Summary – Mathematical Modeling Core Understanding the changes in tumor ecology (“∆-Ecology”) that occur during tumor initiation, progression, and therapy requires careful study of a complex dynamical system involving multiple scales – from molecular to cellular to tissue to systemic. An important tool in this study is the use of mathematical models, which can bridge temporal gaps in clinical and experimental data. Ecological histology data from patients is difficult and rare to obtain, and experimental work, while crucial for teasing apart mechanism and testing hypotheses, cannot fully reproduce the human setting of disease. Mathematical modeling serves as a link between these approaches, allowing ecological principles arising from mechanisms studied in vitro and in vivo to play out in the patient setting, calibrated to available patient data. The Mathematical Modeling Core will develop these models, using a variety of approaches. Key is the use of spatial agent-based models, which can handle the rich diversity of cell types and molecules, as well as the multiple scales involved in tumor ecology and evolution. We have built a platform for developing these models that is fast and flexible, including numerous add-ons that will serve the science in the two projects of this proposal. In addition, our expertise in non-spatial models will be applied in parallel, as these approaches can capture the broad dynamics of tumor growth and the response to treatment in ways that have significant translatable potential, as evidenced by ongoing trials in Evolutionary Therapy at Moffitt. In addition to constructing these models, we will develop tools for initializing, calibrating, and analyzing models based on clinical and pre-clinical data collected in each project. This will involve the use of virtual “Phase i” trials, where virtual patients/mice are generated from a model, taking parameter uncertainty into account. In summary, the Core models will provide insight into the ecological processes that occur during tumor growth and treatment.