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This work provides a defence of the claim that likelihood based methods provide a better framework for performing phylogenetic analyses on molecular sequences than do parsimony based methods under the conditions studied. Novel work introduced in the thesis includes simulation studies that examine the performance oflikelihood based and parsimony based methods at high evolutionary distances. At these distances, many changes accumulate at a single site causing a catastrophic collapse in the performance of the parsimony analysis. In contrast a well understood mathematical theory involving the use of Fisher's information measure describes the decline in performance oflikelihood methods. Further work compares the performance oflikelihood based methods and parsimony methods under heterotachous conditions, i.e. conditions under which a single site will alter its rate of evolution relative to other sites. A recent claim that parsimony based analyses outperform likelihood is rebutted and a likelihood model is introduced and its performance analysed. Finally likelihood based methods are defined in terms of rates. A method for turning these rates into a probability distribution describing the number of changes of interest across a phylogeny is described. This is then compared to the number of changes inferred under a parsimony analysis. When the true model is known, it is shown that the counts of changes inferred under a parsimony based analysis have a low probability of being correct. It is argued that this accounts for the poor performance of parsimony.

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