heuristically, two stochastic processes are dual if one can find a function to study one process by using the other. implicitly, this technique can be traced back to the work of blaise pascal. explicitly, it has been studied in different contexts, including interacting particle systems, and it is a crucial concept in population genetics.

additionally, we will explore the duality between theoretical and applied mathematics. specifically, we will examine instances in which theoretical probability is employed to study biological problems and situations where biological questions inspire interesting mathematical models. this discussion will encompass examples from population genetics, experimental evolution, and public health.