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resistance. A majority of these studies have proposed the explicit management of the balance between sensitive and resistant populations of cells to therapy (Gatenby and Vincent, 2003b; Merlo et al., 2006). One of the earliest examples from Maley et al. suggested the idea of developing a “benign cell booster,” a therapy that explicitly provides competitive advantage to chemosensitive cells (Maley et al., 2004). Since then, multiple studies have suggested and shown that the sensitive cells are likely most fit in the absence of therapy without the need for a “benign booster” (Enriquez-Navas et al., 2016; Bacevic et al., 2017). Exploration of drug holidays, where a therapy is discontinued at various times during treatment, has since gained traction. The purpose of these drug holidays is to intentionally maintain a sufficient level of drug sensitive cells (Hansen et al., 2020; Tabashnik et al., 2013). Upon withdrawing therapy, these sensitive cells compete with and suppress resistant cancer cells, thus prolonging drug efficacy. The seminal work formalizing the judicious use of drug holidays is presented in “Adaptive Therapy” by Gatenby et al. in 2009 (Gatenby et al., 2009b). Continuous or maximum tolerated dose therapies quickly eliminate the entire sensitive population resulting in treatment failure as resistant cells can now grow unchecked, much like the use of DDT and the diamondback moth (Figure 1.5). In-vivo experiments within this work showed that adaptive therapy in ovarian cancer xenografts treated with carboplatin can indeed produce long-term survival. 1.7 Mathematical Modeling as a Bridge The study of integrating evolutionary principles into the understanding and treatment of cancer is rooted heavily in the use of mathematical modeling. Interestingly, mathematical oncology is a relatively new field. Only recently has mathematical oncology been formalized into its own distinct field of study (Gatenby and Maini, 2003; Rockne et al., 2019). This is somewhat surprising, considering the extensive availability of quantitative data in cancer biology. Other fields of study, such as physics and ecology, that are also highly quantitative, have long used mathematical models to interpret results and to guide future experimental design. The use of mathematics in these other fields has provided a bridge between early descriptive science to identification and understanding of first principles. Ironically, the first well known use of mathematical modeling in cancer is the Norton-Simon model that advocated for the maximum tolerated dose paradigm, which in light of evolutionary dynamics is unwise (Norton and Simon, 1977). Mathematical modeling, specifically of prostate cancer, has a relatively long history, mainly due to the availability of a readily available biomarker known as prostate specific antigen or PSA. The measurement of PSA within a patient is obtained through a simple blood draw and can be measured at every appointment. PSA is generally used as a proxy for total tumor volume within a patient and can therefore be used to inform quantitative mathematical models (Hirata et al., 2012). Much of the previous modeling in prostate cancer is focused mainly on the understanding and optimization of applying first line androgen deprivation therapy (ADT) to men with metastatic prostate cancer (Jackson, 2004b,a; Ideta 11

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