Plasmids are extra-chromosomal genetic elements that play a key role in bacterial adaptation and in the spread of antibiotic resistance. Unlike chromosomal genes, plasmids are present in multiple copies per cell and are transmitted through both vertical and horizontal inheritance. This creates evolutionary dynamics that differ fundamentally from classical population genetics, as mutation, selection, and genetic drift interact across two levels: within cells and between cells. In this talk, I introduce stochastic population genetics models that capture the interplay between plasmid copy number, mutational supply, and segregational drift. Our results show that plasmid evolution accelerates with copy number despite the increased drift induced by random segregation, and that plasmid copy number emerges as an evolutionarily optimized trait balancing selective benefit and metabolic cost. These findings illustrate how multilevel stochasticity shapes evolutionary rates and provides a probabilistic (partial) explanation for the rapid emergence of antibiotic resistance. Based on the papers Ramiro-Martínez, P. et al (2026). Plasmid mutation rates scale with copy number. Proceedings of the National Academy of Sciences, 123(4). and Hernandez-Beltran, J. C. R., Miró Pina, V., Siri-Jégousse, A., Palau, S., Peña-Miller, R., & González Casanova, A. (2022). Segregational instability of multicopy plasmids: A population genetics approach. Ecology and Evolution, 12, e9469. https://doi.org/10.1002/ece3.9469