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The efficacy of therapeutics such as antibiotics and cancer immunotherapy is double-edged: as they eradicate agents of disease, they simultaneously select for resistant populations, eventually causing their own obsolescence. This thesis uses a combination of experiments and computational analysis to explore evolutionary paths to resistance taken by populations subject to these powerful therapeutics, with the hope of forming a foundation of understanding upon which therapies that anticipate and respond to resistance can be designed.\nMutations providing resistance to one drug can simultaneously increase resistance to other drugs (positive cross-resistance) or decrease resistance to other drugs (negative cross-resistance). Negative cross-resistance cycling, the sequential use of a drug pair exhibiting reciprocal negative cross- resistance, has been shown to slow down the evolution of antibiotic resistance. However, parameters governing its efficacy have yet to be investigated. Chapter 1 employs high-throughput robotic pipelines and computational analysis to map evolutionary benefits and trade-offs encountered by thousands of antibiotic-resistant Staphylococcus aureus mutants. We uncover a network of primarily positive cross-resistance, and discover a pair of antibiotics showing reciprocal negative cross- resistance. We show that first-step mutants exhibit diverse cross-resistance profiles: even when the majority of mutants show negative cross-resistance, rare positive cross-resistant mutants can appear. We found that selection for resistance to the first drug in small populations can decrease resistance to the second drug, but identical selection conditions in large populations can increase resistance to the second drug through the appearance of rare positive cross-resistant mutants. We further find that, even with small populations and strong bottlenecks, resistance to both drugs can increase through sequential steps of negative cross-resistance cycling. Thus, low diversity is necessary but not sufficient for effective cycling therapies.\nIn contrast to conventional antibiotics, antimicrobial peptides (AMPs) of the human innate immune system have remained effective against a broad spectrum of pathogens throughout human evolution. Understanding cross-resistance among AMPs and between AMPs and antibiotics could direct the design of treatment regimes that are more resilient to the emergence of resistance. Chapter 2 uses computational models and experimental methods inspired by those developed in Chapter 1 to explore Staphylococcus aureus resistance to AMPs, and the resulting cross-resistance to AMPs and conventional antibiotics. This chapter presents preliminary high-throughput and low-cost experimental and computational frameworks for the generation of AMP-resistant strains and measurement of cross-resistance networks. We also present experimental evidence for negative cross- resistance between the AMP lactoferricin-B and both chloramphenicol and ciprofloxacin, indicating potential clinical applications of AMP resistance networks.\nThe emergence of resistance is a frequent and critical problem in cancer immunotherapy. Understanding the mechanisms of resistance is crucial to designing treatments to circumvent patient relapse. Chapter 3 combines sequencing of tumor biopsies and computational analysis to understand the evolutionary trajectories of tumor populations from patients with advanced melanoma during response and relapse on immune checkpoint blockade therapy. We find that multiple, parallel loss-of-function mutations in Beta-2-microglubolin (B2M ), which is essential for MHC Class I antigen presentation, is associated with the acquisition of resistance to checkpoint blockade. In an independent cohort of 105 melanoma patients undergoing immune checkpoint blockade therapy, we find that loss-of-heterozygosity in B2M, but not other genes involved in the antigen presentation machinery, is significantly enriched in non-responders (one-sided fisher exact p=0.03), and associated with poorer survival (log-rank p=0.01). Moreover, complete loss of B2M was only found in non-responders. Thus, B2M loss represents a fundamental mechanism of checkpoint blockade resistance.