Developing Efficient Frameworks for Coalescent-Based Inference in Population Genetics

The exponential growth in genomic datasets has created unprecedented opportunities to study evolutionary processes, but existing population genetic inference methods face critical scalability and interpretability challenges. While the coalescent framework provides a powerful and interpretable backward-in-time approach for connecting observed genetic variation to underlying evolutionary forces, it can be quite computationally inefficient and statistically intractable, especially when dealing with large numbers of spatially distributed individuals or the effects of selection. As a result, current methods rely on low-dimensional representations of the coalescent process for efficient inference. This creates an urgent need for efficient inference frameworks that maintain direct connections to mechanistic evolutionary theory while scaling to modern datasets. This dissertation addresses these challenges via the development of three three novel frameworks that advance coalescent-based inference by bridging forward-time evolutionary models with backward-time genealogical approaches. First, I present a spatial population genetics method that extends isolation-by-distance models to jointly infer local migration surfaces and long-range genetic connections, addressing limitations in current approaches that ignore non-local gene flow patterns. Second, I develop a framework for inferring natural selection from paired data of allele frequency and age estimates by leveraging forward-in-time diffusion approximations. This approach produces unbiased selection coefficient estimates under realistic demographic scenarios, and through this framework I find that the ages of common variants are more useful in distinguishing stronger selection coefficients, following previous results from frequency-based approaches and reconciling claims from recent statistical genetics studies for traits under strong directional selection. Third, I extend this inference to the Ancestral Selection Graph (ASG) framework, developing rates for selection strength estimation that utilize forward-in-time transition probabilities. While this approach shows promise for faster inference compared to structured coalescent methods, I demonstrate that the signal is primarily driven by age information, indicating the need for further exploration in this space. However, this work outlines a potential way to bridge the gap between diffusion-based selection theory with modern tree-based inference methods. Each method is validated through extensive simulations. Importantly, the frameworks presented here advance our ability to extract interpretable evolutionary insights from large-scale genomic datasets efficiently, with applications ranging from statistical genetics to conservation genetics.