  We propose a $\tau$-leaping simulation algorithm for stochastic systems
subject to fast environmental changes. Similar to conventional $\tau$-leaping
the algorithm proceeds in discrete time steps, but as a principal addition it
captures environmental noise beyond the adiabatic limit. The key idea is to
treat the input rates for the $\tau$-leaping as (clipped) Gaussian random
variables with first and second moments constructed from the environmental
process. In this way, each step of the algorithm retains environmental
stochasticity to sub-leading order in the time scale separation between system
and environment. We test the algorithm on several toy examples with discrete
and continuous environmental states, and find good performance in the regime of
fast environmental dynamics. At the same time, the algorithm requires
significantly less computing time than full simulations of the combined system
and environment. In this context we also discuss several methods for the
simulation of stochastic population dynamics in time-varying environments with
continuous states.
