Before revision:  We show how leaping allows for statistical investigations beyond the reach of "exact-stochastic" methods and demonstrate how one can uncover, via such investigations, subtle stochastic effects that would be ignored in deterministic treatments. We then show, using examples taken from the literature, that conditions identified here as lending well to leaping do, in fact, arise in natural biological systems. This leads us to discuss and demonstrate how the statistical information garnered from a leaping study can be used to infer mechanistic details of a biological process and motivate experiments .
After revision:  We show how leaping allows for statistical investigations beyond the reach of "exact-stochastic" methods and demonstrate how one can uncover, via such investigations, subtle stochastic effects that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly-used "exact" stochastic methods. We also illustrate prime bottlenecks that can hinder the approach and discuss possible strategies for overcoming them .