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Sporophytic self-incompatibility is a genetically controlled inbreeding prevention mechanism, which is prevalent in the Brassicaceae, and has been reported in a variety of high profile species. Despite the benefits of preventing self-fertilization in terms of maintaining genetic diversity, variation in the strength of self-incompatibility (SI) has also been well documented, as has a shift from SI to inbreeding at the species and population levels. An important underlying driving force behind a switch to inbreeding could be the reproductive assurance provided by not requiring an unrelated mating partner for sexual reproduction. This could be beneficial for a species undergoing rapid colonization, because only a single individual is required to begin a sexually reproducing colony after a long-distance dispersal event (Baker’s law), which is characteristic of the plight of many species after the last glacial maxima. The purpose of my thesis was to evaluate the effects of variation in mating system on post-glacial colonization, using two model species that show intraspecific variation in outcrossing rates. The first, Arabidopsis lyrata, represents an excellent model system to assess post-glacial colonization history because it exhibits broad geographical and ecological ranges, and has a recently completed genome sequence. In North America, A. lyrata has further benefits as a model system, namely it exhibits variation in the strength of SI and shift to SC at the population level, which is not observed in Europe. The second species is Arabis alpina, which also appears to show population level variation in mating system strength in Europe based on variation in FIS. This has been putatively linked to colonization history after the last glacial maxima. Unlike in A. lyrata however, its mating system has not been characterized. Mating system delimitation in A. alpina has the potential to aid the interpretation of patterns of ecological genetic diversity, which may in part be influenced by local or regional stochastic changes to mating system variation. My first objective was to identify if A. alpina had a functioning SI system based on both self-fertilization experiments, and allozyme based outcrossing rate estimations. I found strong evidence to suggest the presence of a functional barrier preventing self-fertilization in A. alpina. I identified multiple putative SRK alleles (the female determinant of self-incompatibility), suggesting that the same type of sporophytic system seen in other Brassicaceae species governs SI in this species. I also demonstrated linkage of SI phenotype to some SRK genotypes by diallel crosses, strengthening the case for a functional SI system in this species. Further to this I demonstrate variation in mating system strength between populations, and autonomous inbreeding was seen in a single population. I note that the potential changes in SI status coincide with areas suspected to differ in post-glacial history based on allozyme diversity reported in previous work. While the number of populations sampled was insufficient to link mating system variation to colonization history in A. alpina, mating system variation has been more extensively characterized in North American A. lyrata, allowing more fine-scale resolution of population structure and post-glacial colonization history; an underlying objective of my thesis. I used three molecular marker systems (cpDNA, nuclear micro-satellites and allozymes) to assess these phylogeographic questions, and present evidence of three putative colonization routes for the Great Lakes region. These putative routes are congruent with those described in other species, particularly amphibians and reptiles. Further to this I considered the possible location of glacial refugia, and likelihood that plant taxa may have survived during Pleistocene glaciation in close proximity to the Laurentide Ice Sheet, particularly in Illinois, Indiana, Wisconsin and Minnesota, which may also be true for some animal taxa. I examined patterns of population structure, and scenarios that may have influenced this, and present support for the previously documented theory of multiple breakdowns in SI in this geographic region. My final objective was to assess the suitability of the three marker systems for phylogeographic reconstruction in A. lyrata, by comparing and contrasting the patterns of population structure, and colonization history suggested by each system. Levels of variation observed between the marker systems used varied, and I explored how these patterns complemented and contradicted each other. As expected, the nuclear micro-satellite loci represent the system with the greatest genetic diversity, but do not allow meaningful conclusions to be drawn regarding colonization history because of low levels of shared variation between populations. Conversely, the allozyme loci presented much lower levels of genetic diversity, but support population structuring conclusions based on both cpDNA data and previous studies of A. lyrata and other taxa in this area. The cpDNA marker (trnF) represents a somewhat contentious system to use for phylogeography in A. lyrata, as it contains a tandem array of highly variable, but complexly evolving duplications (pseudogenes). I concluded that these structural changes could be phylogenetically informative when pseudogene evolutionary relationships can be resolved This was based on variation in patterns of diversity, and the subsequent population structure change that occurred when using different methods of assessing trnF variation.

The AdS/CFT correspondence has long been used as a tool for understanding non-perturbative phenomena in gauge theories because it is an example of a 'strong-weak' duality: when one side of the duality is weakly coupled, the other is strongly coupled and vice-versa. Hence strongly coupled phenomena can be studied by looking at the weakly coupled side of the duality. In its original form the correspondence proposes a duality between type IIB superstring theory on AdSs x S5 and an M = 4 supersymmetric Yang-Mills theory in four dimensions. In this thesis we investigate proposed duals to QCD-itself. Duals to QCD fall into two categories: 'top-down' and 'bottom-up'. We take inspiration from both by truncating a consistent solution to the type IlB supergravity equations of motion (top-down). This model demonstrates dynamical chiral symmetry breaking, has a running coupling and contains a holographic description of the vector meson sector. By artificially extending the existing U(l) symmetry to SU(2) (bottom- up) we then obtain a holographic description of the axial vector sector. We show that this model reproduces the masses and decay constants of the lightest mesons to the 10% level. By regulating the UV with a sharp cut-off we can reproduce the p meson masses to. within 2%. Finally we demonstrate that this model can be used to reproduce a very good agreement with hadroriization data for particle production over a range of four orders of magnitude.