TroX: a new method to learn about the genesis of aneuploidy from trisomic products of conception.

MOTIVATION: An estimated 10-30% of clinically recognized conceptions are aneuploid, leading to spontaneous miscarriages, in vitro fertilization failures and, when viable, severe developmental disabilities. With the ongoing reduction in the cost of genotyping and DNA sequencing, the use of high-density single nucleotide polymorphism (SNP) markers for clinical diagnosis of aneuploidy and biomedical research into its causes is becoming common practice. A reliable, flexible and computationally feasible method for inferring the sources of aneuploidy is thus crucial. RESULTS: We propose a new method, TroX, for analyzing human trisomy data using high density SNP markers from a trisomic individual or product of conception and one parent. Using a hidden Markov model, we infer the stage of the meiotic error (I or II) and the individual in which non-disjunction event occurred, as well as the crossover locations on the trisomic chromosome. A novel and important feature of the method is its reliance on data from the proband and only one parent, reducing the experimental cost by a third and enabling a larger set of data to be used. We evaluate our method by applying it to simulated trio data as well as to genotype data for 282 trios that include a child trisomic for chromosome 21. The analyses show the method to be highly reliable even when data from only one parent are available. With the increasing availability of DNA samples from mother and fetus, application of approaches such as ours should yield unprecedented insights into the genetic risk factors for aneuploidy. AVAILABILITY AND IMPLEMENTATION: An R package implementing TroX is available for download at http://przeworski.uchicago.edu/.

Evolutionary history inferred from the de novo assembly of a nonmodel organism, the blue-eyed black lemur.

Lemurs, the living primates most distantly related to humans, demonstrate incredible diversity in behaviour, life history patterns and adaptive traits. Although many lemur species are endangered within their native Madagascar, there is no high-quality genome assembly from this taxon, limiting population and conservation genetic studies. One critically endangered lemur is the blue-eyed black lemur Eulemur flavifrons. This species is fixed for blue irises, a convergent trait that evolved at least four times in primates and was subject to positive selection in humans, where 5' regulatory variation of OCA2 explains most of the brown/blue eye colour differences. We built a de novo genome assembly for E. flavifrons, providing the most complete lemur genome to date, and a high confidence consensus sequence for close sister species E. macaco, the (brown-eyed) black lemur. From diversity and divergence patterns across the genomes, we estimated a recent split time of the two species (160 Kya) and temporal fluctuations in effective population sizes that accord with known environmental changes. By looking for regions of unusually low diversity, we identified potential signals of directional selection in E. flavifrons at MITF, a melanocyte development gene that regulates OCA2 and has previously been associated with variation in human iris colour, as well as at several other genes involved in melanin biosynthesis in mammals. Our study thus illustrates how whole-genome sequencing of a few individuals can illuminate the demographic and selection history of nonmodel species.

Effect of epistasis and linkage on fixation probability in three-locus models: an ancestral recombination-selection graph approach.

We study the probability of ultimate fixation of a single new mutant arising in an individual chosen at random at a locus linked to two other loci carrying previously arisen mutations. This is done using the Ancestral Recombination-Selection Graph (ARSG) in a finite population in the limit of a large population size, which is also known as the Ancestral Influence Graph (AIG). An analytical expansion of the fixation probability with respect to population-scaled recombination rates and selection intensities is obtained. The coefficients of the expansion are expressed in terms of the initial state of the population and the epistatic interactions among the selected loci. Under the assumption of weak selection at tightly linked loci, the sign of the leading term, which depends on the signs of epistasis and initial linkage disequilibrium, determines whether an increase in recombination rates increases the chance of ultimate fixation of the new mutant. If mutants are advantageous, this is the case when epistasis is positive or null and the initial linkage disequilibrium is negative, which is an expected state in a finite population under directional selection. Moreover, this is also the case for a neutral mutant modifier coding for higher recombination rates if the same conditions hold at the selected loci. Under the same conditions, deleterious mutants are disfavored for ultimate fixation and neutral modifiers for higher recombination rates still favored. The recombination rates between the modifier locus and the selected loci do not come into play in the leading terms of the approximation for the fixation probability, but they do in higher-order terms.

Finite populations, finite resources, and the evolutionary maintenance of genetic recombination.

