Using a Combination of Phylogenetic Comparative and Paleobotanical Methods to Elucidate Patterns of Lineage Selection in Rosales (Plantae: Anthophyta)

An increasing focus in evolutionary biology is on the interplay between mesoscale ecological and evolutionary processes such as population demographics, habitat tolerance, and especially geographic distribution, as potential drivers responsible for patterns of diversification and extinction over geologic time. However, few studies to date connect organismal processes such as survival and reproduction through mesoscale patterns to long-term macroevolutionary trends. In my dissertation, I investigate how mechanism of seed dispersal, mediated through geographic range size, influences diversification rates in the Rosales (Plantae: Anthophyta). In my first chapter, I validate the phylogenetic comparative methods that I use in my second and third chapters. Available state speciation and extinction (SSE) models assumptions about evolution known to be false through fossil data. I show, however, that as long as net diversification rates remain positive – a condition likely true for the Rosales – these violations of SSE’s assumptions do not cause significantly biased results. With SSE methods validated, my second chapter reconstructs three associations that appear to increase diversification rate for Rosalean genera: (1) herbaceous habit; (2) a three-way interaction combining animal dispersal, high within-genus species richness, and geographic range on multiple continents; (3) a four-way interaction combining woody habit with the other three characteristics of (2). I suggest that the three- and four-way interactions represent colonization ability and resulting extinction resistance in the face of late Cenozoic climate change; however, there are other possibilities as well that I hope to investigate in future research. My third chapter reconstructs the phylogeographic history of the Rosales using both non-fossil-assisted SSE methods as well as fossil-informed traditional phylogeographic analysis. Ancestral state reconstructions indicate that the Rosaceae diversified in North America while the other Rosalean families diversified elsewhere, possibly in Eurasia. SSE is able to successfully identify groups of genera that were likely to have been ancestrally widespread, but has poorer taxonomic resolution than methods that use fossil data. In conclusion, these chapters together suggest several potential causal links between organismal, mesoscale, and geologic scale processes, but further work will be needed to test the hypotheses that I raise here.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.

Are Videogames Art?

My dissertation defends a positive answer to the question: “Can a videogame be a work of art? ” To achieve this goal I develop definitions of several concepts, primarily ‘art’, ‘games’, and ‘videogames’, and offer arguments about the compatibility of these notions. In Part One, I defend a definition of art from amongst several contemporary and historical accounts. This definition, the Intentional-Historical account, requires, among other things, that an artwork have the right kind of creative intentions behind it, in short that the work be intended to be regarded in a particular manner. This is a leading account that has faced several recent objections that I address, particular the buck-passing theory, the objection against non-failure theories of art, and the simultaneous creation response to the ur-art problem, while arguing that it is superior to other theories in its ability to answer the question of videogames’ art status. Part Two examines whether games can exhibit the art-making kind of creative intention. Recent literature has suggested that they can. To verify this a definition of games is needed. I review and develop the most promising account of games in the literature, the over-looked account from Bernard Suits. I propose and defend a modified version of this definition against other accounts. Interestingly, this account entails that games cannot be successfully intended to be works of art because games are goal-directed activities that require a voluntary selection of inefficient means and that is incompatible with the proper manner of regarding that is necessary for something to be an artwork. While the conclusions of Part One and Part Two may appear to suggest that videogames cannot be works of art, Part Three proposes and defends a new account of videogames that, contrary to first appearances, implies that not all videogames are games. This Intentional-Historical Formalist account allows for non-game videogames to be created with an art-making intention, though not every non-ludic videogame will have an art-making intention behind it. I then discuss examples of videogames that are good candidates for being works of art. I conclude that a videogame can be a work of art, but that not all videogames are works of art. The thesis is significant in several respects. It is a continuation of academic work that has focused on the definition and art status of videogames. It clarifies the current debate and provides a positive account of the central issues that has so far been lacking. It also defines videogames in a way that corresponds better with the actual practice of videogame making and playing than other definitions in the literature. It offers further evidence in defense of certain theories of art over others, providing a close examination of videogames as a new case study for potential art objects and for aesthetic and artistic theory in general. Finally, it provides a compelling answer to the question of whether videogames can be art. This project also provides the groundwork for new evaluative, critical, and appreciative tools for engagement with videogames as they develop as a medium. As videogames mature, more people, both inside and outside academia, have increasing interest in what they are and how to understand them. One place many have looked is to the practice of art appreciation. My project helps make sense of which appreciative and art-critical tools and methods are applicable to videogames.

Phase transitions in gene networks evolved under different selection rules

Mathematical models of gene regulation are a powerful tool for understanding the complex features of genetic control. While various modeling efforts have been successful at explaining gene expression dynamics, much less is known about how evolution shapes the structure of these networks. An important feature of gene regulatory networks is their stability in response to environmental perturbations. Regulatory systems are thought to have evolved to exist near the transition between stability and instability, in order to have the required stability to environmental fluctuations while also being able to achieve a wide variety of functions (corresponding to different dynamical patterns). We study a simplified model of gene network evolution in which links are added via different selection rules. These growth models are inspired by recent work on `explosive' percolation which shows that when network links are added through competitive rather than random processes, the connectivity phase transition can be significantly delayed, and when it is reached, it appears to be first order (discontinuous, e.g., going from no failure at all to large expected failure) instead of second order (continuous, e.g., going from no failure at all to very small expected failure). We find that by modifying the traditional framework for networks grown via competitive link addition to capture how gene networks evolve to avoid damage propagation, we also see significant delays in the transition that depend on the selection rules, but the transitions always appear continuous rather than `explosive'.