Conditions for the validity of SNP-based heritability estimation

The estimation of additive genetic variance of body size in a wild passerine is sensitive to the method used to estimate relatedness among the individuals

Assessing additive genetic variance is a crucial step in predicting the evolutionary response of a target trait. However, the estimated genetic variance may be sensitive to the methodology used, e.g., the way relatedness is assessed among the individuals, especially in wild populations where social pedigrees can be inaccurate. To investigate this possibility, we investigated the additive genetic variance in tarsus length, a major proxy of skeletal body size in birds. The model species was the collared flycatcher (Ficedula albicollis), a socially monogamous but genetically polygamous migratory passerine. We used two relatedness matrices to estimate the genetic variance: (1) based solely on social links and (2) a genetic similarity matrix based on a large array of single-nucleotide polymorphisms (SNPs). Depending on the relatedness matrix considered, we found moderate to high additive genetic variance and heritability estimates for tarsus length. In particular, the heritability estimates were higher when obtained with the genetic similarity matrix instead of the social pedigree. Our results confirm the potential for this crucial trait to respond to selection and highlight methodological concerns when calculating additive genetic variance and heritability in phenotypic traits. We conclude that using a social pedigree instead of a genetic similarity matrix to estimate relatedness among individuals in a genetically polygamous wild population may significantly deflate the estimates of additive genetic variation.

Biobank-scale methods and projections for sparse polygenic prediction from machine learning

In this paper we characterize the performance of linear models trained via widely-used sparse machine learning algorithms. We build polygenic scores and examine performance as a function of training set size, genetic ancestral background, and training method. We show that predictor performance is most strongly dependent on size of training data, with smaller gains from algorithmic improvements. We find that LASSO generally performs as well as the best methods, judged by a variety of metrics. We also investigate performance characteristics of predictors trained on one genetic ancestry group when applied to another. Using LASSO, we develop a novel method for projecting AUC and correlation as a function of data size (i.e., for new biobanks) and characterize the asymptotic limit of performance. Additionally, for LASSO (compressed sensing) we show that performance metrics and predictor sparsity are in agreement with theoretical predictions from the Donoho-Tanner phase transition. Specifically, a future predictor trained in the Taiwan Precision Medicine Initiative for asthma can achieve an AUC of [Formula: see text] and for height a correlation of [Formula: see text] for a Taiwanese population. This is above the measured values of [Formula: see text] and [Formula: see text], respectively, for UK Biobank trained predictors applied to a European population.

Estimating heritability of song considering within-individual variance in a wild songbird: The collared flycatcher

Heritable genetic variation is a prerequisite for adaptive evolution; however, our knowledge about the heritability of plastic traits, such as behaviors, is scarce, especially in wild populations. In this study, we investigated the heritability of song traits in the collared flycatcher (Ficedula albicollis), a small oscine passerine with complex songs involved in sexual selection. We recorded the songs of 81 males in a natural population and obtained various measures describing the frequency, temporal organization, and complexity of each song. As we had multiple songs from each individual, we were able to statistically account for the first time for the effect of within-individual variance on the heritability of song. Heritability was calculated from the variance estimates of animal models relying on a genetic similarity matrix based on Single Nucleotide Polymorphism screening. Overall, we found small additive genetic variance and heritability values in all song traits, highlighting the role of environmental factors in shaping bird song.

Multivariate estimation of factor structures of complex traits using SNP-based genomic relationships

Background

Heritability and genetic correlation can be estimated from genome-wide single-nucleotide polymorphism (SNP) data using various methods. We recently developed multivariate genomic-relatedness-based restricted maximum likelihood (MGREML) for statistically and computationally efficient estimation of SNP-based heritability (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h^2_{\text{SNP}}$$\end{document}hSNP2) and genetic correlation (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _G$$\end{document}ρG) across many traits in large datasets. Here, we extend MGREML by allowing it to fit and perform tests on user-specified factor models, while preserving the low computational complexity.

