Clustering microarray data is a helpful way of identifying genes which are biologically related. Unfortunately, when attempting to cluster microarray data, certain issues must be considered including: the uncertainty in the number of true clusters; the expression of a given gene is often a ected by the expression of other genes; and microarray data is usually high dimensional. This thesis outlines a Bayesian in nite Gaussian mixture model which addresses the issues outlined above by: not requiring the researcher to specify the number of clusters expected, applying a non-diagonal covariance structure, and using mixtures of factor analyzers and extensions thereof to structure the covariance matrix such that it is based on a few latent variables. This approach will be illustrated on real and simulated data.

Patients with a history of lateral ankle sprain (LAS) may experience different levels of mechanical and/or sensorimotor deficits following their injuries. Although various factors, such as structural damage, sensorimotor adaptation, perceived instability, swelling and/or pain, can develop and perpetuate the condition of chronic ankle instability (CAI), most previous CAI research on biomechanics has considered all patients with CAI as a homogeneous group. Recent research has clustered patients with CAI into six distinct movement patterns during a maximal jump-landing/cutting task. This approach could motivate clinicians to develop appropriate rehabilitation programs for each patient with CAI depending on their movement patterns. However, evaluating patients with CAI for the quality of movement and sensorimotor deficits using a 3D motion capture system and a force plate is not easily accessible in clinical settings. PURPOSE: (i) to identify subgroups within the CAI population based on their movement patterns using inertial measurement unit (IMU) devices and (ii) to characterize each subgroup's functional movement patterns during maximal jump-landing/cutting relative to the uninjured controls. METHODS: A total of 100 patients with CAI (height = 1.76 ± 0.1 m, mass = 74.0 ± 14.9 kg) were assessed according to the Foot and Ankle Ability Measure (FAAM) (ADL: 84.3 ± 7.6%, Sport: 63.6 ± 8.6%) and the Ankle Instability Instrument (AII) (6.7 ± 1.2) and were fit into clusters based on their movement strategy during the maximal jump-landing/cutting task. A total of 21 uninjured controls (height = 1.74 ± 0.1 m, mass = 70.7 ± 13.4 kg) were compared with each cluster. Seven IMU sensors were placed on the base of the lumbar spine, lower and upper legs, and feet and participants performed 5 trials of the maximal jump-landing/cutting test. Joint kinematics in the lower extremity were collected during the task using IMU sensors. Data were reduced to functional curves; kinematic data from the sagittal and frontal planes were reduced to a single representative curve for each plane. Then, representative curves were clustered using a Bayesian clustering technique. Functional analyses of variance were used to identify between-group differences for outcome measures and describe specific movement characteristics of each subgroup. Pairwise comparison functions as well as 95% confidence interval (CI) bands were plotted to determine specific differences. If 95% CI bands did not cross the zero line, we considered the difference significant. RESULTS: Four distinct clusters were identified from the sagittal- and frontal-plane kinematic data. Specific movement patterns in each cluster compared to either uninjured controls or rest of patients with CAI were also identified. CONCLUSION: The IMUs were able to distinguish 4 clusters within the CAI population based on distinct movement patterns during a maximal jump-landing/cutting task. Thus, IMUs can be effective measuring devices to distinguish and characterize multiple distinct movement patterns without relying on a traditional 3D motion capture system. Clinicians should consider utilizing IMU devices to measure and evaluate specific movement patterns in the CAI population during multiplanar demanding tests before developing appropriate treatment interventions in clinical settings.

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden Markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretical approach to define an optimality criterion for clusterings and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We consider several loss functions to compare partitions and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on both artificial and real datasets for three different clustering models: Gaussian mixtures, stochastic block models and latent block models for networks.

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In this thesis relationships and the occurrence of reticulate evolutionary events in the club moss genus Diphasiastrum are investigated. Diphasiastrum is initially established as a monophyletic group within Lycopodiaceae using non recombinant chloroplast sequence data. Support is obtained for eight distinct parental lineages in Diphasiastrum, and relationships among the putative parent taxa in the hypothesized hybrid complexes; D. alpinum, D. complanatum, D. digitatum, D. multispicatum, D. sitchense, D. tristachyum and D. veitchii are presented. Feulgen DNA image densitometry data and sequence data obtained from three nuclear regions, RPB2, LEAFY and LAMB4, were used to infer the origins of three different taxa confirmed to be allopolyploid; D. zanclophyllum from South Africa, D. wightianum from Malaysia and an undescribed taxon from China. The two Asian polyploids have originated from two different hybrid combinations, D. multispicatum x D. veitchii and D. tristachyum x D. veitchii. Diphasiastrum zanclophyllum originates from a cross between D. digitatum and an unidentified diploid taxon. The occurrence of three homoploid hybrid combinations commonly recognized in Europe, D. alpinum x D. complanatum, D. alpinum x D. tristachyum and D. complanatum x D. tristachyum, are verified using the same three nuclear regions. Two of the three hybrid combinations are also shown to have originated from reciprocal crosses. Admixture analyses performed on an extended, dataset similarly identified predominately F1 hybrids and backcrosses. The observations and common recognition of hybrid species in the included populations are hence most likely due to frequent observations of neohybrids in hybrid zones. Reticulate patterns are, however, prominent in the presented dataset. Hence future studies addressing evolutionary and ecological questions in Diphasiastrum should emphasize the impact of gene flow between parent lineages rather than speciation as the result of hybridization.

The accurate assessment of forest persistence under environmental change is dependent on the fundamental understanding of the genetic consequences of human intervention and its comparison to that of natural processes, as declines in genetic diversity and changes in its structuring can compromise the adaptive ability of a population. The European beech, Fagus sylvatica, has experienced prolonged human impact over its 14 million ha range with contemporary forests harbouring high ecological, economic, and cultural value. Historical traditional management practices, such as coppicing and pollarding, have impacted a large portion of Europe’s forests. This form of management encouraged vegetative regeneration, prolonging the longevity of individual trees. In several cases, the structure and function of managed trees and their associated ecosystems were significantly altered. Specifically, coppiced beech forests in Europe displayed significantly larger extents of spatial genetic structuring compared to their natural counterparts, revealing a change in the genetic composition of the population due to decades of management. Humans have also aided in the dispersal of beech within and outside of its natural range. In Great Britain, the putative native range retained signals of past colonisation dynamics. However, these signals were obscured by the wide-spread translocation of the species throughout the country. Evidence of post-glacial colonisation dynamics can be found in Sweden as well. In contrast to Britain, the structure of this natural leading range edge displays a gradual reduction in population size where isolation was found to have acted as an effective barrier to gene flow reducing the genetic diversity of populations.