This thesis consists of five papers published in peer-reviewed journals, two of which focus on method development of time-serial inference, represented by publications in methodology journals, and three others that describe collaborative data applications based on experimental evolution projects, which are published in biological journals. The first methodology publication (Chapter 2) is a comparison study of recently-introduced time-serial methods, performed using a systematic approach to evaluate, through simulation, the strengths and weaknesses of each method in quantifying selection coefficients from time-sampled data sets. The second methodology chapter (Chapter 3) introduced a novel method extending Wright-Fisher Approximate Bayesian Computation (WFABC) to detect and quantify changes in selection strength from temporal allele trajectories. This method was particularly novel in its use of simulation-based inference to detect and quantify €˜changes€™ in evolutionary trajectories, which involved the application of Change-Point Analysis. In the first data application (Chapter 4), a time-sampled experiment of echovirus 11 evolved under the disinfectant (chlorine dioxide) was assessed on the associated genotypic and phenotypic trait in collaboration with the Environmental Chemistry Laboratory (LCE) at EPFL. This study contributes to a better understanding of disinfection resistance in waterborne viruses by identifying the mutations associated with enhanced replicative fitness. In the next application (Chapter 5), a comprehensive time-serial analysis was performed on experimental evolution data of echovirus 11 on UVC adaptation in collaboration with the Environmental Chemistry Laboratory (LCE). This study shows that the UVC adaptation of echovirus 11 is associated with a decrease in the virus mutation rate, which is an evidence of the ability of echovirus 11 to adapt to the commonly used disinfectant procedure of UVC radiation in clinical settings and water treatment plants. Additionally, a paper implementing Change-Point WFABC (CP-WFABC) to assess the experimental evolution of influenza A virus is shown in Appendix; specifically, the effects of a novel mutagenic drug (favipiravir) on adaptive allele trajectories were evaluated, with results indicating mutation meltdown under a high drug dosage.