Purifying selection can substantially alter patterns of molecular evolution. Its main effect is to reduce overall levels of genetic variation, leading to a reduced effective population size. However, it also distorts genealogies relative to neutral expectations. A structured coalescent method has been used to describe this effect, and forms the basis for numerical methods and simulations. In this study, we extend this approach by making the additional approximation that lineages may be treated independently, which is valid only in the strong selection regime. We show that in this regime, the distortions due to purifying selection can be described by a time-dependent effective population size and mutation rate, confirming earlier intuition. We calculate simple analytical expressions for these functions, N(e)(t) and U(e)(t). These results allow us to describe the structure of genealogies in a population under strong purifying selection as equivalent to a purely neutral population with varying population size and mutation rate, thereby enabling the use of neutral methods of inference and estimation for populations in the strong selection regime.