  Genetic recombination is one of the most important mechanisms that can
generate and maintain diversity, and recombination information plays an
important role in population genetic studies. However, the phenomenon of
recombination is extremely complex, and hence simulation methods are
indispensable in the statistical inference of recombination. So far there are
mainly two classes of simulation models practically in wide use: back-in-time
models and spatially moving models. However, the statistical properties shared
by the two classes of simulation models have not yet been theoretically
studied. Based on our joint research with CAS-MPG Partner Institute for
Computational Biology and with Beijing Jiaotong University, in this paper we
provide for the first time a rigorous argument that the statistical properties
of the two classes of simulation models are identical. That is, they share the
same probability distribution on the space of ancestral recombination graphs
(ARGs). As a consequence, our study provides a unified interpretation for the
algorithms of simulating coalescent with recombination, and will facilitate the
study of statistical inference on recombination.
