inferring phylogenetic trees and their edge lengths.