Ancestral haplotype reconstruction in endogamous populations using identity-by-descent.

In this work we develop a novel algorithm for reconstructing the genomes of ancestral individuals, given genotype or sequence data from contemporary individuals and an extended pedigree of family relationships. A pedigree with complete genomes for every individual enables the study of allele frequency dynamics and haplotype diversity across generations, including deviations from neutrality such as transmission distortion. When studying heritable diseases, ancestral haplotypes can be used to augment genome-wide association studies and track disease inheritance patterns. The building blocks of our reconstruction algorithm are segments of Identity-By-Descent (IBD) shared between two or more genotyped individuals. The method alternates between identifying a source for each IBD segment and assembling IBD segments placed within each ancestral individual. Unlike previous approaches, our method is able to accommodate complex pedigree structures with hundreds of individuals genotyped at millions of SNPs. We apply our method to an Old Order Amish pedigree from Lancaster, Pennsylvania, whose founders came to North America from Europe during the early 18th century. The pedigree includes 1338 individuals from the past 12 generations, 394 with genotype data. The motivation for reconstruction is to understand the genetic basis of diseases segregating in the family through tracking haplotype transmission over time. Using our algorithm thread, we are able to reconstruct an average of 224 ancestral individuals per chromosome. For these ancestral individuals, on average we reconstruct 79% of their haplotypes. We also identify a region on chromosome 16 that is difficult to reconstruct-we find that this region harbors a short Amish-specific copy number variation and the gene HYDIN. thread was developed for endogamous populations, but can be applied to any extensive pedigree with the recent generations genotyped. We anticipate that this type of practical ancestral reconstruction will become more common and necessary to understand rare and complex heritable diseases in extended families.

A population genetic interpretation of GWAS findings for human quantitative traits.

Human genome-wide association studies (GWASs) are revealing the genetic architecture of anthropomorphic and biomedical traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architecture is shaped by basic population genetics processes-notably, by mutation, natural selection, and genetic drift. Because many quantitative traits are subject to stabilizing selection and because genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabilizing selection in a multidimensional trait space. We solve the model for the phenotypic distribution and allelic dynamics at steady state and derive robust, closed-form solutions for summary statistics of the genetic architecture. Our results provide a simple interpretation for missing heritability and why it varies among traits. They predict that the distribution of variances contributed by loci identified in GWASs is well approximated by a simple functional form that depends on a single parameter: the expected contribution to genetic variance of a strongly selected site affecting the trait. We test this prediction against the results of GWASs for height and body mass index (BMI) and find that it fits the data well, allowing us to make inferences about the degree of pleiotropy and mutational target size for these traits. Our findings help to explain why the GWAS for height explains more of the heritable variance than the similarly sized GWAS for BMI and to predict the increase in explained heritability with study sample size. Considering the demographic history of European populations, in which these GWASs were performed, we further find that most of the associations they identified likely involve mutations that arose shortly before or during the Out-of-Africa bottleneck at sites with selection coefficients around s = 10-3.

Correction: The population genetics of human disease: The case of recessive, lethal mutations.

[This corrects the article DOI: 10.1371/journal.pgen.1006915.].

The population genetics of human disease: The case of recessive, lethal mutations.

Do the frequencies of disease mutations in human populations reflect a simple balance between mutation and purifying selection? What other factors shape the prevalence of disease mutations? To begin to answer these questions, we focused on one of the simplest cases: recessive mutations that alone cause lethal diseases or complete sterility. To this end, we generated a hand-curated set of 417 Mendelian mutations in 32 genes reported to cause a recessive, lethal Mendelian disease. We then considered analytic models of mutation-selection balance in infinite and finite populations of constant sizes and simulations of purifying selection in a more realistic demographic setting, and tested how well these models fit allele frequencies estimated from 33,370 individuals of European ancestry. In doing so, we distinguished between CpG transitions, which occur at a substantially elevated rate, and three other mutation types. Intriguingly, the observed frequency for CpG transitions is slightly higher than expectation but close, whereas the frequencies observed for the three other mutation types are an order of magnitude higher than expected, with a bigger deviation from expectation seen for less mutable types. This discrepancy is even larger when subtle fitness effects in heterozygotes or lethal compound heterozygotes are taken into account. In principle, higher than expected frequencies of disease mutations could be due to widespread errors in reporting causal variants, compensation by other mutations, or balancing selection. It is unclear why these factors would have a greater impact on disease mutations that occur at lower rates, however. We argue instead that the unexpectedly high frequency of disease mutations and the relationship to the mutation rate likely reflect an ascertainment bias: of all the mutations that cause recessive lethal diseases, those that by chance have reached higher frequencies are more likely to have been identified and thus to have been included in this study. Beyond the specific application, this study highlights the parameters likely to be important in shaping the frequencies of Mendelian disease alleles.

Conditional frequency spectra as a tool for studying selection on complex traits in biobanks.

Natural selection on complex traits is difficult to study in part due to the ascertainment inherent to genome-wide association studies (GWAS). The power to detect a trait-associated variant in GWAS is a function of frequency and effect size - but for traits under selection, the effect size of a variant determines the strength of selection against it, constraining its frequency. To account for GWAS ascertainment, we propose studying the joint distribution of allele frequencies across populations, conditional on the frequencies in the GWAS cohort. Before considering these conditional frequency spectra, we first characterized the impact of selection and non-equilibrium demography on allele frequency dynamics forwards and backwards in time. We then used these results to understand conditional frequency spectra under realistic human demography. Finally, we investigated empirical conditional frequency spectra for GWAS variants associated with 106 complex traits, finding compelling evidence for either stabilizing or purifying selection. Our results provide insight into polygenic score portability and other properties of variants ascertained with GWAS, highlighting the utility of conditional frequency spectra.

The impact of recent population history on the deleterious mutation load in humans and close evolutionary relatives.

Over the past decade, there has been both great interest and confusion about whether recent demographic events-notably the Out-of-Africa-bottleneck and recent population growth-have led to differences in mutation load among human populations. The confusion can be traced to the use of different summary statistics to measure load, which lead to apparently conflicting results. We argue, however, that when statistics more directly related to load are used, the results of different studies and data sets consistently reveal little or no difference in the load of non-synonymous mutations among human populations. Theory helps to understand why no such differences are seen, as well as to predict in what settings they are to be expected. In particular, as predicted by modeling, there is evidence for changes in the load of recessive loss of function mutations in founder and inbred human populations. Also as predicted, eastern subspecies of gorilla, Neanderthals and Denisovans, who are thought to have undergone reductions in population sizes that exceed the human Out-of-Africa bottleneck in duration and severity, show evidence for increased load of non-synonymous mutations (relative to western subspecies of gorillas and modern humans, respectively). A coherent picture is thus starting to emerge about the effects of demographic history on the mutation load in populations of humans and close evolutionary relatives.

The deleterious mutation load is insensitive to recent population history.

Human populations have undergone major changes in population size in the past 100,000 years, including recent rapid growth. How these demographic events have affected the burden of deleterious mutations in individuals and the frequencies of disease mutations in populations remains unclear. We use population genetic models to show that recent human demography has probably had little impact on the average burden of deleterious mutations. This prediction is supported by two exome sequence data sets showing that individuals of west African and European ancestry carry very similar burdens of damaging mutations. We further show that for many diseases, rare alleles are unlikely to contribute a large fraction of the heritable variation, and therefore the impact of recent growth is likely to be modest. However, for those diseases that have a direct impact on fitness, strongly deleterious rare mutations probably do have an important role, and recent growth will have increased their impact.

Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa pendulum.

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped nonlinear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the "Kapitsa pendulum" effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.