Two of the most challenging goals of evolutionary biology are to reconstruct the evolutionary relationships among all extant species and to understand the process by which new species form. Accomplishing these goals will require accurate computational methods for reconstructing phylogenetic trees, general analytic models of speciation, and powerful statistical tools for studying the process of speciation in natural systems. In the first chapter, I study the effects of improper model assumption on estimates of phylogeny. Using DNA sequence data simulated under a variety of models of sequence evolution, I demonstrate that use of oversimplified models can result in erroneous phylogeny estimates. This result suggests that if the models currently utilized are oversimplified then current estimates of phylogeny may be inaccurate and more complex models need to be developed and employed. In the second and third chapters, I study one process thought to be important in completing the final stages of speciation: reinforcement. Using simulations of a hybrid zone, I show that the process of reinforcement can result in patterns other than reproductive character displacement. I also show that speciation by reinforcement is more likely when the genes involved in reproductive isolation are sex-linked. In the fourth chapter, I develop a statistical method of quantifying the degree of isolation between species undergoing divergence. Using genotype data obtained from natural hybrid zones, this novel method can be used to estimate the fitness of hybrids during different stages of their life cycle. This approach offers a new approach to empirical biologists studying extrinsic postzygotic isolation in natural systems.

This dissertation work is part of a larger research effort involving soil-aquifer treatment (SAT). The dissertation's focus was to investigate meta-heuristic (global) optimization methods suitable for developing water resources decision support system (DSS), particularly to optimally design and operate groundwater storage and recovery projects. The effort included developing an integrated simulation-optimization management model for complex aquifer recharge/extraction operation considering water quality transformation. The research demonstrated successful integration of three-dimensional hydraulic, water quality, and particle tracking models with shuffled complex evolution (SCE) optimization algorithm. It also included developing the shuffled frog leaping algorithm (SFLA), a meta-heuristic optimization technique for solving discrete/combinatorial problems, and its application to aid decision making in water supply and distribution system optimization issues. SFLA is a memetic, meta-heuristic population-based cooperative search metaphor inspired by natural memetics. SFLA was developed by extending the logic of two existing global optimization techniques for continuous optimization problems. The local search is completed using an extension of the particle swami optimization (PSO) method, and the global exploration is performed by a technique similar to that used in the shuffled complex evolution (SCE) algorithm. SFLA was tested favorably on several literature test functions and engineering problems that present difficulties to many global optimization problems. The effectiveness and suitability of this algorithm has also been demonstrated by applying it to a groundwater model calibration problem and several water distribution system design problems that are considered as benchmark problems in the literature. The comparison of SFLA with other existing global optimization methods, such as genetic algorithms (GA), in terms of the likelihood and efficiency of converging to a global optimal solution, suggests that SFLA can be an effective algorithm for solving discrete/combinatorial optimization problems.

published_or_final_version / Applied Statistics / Master / Master of Social Sciences

published_or_final_version / Statistics / Master / Master of Social Sciences

published_or_final_version / Applied Statistics / Master / Master of Social Sciences

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / abstract / toc / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy