The overall conclusions from this study are that irregular A,C,G,T compositions are an important and possible general cause of patterns that can mislead tree-reconstruction methods, even when high bootstrap values are obtained.
Spectral analysis using the Fast Hadamard transform allows optimal trees to be found for at least 20 taxa and perhaps for up to 30 taxa, and a corresponding spectral analysis for distance data is introduced.
A direct method for calculating expected data from an evolutionary model for two state characters is described, and it is shown that for n = 4 taxa, parsimony will always converge to the correct tree, but there are examples with n = 5 where Parsimony will converge on an incorrect tree, even for equal rates of evolution.
A simulation study of the phylogenetic methods UPGMA, neighbor joining, maximum parsimony, and maximum likelihood for a five-taxon tree under a molecular clock identified another region of the parameter space where, although consistent for a given method, some incorrect trees were each selected with up to twice the frequency of the correct tree for sequences of bounded length.
Results are in contrast to the view that molecular rates are time dependent, and the rate of evolution of the same HVR I region, determined using DNA sequences from 162 known age sub-fossil bones spanning a 37,000-year period, was 0.7%.
Improved conditional down-weighting techniques to reduce noise relative to signal for deeper divergences and find increased agreement between data sets are described and form a basis for further testing with both nuclear-coding sequences and rare genomic changes.
Most major divergences amongst lineages leading to modern orders, appear to occur well before the Cretaceous/Tertiary (K/T) boundary, particularly the possibility of competition between the small dinosaurs and the new mammal clades.
The evolutionary tree for mammals is expected to be resolved quickly, and the stability of trees from independent data sets, as detected from a triplet Markov analysis.
The extension ofrete Fourier transformations to provide invertible relationships between a phylogenetic tree T (with three probability parameters of nucleotide substitution on each edge corresponding to Kimura's 3ST model) and the expected frequencies of the nucleotide patterns in the sequences is reported.