With the advent of automated sequencing, sequence data are now available to help us understand the functioning of our genome, as well as its history. To date,powerful methods such as maximum likelihood have been used to estimate its mode and tempo of evolution and its branching pattern. However, these methods appear to have some limitations. The purpose of this thesis is to examine these issues in light of Bayesian modelling, taking advantage of some recent advances in Bayesian computation. Firstly, Bayesian methods to estimate divergence dates when rates of evolution vary from lineage to lineages are extended and compared. The power of the technique is demonstrated by analysing twenty-two genes sampled across the metazoans to test the Cambrian explosion hypothesis. While the molecular clock gives divergence dates at least twice as old as those indicated by the fossil records, it is shown (i) that modelling rate change gives results consistent with the fossils, (ii) that this improves dramatically the fit to the data and (iii) that these results are not dependent on the choice of a specific model of rate change.Results from this analysis support a molecular explosion of the metazoans about 600 million years (MY) ago, i.e. only some 50 MY before the morphological Cambrian explosion. Secondly, two new Bayesian tests of phylogenetic trees are developed. The first aims at selecting the correct tree, while the second constructs confidence sets of trees. Two other tests are also developed, in the frequentist framework. Based on p-values adjusted for multiple comparisons,they are built to match their Bayesian counterparts. These four new tests are compared with previous tests. Their sensitivity to model misspecification and the problem of regions is discussed. Finally, some extensions to the models examined are made to estimate divergence dates from data of multiple genes, and to detect positive selection.

One of the great unsolved evolutionary questions concerns the origin and phylogeny of the major animal phyla that appeared in the fossil record more than 540 million years ago, during the Cambrian explosion. Although new molecular information has been very useful, we still have little understanding about the origin of most of the phyla of bilaterians living today. The richly diverse fossil remains from this critical early Cambrian interval are particularly well exposed in China, where exceptionally-preserved fossil lophotrochozoans including brachiopods are particularly abundant. In particular the exceptionally-preserved Cambrian lophophorates from the Chengjiang and Guanshan Lagerstätten have offered new sources of critical palaeobiological data that have been shown to be important for understanding the early ecology and evolution of lophotrochozoans. This thesis comprises a detailed study of new, abundant, exceptionally-preserved material of five lophotrochozoan species from the Chengjiang and Guanshan Lagerstätten. Kuangshanotreta malungensis from Chengjiang is the earliest known example of an attached acrotretoid brachiopod representing the oldest evidence about the palaeoecology of the diverse yet, enigmatic acrotretoid linguliform stock that comprises an important component of the Cambrian evolutionary fauna. Eoglossa chengjiangensis from Chengjiang is the earliest known representative of the Glossellinae. Diandongia pista occurs abundantly both in the Chengjiang fauna and the younger Guanshan fauna, and it’s exceptionally well-preserved and strongly mineralized shells shows that it belongs within the Botsfordiidae. In contrast, the last two species from Chengjiang examined for this thesis - Yuganotheca elegans and Cotyledion tylodes belong within the stem of the Brachiopoda and the Lophotrochozoan entoprocts.

The evolutionary origins of animal phyla are intimately linked with the Cambrian explosion, a period of radical ecological and evolutionary innovation that begins approximately 540 Mya and continues for some 20 million years, during which most major animal groups appear. Lophotrochozoa, a major group of protostome animals that includes molluscs, annelids and brachiopods, represent a significant component of the oldest known fossil records of biomineralised animals, as disclosed by the enigmatic ‘small shelly fossil’ faunas of the early Cambrian. Determining the affinities of these scleritome taxa is highly informative for examining Cambrian evolutionary patterns, since many are supposed stem-group Lophotrochozoa. The main focus of this thesis pertained to the stem-group of the Brachiopoda, a highly diverse and important clade of suspension feeding animals in the Palaeozoic era, which are still extant but with only with a fraction of past diversity. Major findings include adding support for tommotiid affinity as stem-group lophophorates. Determining morphological character homologies vital to reconstructing the brachiopod stem-group was achieved by comparing Cambrian Lagerstätten with the widespread biomineralised record of Cambrian stem-brachiopods and small shelly fossils. Polarising character changes associated with the putative transition from scleritome organisms to crown-group brachiopods was furthered by the description of an enigmatic agglutinated tubular lophophorate Yuganotheca elegans from the Chengjiang Lagerstätte, China, which possesses an unusual combination of phoronid, brachiopod and tommotiid characters. These efforts were furthered by the use of X-ray tomographic techniques that revealed novel anatomical features, including exceptionally preserved setae in the tommotiid Micrina. The evidence for a common origin of columnar brachiopod shell structures in the tommotiids is suggested and critically examined. Enigmatic and problematic early and middle Cambrian lophotrochozoans are newly described or re-described in light of new evidence, namely: the stem-brachiopod Mickwitzia occidens Walcott from the Indian Springs Lagerstätte, Nevada; a putative stem-group entoproct Cotyledion tylodes Luo and Hu from Chengjiang, China; a new enigmatic family of rhynchonelliform brachiopods exemplified by the newly described Tomteluva perturbata from the Stephen Formation, Canada; and the tommotiid Micrina etheridgei (Tate) from the Flinders Ranges, South Australia. Cladistic analyses of fossil morphological data supports a monophyletic Brachiopoda.