  Evolutionary forces shape patterns of genetic diversity within populations
and contribute to phenotypic variation. In particular, recurrent positive
selection has attracted significant interest in both theoretical and empirical
studies. However, most existing theoretical models of recurrent positive
selection cannot easily incorporate realistic confounding effects such as
interference between selected sites, arbitrary selection schemes, and
complicated demographic processes. It is possible to quantify the effects of
arbitrarily complex evolutionary models by performing forward population
genetic simulations, but forward simulations can be computationally prohibitive
for large population sizes ($> 10^5$). A common approach for overcoming these
computational limitations is rescaling of the most computationally expensive
parameters, especially population size. Here, we show that ad hoc approaches to
parameter rescaling under the recurrent hitchhiking model do not always provide
sufficiently accurate dynamics, potentially skewing patterns of diversity in
simulated DNA sequences. We derive an extension of the recurrent hitchhiking
model that is appropriate for strong selection in small population sizes, and
use it to develop a method for parameter rescaling that provides the best
possible computational performance for a given error tolerance. We perform a
detailed theoretical analysis of the robustness of rescaling across the
parameter space. Finally, we apply our rescaling algorithms to parameters that
were previously inferred for Drosophila, and discuss practical considerations
such as interference between selected sites.
