Heating the Early Universe : Numerical Methods and Their Analysis

During the epoch when the first collapsed structures formed (6<z<50) our Universe went through an extended period of changes. Some of the radiation from the first stars and accreting black holes in those structures escaped and changed the state of the Intergalactic Medium (IGM). The era of this global phase change in which the state of the IGM was transformed from cold and neutral to warm and ionized, is called the Epoch of Reionization.In this thesis we focus on numerical methods to calculate the effects of this escaping radiation. We start by considering the performance of the cosmological radiative transfer code C2-Ray. We find that although this code efficiently and accurately solves for the changes in the ionized fractions, it can yield inaccurate results for the temperature changes. We introduce two new elements to improve the code. The first element, an adaptive time step algorithm, quickly determines an optimal time step by only considering the computational cells relevant for this determination. The second element, asynchronous evolution, allows different cells to evolve with different time steps. An important constituent of methods to calculate the effects of ionizing radiation is the transport of photons through the computational domain or ``ray-tracing''. We devise a novel ray tracing method called PYRAMID which uses a new geometry - the pyramidal geometry. This geometry shares properties with both the standard Cartesian and spherical geometries. This makes it on the one hand easy to use in conjunction with a Cartesian grid and on the other hand ideally suited to trace radiation from a radially emitting source. A time-dependent photoionization calculation not only requires tracing the path of photons but also solving the coupled set of photoionization and thermal equations. Several different solvers for these equations are in use in cosmological radiative transfer codes. We conduct a detailed and quantitative comparison of four different standard solvers in which we evaluate how their accuracy depends on the choice of the time step. This comparison shows that their performance can be characterized by two simple parameters and that the C2-Ray generally performs best.

Adaptation and Constraint in the Plant Reproductive Phase

Conservatism is a central theme of organismic evolution. Related species share characteristics due to their common ancestry. Some concern have been raised among evolutionary biologists, whether such conservatism is an expression of natural selection or of a constrained ability to adapt. This thesis explores adaptations and constraints within the plant reproductive phase, particularly in relation to the evolution of fleshy fruit types (berries, drupes, etc.) and the seasonal timing of flowering and fruiting. The different studies were arranged along a hierarchy of scale, with general data sets sampled among seed plants at the global scale, through more specific analyses of character evolution within the genus Rhamnus s.l. L. (Rhamnaceae), to descriptive and experimental field studies in a local population of Frangula alnus (Rhamnaceae). Apart from the field study, this thesis is mainly based on comparative methods explicitly incorporating phylogenetic relationships. The comparative study of Rhamnus s.l. species included the reconstruction of phylogenetic hypotheses based on DNA sequences. Among geographically overlapping sister clades, biotic pollination was not correlated with higher species richness when compared to wind pollinated plants. Among woody plants, clades characterized by fleshy fruit types were more species rich than their dry-fruited sister clades, suggesting that the fleshy fruit is a key innovation in woody habitats. Moreover, evolution of fleshy fruits was correlated with a change to more closed (darker) habitats. An independent contrast study within Rhamnus s.l. documented allometric relations between plant and fruit size. As a phylogenetic constraint, allometric effects must be considered weak or non-existent, though, as they did not prevail among different subclades within Rhamnus s.l. Fruit size was correlated with seed size and seed number in F. alnus. This thesis suggests that frugivore selection on fleshy fruit may be important by constraining the upper limits of fruit size, when a plant lineage is colonizing (darker) habitats where larger seed size is adaptive. Phenological correlations with fruit set, dispersal, and seed size in F. alnus, suggested that the evolution of reproductive phenology is constrained by trade-offs and partial interdependences between flowering, fruiting, dispersal, and recruitment phases. Phylogenetic constraints on the evolution of phenology were indicated by a lack of correlation between flowering time and seasonal length within Rhamnus cathartica and F. alnus, respectively. On the other hand, flowering time was correlated with seasonal length among Rhamnus s.l. species. Phenological differences between biotically and wind pollinated angiosperms also suggested adaptive change in reproductive phenology.