Final answer:
The mathematical modeling of biological systems can incorporate both stochastic and deterministic models. Phenomenon1 can indeed be modeled stochastically to capture its inherent variability, which can profoundly impact the subsequent deterministic models of phenomenon2.
Step-by-step explanation:
Mathematical modeling of biological systems can integrate both stochastic and deterministic approaches. While a deterministic model consists of partial differential equations (PDEs) and provides a predictable outcome given a set of initial conditions, a stochastic model incorporates randomness, which can capture the inherent variability and unexpected fluctuations in biological phenomena. For phenomenon1 and phenomenon2, which are causally dependent and involve feedback loops, it is indeed plausible to model phenomenon1 stochastically. This approach would allow researchers to account for the inherent uncertainty and variability in the initial phenomenon while maintaining the capacity to study its effects on the subsequent deterministic models.
The benefits of theoretical analysis are profound, as they provide deeper insight and quantifiable predictions, highlighting interrelations such as those between cell shape, structure, adhesion, and force. Biological systems, with their dynamic homeostasis, are rich in nonlinear phenomena and positive feedback mechanisms, which can be aptly represented through both deterministic and stochastic models. Therefore, despite phenomenon2's deterministic model involving 3 PDEs, it is theoretically feasible and can be immensely insightful to model phenomenon1 with a stochastic framework, given that it incorporates the unpredictability and complexity of biological systems.