Understanding admixture fractions: theory and estimation of gene-flow.

Estimation of admixture proportions has become one of the most commonly used computational tools in population genomics. However, there is remarkably little population genetic theory on statistical properties of these variables. We develop theoretical results that can accurately predict means and variances of admixture proportions within a population using models with recombination and genetic drift.

Estimating the timing of multiple admixture events using 3-locus linkage disequilibrium.

Estimating admixture histories is crucial for understanding the genetic diversity we see in present-day populations. Allele frequency or phylogeny-based methods are excellent for inferring the existence of admixture or its proportions. However, to estimate admixture times, spatial information from admixed chromosomes of local ancestry or the decay of admixture linkage disequilibrium (ALD) is used.

Genome-wide ancestry patterns in Rapanui suggest pre-European admixture with Native Americans.

Background: Rapa Nui (Easter Island), located in the easternmost corner of the Polynesian Triangle, is one of the most isolated locations on the planet inhabited by humans. Archaeological and genetic evidence suggests that the island was first colonized by Polynesians around AD 1200, during their eastward expansion. Although it remains contentious whether Polynesians reached South America, suggestive evidence has been brought forward supporting the possibility of Native American contact prior to the European "discovery" of the island in AD 1722.

The lengths of admixture tracts.

The distribution of admixture tract lengths has received considerable attention, in part because it can be used to infer the timing of past gene flow events between populations. It is commonly assumed that these lengths can be modeled as independently and identically distributed (iid) exponential random variables. This assumption is fundamental for many popular methods that analyze admixture using hidden Markov models.

On detecting incomplete soft or hard selective sweeps using haplotype structure.

We present a new haplotype-based statistic (nSL) for detecting both soft and hard sweeps in population genomic data from a single population. We compare our new method with classic single-population haplotype and site frequency spectrum (SFS)-based methods and show that it is more robust, particularly to recombination rate variation. However, all statistics show some sensitivity to the assumptions of the demographic model.

Phylogenetic analysis using Lévy processes: finding jumps in the evolution of continuous traits.

Gaussian processes, a class of stochastic processes including Brownian motion and the Ornstein-Uhlenbeck process, are widely used to model continuous trait evolution in statistical phylogenetics. Under such processes, observations at the tips of a phylogenetic tree have a multivariate Gaussian distribution, which may lead to suboptimal model specification under certain evolutionary conditions, as supposed in models of punctuated equilibrium or adaptive radiation. To consider non-normally distributed continuous trait evolution, we introduce a method to compute posterior probabilities when modeling continuous trait evolution as a Lévy process.