  Widely used models in genetics include the Wright-Fisher diffusion and its
moment dual, Kingman's coalescent. Each has a multilocus extension but under
neither extension is the sampling distribution available in closed-form, and
their computation is extremely difficult. In this paper we derive two new
multilocus population genetic models, one a diffusion and the other a
coalescent process, which are much simpler than the standard models, but which
capture their key properties for large recombination rates. The diffusion model
is based on a central limit theorem for density dependent population processes,
and we show that the sampling distribution is a linear combination of moments
of Gaussian distributions and hence available in closed-form. The coalescent
process is based on a probabilistic coupling of the ancestral recombination
graph to a simpler genealogical process which exposes the leading dynamics of
the former. We further demonstrate that when we consider the sampling
distribution as an asymptotic expansion in inverse powers of the recombination
parameter, the sampling distributions of the new models agree with the standard
ones up to the first two orders.
