Modeling the dynamics of CRISPR arrays in microbial communities

CRISPR-Cas systems provide adaptive immunity in prokaryotes by incorporating short sequences of viral DNA, known as spacers, into the CRISPR arrays in the host genome. These spacers enable defense against future viral infections, which can be persistent in the long-term (endemic) or transitory (epidemic). The finite size of CRISPR arrays imposes a trade-off between remaining updated and retaining long-term memory in complex environments which is still subject to understanding. This thesis presents a mathematical and computational model that simulates the evolution of CRISPR arrays in microbial communities, distinguishing between spacers targeting endemic versus epidemic viruses. The model explores a continuous spectrum of viral scenarios—from exclusively endemic to purely epidemic compositions—while incorporating parameters that modulate selection pressure, crossover point between viral incidences, and the relative abundance of endemic viruses. Simulations reveal that these parameters govern whether CRISPR arrays prioritize short-term or long-term immune memory. Results indicate that long-term immunity emerges under low selection pressure and stable viromes, conditions consistent with observations in environments such as the human gut microbiome. In contrast, environments with high viral turnover, such as hydrothermal vents, are expected to favor rapidly updating arrays with short-term specialization. The model successfully reproduces key patterns observed in empirical studies and offers testable predictions about array structure and ecological adaptation. Although simplified, the model identifies fundamental variables influencing CRISPR array dynamics and provides a foundation for further empirical integration. It offers a conceptual framework for understanding immune memory in prokaryotes and guiding future studies on microbial evolution in diverse viral ecosystems.