  When long-lived, balancing selection can lead to trans-species polymorphisms
that are shared by two or more species identical by descent. In this case, the
gene genealogies at the selected sites cluster by allele instead of by species
and, because of linkage, nearby neutral sites also have unusual genealogies.
Although it is clear that this scenario should lead to discernible footprints
in genetic variation data, notably the presence of additional neutral
polymorphisms shared between species and the absence of fixed differences, the
effects remain poorly characterized. We focus on the case of a single site
under long-lived balancing selection and derive approximations for summaries of
the data that are sensitive to a trans-species polymorphism: the length of the
segment that carries most of the signals, the expected number of shared neutral
SNPs within the segment and the patterns of allelic associations among them.
Coalescent simulations of ancient balancing selection confirm the accuracy of
our approximations. We further show that for humans and chimpanzees, and more
generally for pairs of species with low genetic diversity levels, the patterns
of genetic variation on which we focus are highly unlikely to be generated by
neutral recurrent mutations, so these statistics are specific as well as
sensitive. We discuss the implications of our results for the design and
interpretation of genome scans for ancient balancing selection in apes and
other taxa.