Most previous models for the evolution of sex implicitly assume infinite population sizes and limitless resources. However, because favorable mutations are very rare and eukaryotic populations are finite, it has already been shown that multiple favorable mutants virtually never occur by chance. Therefore, sex is required to combine different favorable mutations into a single lineage. Second, we show that even when multiple favorable mutations do coexist, competition between genotypes can create negative epistasis for fitness, thus favoring recombination. Competition is especially effective when selection is at the level of viability in K-selected species living in a resource-limited environment. This means that recombination is advantageous both for incorporating new favorable mutations into the gene pool and for accelerating their increase to fixation. These advantages of recombination are diminished, however, as genome sizes decrease or as the amount of competition within the species is a less important component of selection.

A Prospective Analysis of Genetic Variants Associated with Human Lifespan.

We present a massive investigation into the genetic basis of human lifespan. Beginning with a genome-wide association (GWA) study using a de-identified snapshot of the unique AncestryDNA database - more than 300,000 genotyped individuals linked to pedigrees of over 400,000,000 people - we mapped six genome-wide significant loci associated with parental lifespan. We compared these results to a GWA analysis of the traditional lifespan proxy trait, age, and found only one locus, APOE, to be associated with both age and lifespan. By combining the AncestryDNA results with those of an independent UK Biobank dataset, we conducted a meta-analysis of more than 650,000 individuals and identified fifteen parental lifespan-associated loci. Beyond just those significant loci, our genome-wide set of polymorphisms accounts for up to 8% of the variance in human lifespan; this value represents a large fraction of the heritability estimated from phenotypic correlations between relatives.

Joint stationary moments of a two-island diffusion model of population subdivision.

An expression for joint stationary moments of a diffusion approximation to a generalized Wright-Fisher model, corresponding to two finite populations of equal sizes, with migration and mutation, is derived. This gives a complete description of the stationary distribution of allele frequencies in the balance between migration, mutation and genetic drift. We derive the sampling formula in terms of the joint stationary moments, and we also prove that the diffusion process corresponding to this model of population division is not reversible.

Estimates of the Heritability of Human Longevity Are Substantially Inflated due to Assortative Mating.

Human life span is a phenotype that integrates many aspects of health and environment into a single ultimate quantity: the elapsed time between birth and death. Though it is widely believed that long life runs in families for genetic reasons, estimates of life span "heritability" are consistently low (∼15-30%). Here, we used pedigree data from Ancestry public trees, including hundreds of millions of historical persons, to estimate the heritability of human longevity. Although "nominal heritability" estimates based on correlations among genetic relatives agreed with prior literature, the majority of that correlation was also captured by correlations among nongenetic (in-law) relatives, suggestive of highly assortative mating around life span-influencing factors (genetic and/or environmental). We used structural equation modeling to account for assortative mating, and concluded that the true heritability of human longevity for birth cohorts across the 1800s and early 1900s was well below 10%, and that it has been generally overestimated due to the effect of assortative mating.

Clustering of 770,000 genomes reveals post-colonial population structure of North America.

Despite strides in characterizing human history from genetic polymorphism data, progress in identifying genetic signatures of recent demography has been limited. Here we identify very recent fine-scale population structure in North America from a network of over 500 million genetic (identity-by-descent, IBD) connections among 770,000 genotyped individuals of US origin. We detect densely connected clusters within the network and annotate these clusters using a database of over 20 million genealogical records. Recent population patterns captured by IBD clustering include immigrants such as Scandinavians and French Canadians; groups with continental admixture such as Puerto Ricans; settlers such as the Amish and Appalachians who experienced geographic or cultural isolation; and broad historical trends, including reduced north-south gene flow. Our results yield a detailed historical portrait of North America after European settlement and support substantial genetic heterogeneity in the United States beyond that uncovered by previous studies.

Fixation probability in a two-locus model by the ancestral recombination-selection graph.

We use the ancestral influence graph (AIG) for a two-locus, two-allele selection model in the limit of a large population size to obtain an analytic approximation for the probability of ultimate fixation of a single mutant allele A. We assume that this new mutant is introduced at a given locus into a finite population in which a previous mutant allele B is already segregating with a wild type at another linked locus. We deduce that the fixation probability increases as the recombination rate increases if allele A is either in positive epistatic interaction with B and allele B is beneficial or in no epistatic interaction with B and then allele A itself is beneficial. This holds at least as long as the recombination fraction and the selection intensity are small enough and the population size is large enough. In particular this confirms the Hill-Robertson effect, which predicts that recombination renders more likely the ultimate fixation of beneficial mutants at different loci in a population in the presence of random genetic drift even in the absence of epistasis. More importantly, we show that this is true from weak negative epistasis to positive epistasis, at least under weak selection. In the case of deleterious mutants, the fixation probability decreases as the recombination rate increases. This supports Muller's ratchet mechanism to explain the accumulation of deleterious mutants in a population lacking recombination.