  Large whole-genome sequencing projects have provided access to much of the
rare variation in human populations, which is highly informative about
population structure and recent demography. Here, we show how the age of rare
variants can be estimated from patterns of haplotype sharing and how these ages
can be related to historical relationships between populations. We investigate
the distribution of the age of variants occurring exactly twice (f2 variants)
in a worldwide sample sequenced by the 1000 Genomes Project, revealing enormous
variation across populations. The median age of haplotypes carrying f2 variants
is 50 to 160 generations across populations within Europe or Asia, and 170 to
320 generations within Africa. Haplotypes shared between continents are much
older with median ages for haplotypes shared between Europe and Asia ranging
from 320 to 670 generations. The distribution of the ages of f2 haplotypes is
informative about their demography, revealing recent bottlenecks, ancient
splits, and more modern connections between populations. We see the signature
of selection in the observation that functional variants are significantly
younger than nonfunctional variants of the same frequency. This approach is
relatively insensitive to mutation rate and complements other nonparametric
methods for demographic inference.
