Applying mathematical and statistical methods to the investigation of complex biological questions

The research presented in this dissertation integrates data and theory to examine three important topics in biology. In the first chapter, I investigate genetic variation at two loci involved in a genetic incompatibility in the genus Xiphophorus. In this genus, hybrids develop a fatal melanoma due to the interaction of an oncogene and its repressor. Using the genetic variation data from each locus, I fit evolutionary models to test for coevolution between the oncogene and the repressor. The results of this study suggest that the evolutionary trajectory of a microsatellite element in the proximal promoter of the repressor locus is affected by the presence of the oncogene. This study significantly advances our understanding of how loci involved in both a genetic incompatibility and a genetically determined cancer evolve. Chapter two addresses the role polyploidy, or whole genome duplication, has played in generating flowering plant diversity. The question of whether polyploidy events facilitate diversification has received considerable attention among plant and evolutionary biologists. To address this question, I estimated the speciation and genome duplication rates for 60 genera of flowering plants. The results suggest that diploids, as opposed to polyploids, generate more species diversity. This study represents the broadest comparative analysis to date of the effect of polyploidy on flowering plant diversity. In the final chapter, I develop a computational method for designing disease surveillance networks. The method is a data-driven, geographic optimization of surveillance sites. Networks constructed using this method are predicted to significantly outperform existing networks, in terms of information quality, efficiency, and robustness. This work involved the coordinated efforts of researchers in biology, epidemiology, and operations research with public health decision makers. Together, the results of this dissertation demonstrate the utility of applying quantitative theory and statistical methods to data in order to address complex, biological processes.