Inferring Fitness Parameters from Genetic Time-Series Data: Statistical Analysis and Algorithms

Fitness describes differences in reproductive success and is a central quantity governing evolutionary change. Genetic time-series data, such as mutant allele frequency trajectories, capture temporal changes in allele frequencies and allow the inference of fitness parameters. Recent technological developments have made it possible to collect increasing amounts of genetic time-series data, thereby motivating the development of many estimators for fitness parameter inference. Despite these efforts, a rigorous statistical understanding of the performance of these estimators and their dependence on system parameters remains limited. In addition, fitness effects may be non-additive, and jointly inferring additive and non-additive components is difficult when only limited measurements are available. This thesis addresses these challenges using the marginal path likelihood framework, which connects stochastic evolutionary models with observed genetic time-series data. Closed-form estimators are derived within this framework to analyze fitness parameter inference and to develop estimation algorithms. The first part of this thesis establishes a statistical framework that quantifies how randomness arising from limited sampling and genetic drift affects estimator performance. By decomposing these sources of randomness, the analysis identifies key quantities that determine estimator precision, clarifies their independent and relative effects, and characterizes how temporal integration mitigates them through distinct scaling behaviors. The second part develops a fully interpretable method for jointly estimating additive and non-additive fitness effects under complex evolutionary models, using only single mutant allele frequency trajectories. Together, these studies strengthen the theoretical understanding of fitness parameter inference from genetic time-series data, providing guidance for practical analysis, evolutionary modeling, and experimental design.