Exploring properties of diversity measures in character data

This thesis investigates the limitations of circular approximations of split systems and introduces novel diversity measures for biodiversity assessments of multiple populations. Through a comprehensive analysis of simulated datasets and SNP data from anadromous Atlantic Salmon (Salmo Salar) populations, this research evaluates the efficacy of circular approximations in identifying maximum diversity set(s), where diversity is measured by Split System Diversity (SSD), an extension of Phylogenetic Diversity (PD). The findings reveal that while circular approximations offer computational efficiency, they can produce notable discrepancies in the maximum diversity sets compared to the true optimal sets. These discrepancies range from minor differences in Atlantic salmon data to substantial deviations in the simulated data. Innovative methods of simulating split systems are used involving graphs and hypergraphs to reach the substantial discrepancies. These results underscore the necessity of balancing computational efficiency with accuracy in conservation applications. This thesis additionally introduces new diversity measures designed to capture the diversity of multiple populations. Four approaches —Pooling, Averaging, Pairwise Differencing, and Fixing— are proposed to extend existing diversity measures defined for a single population to a collection of populations. Applying these methods to both Heterozygosity and SSD, the study explores the correlations between the approaches and their utility across multiple populations of Atlantic salmon in a conservation context. Another application, beyond conservation, is tracking changes in pathogen diversity caused by vaccination over time. The impact of new selective regimes, such as those exerted by Pneumococcal Conjugate Vaccines (PCVs), on genetic diversity in bacterial populations is explored. This was done by applying the introduced population-level SSD measures to data from Streptococcus pneumoniae isolates collected over six years. The study identifies significant shifts in genetic diversity, which highlights the dynamic responses of bacterial populations to vaccination efforts. These findings emphasize the need for continuous monitoring and adaptive strategies in vaccination programs to manage serotype replacement and resistance effectively. Finally, several avenues for further investigation that arise from the present work are posed.