Studying natural selection is of great importance to understand how different organisms adapt to different environmental conditions. However, natural selection does not act in isolation; it interacts with other evolutionary mechanisms such as mutation, genetic drift, migration, and genetic linkage, all of which collectively shape the genetic and phenotypic composition of populations. In this thesis, we explore the interplay between natural selection and two key evolutionary mechanisms: genetic linkage and migration.

Because sites that are closer together in the genome are more likely to be inherited together, elimination of deleterious variants can reduce variation at linked neutral sites. This process is known as background selection. In Chapter 2, we investigate how background selection influences the frequency trajectory of a single selected locus under both additive and underdominant selection. We then extend this analysis to explore its impact on the genetic architecture and evolution of complex traits, including a complex disease under directional selection and a quantitative trait under stabilizing selection. Our findings demonstrate that background selection can have a profound effect on complex traits that cannot be inferred by assuming independent selection on individual variants. For example, in some cases, background selection can increase disease prevalence.

Another important factor that affects the allele frequency of a selected locus is gene flow. Allele frequency changes that cannot be explained by genetic drift can signal natural selection; however, these changes may also result from migration. Failing to properly account for allele frequency shifts caused by gene flow can lead to false signals of selection. This issue becomes particularly relevant in our case study, where we aim to detect selection using ancient DNA (aDNA) samples from the island of Sardinia, as described in Chapter 3. To address this challenge, we introduce a novel method for detecting selection in ancient DNA while accounting for gene flow in Chapter 4. We validate our method through extensive simulations and apply it to empirical aDNA data from the Carpathian Basins.

Finally, based on insights gained from these projects, Chapter 5 discusses future directions for refining selection inference approaches and advancing our understanding of trait evolution while accounting for genetic linkage and gene flow.