  Long-range migrations and the resulting admixtures between populations have
been important forces shaping human genetic diversity. Most existing methods
for detecting and reconstructing historical admixture events are based on
allele frequency divergences or patterns of ancestry segments in chromosomes of
admixed individuals. An emerging new approach harnesses the exponential decay
of admixture-induced linkage disequilibrium (LD) as a function of genetic
distance. Here, we comprehensively develop LD-based inference into a versatile
tool for investigating admixture. We present a new weighted LD statistic that
can be used to infer mixture proportions as well as dates with fewer
constraints on reference populations than previous methods. We define an
LD-based three-population test for admixture and identify scenarios in which it
can detect admixture events that previous formal tests cannot. We further show
that we can uncover phylogenetic relationships among populations by comparing
weighted LD curves obtained using a suite of references. Finally, we describe
several improvements to the computation and fitting of weighted LD curves that
greatly increase the robustness and speed of the calculations. We implement all
of these advances in a software package, ALDER, which we validate in
simulations and apply to test for admixture among all populations from the
Human Genome Diversity Project (HGDP), highlighting insights into the admixture
history of Central African Pygmies, Sardinians, and Japanese.