Results

Using simulations, we show that MGREML yields consistent estimates and valid inferences for such factor models at low computational cost (e.g., for data on 50 traits and 20,000 individuals, a saturated model involving 50 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h^2_{\text{SNP}}$$\end{document}hSNP2’s, 1225 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _G$$\end{document}ρG’s, and 50 fixed effects is estimated and compared to a restricted model in less than one hour on a single notebook with two 2.7 GHz cores and 16 GB of RAM). Using repeated measures of height and body mass index from the US Health and Retirement Study, we illustrate the ability of MGREML to estimate a factor model and test whether it fits the data better than a nested model. The MGREML tool, the simulation code, and an extensive tutorial are freely available at https://github.com/devlaming/mgreml/.

Conclusion

MGREML can now be used to estimate multivariate factor structures and perform inferences on such factor models at low computational cost. This new feature enables simple structural equation modeling using MGREML, allowing researchers to specify, estimate, and compare genetic factor models of their choosing using SNP data.

Genetic and environmental contributions to IQ in adoptive and biological families with 30-year-old offspring

While adoption studies have provided key insights into the influence of the familial environment on IQ scores of adolescents and children, few have followed adopted offspring long past the time spent living in the family home. To improve confidence about the extent to which shared environment exerts enduring effects on IQ, we estimated genetic and environmental effects on adulthood IQ in a unique sample of 486 biological and adoptive families. These families, tested previously on measures of IQ when offspring averaged age 15, were assessed a second time nearly two decades later ( M offspring age = 32 years). We estimated the proportions of the variance in IQ attributable to environmentally mediated effects of parental IQs, sibling-specific shared environment, and gene-environment covariance to be .01 [95% CI .00, .02], .04 [95% CI .00, .15], and .03 [95% CI .00, .07] respectively; these components jointly accounted for 8 percent of the IQ variance in adulthood. The heritability was estimated to be .42 [95% CI .21, .64]. Together, these findings provide further evidence for the predominance of genetic influences on adult intelligence over any other systematic source of variation.

8q24 genetic variation and comprehensive haplotypes altering familial risk of prostate cancer

The 8q24 genomic locus is tied to the origin of numerous cancers. We investigate its contribution to hereditary prostate cancer (HPC) in independent study populations of the Nashville Familial Prostate Cancer Study and International Consortium for Prostate Cancer Genetics (combined: 2,836 HPC cases, 2,206 controls of European ancestry). Here we report 433 variants concordantly associated with HPC in both study populations, accounting for 9% of heritability and modifying age of diagnosis as well as aggressiveness; 183 reach genome-wide significance. The variants comprehensively distinguish independent risk-altering haplotypes overlapping the 648 kb locus (three protective, and four risk (peak odds ratios: 1.5, 4, 5, and 22)). Sequence of the near-Mendelian haplotype reveals eleven causal mutation candidates. We introduce a linkage disequilibrium-based algorithm discerning eight independent sentinel variants, carrying considerable risk prediction ability (AUC = 0.625) for a single locus. These findings elucidate 8q24 locus structure and correlates for clinical prediction of prostate cancer risk.

Biologically Defined or Biologically Informed Traits Are More Heritable Than Clinically Defined Ones: The Case of Oral and Dental Phenotypes

The genetic basis of oral health has long been theorized, but little information exists on the heritable variance in common oral and dental disease traits explained by the human genome. We sought to add to the evidence base of heritability of oral and dental traits using high-density genotype data in a well-characterized community-based cohort of middle-age adults. We used genome-wide association (GWAS) data combined with clinical and biomarker information in the Dental Atherosclerosis Risk In Communities (ARIC) cohort. Genotypes comprised SNPs directly typed on the Affymetrix Genome-Wide Human SNP Array 6.0 chip with minor allele frequency of >5% (n = 656,292) or were imputed using HapMap II-CEU (n = 2,104,905). We investigated 30 traits including "global" [e.g., number of natural teeth (NT) and incident tooth loss], clinically defined (e.g., dental caries via the DMFS index, periodontitis via the CDC/AAP and WW17 classifications), and biologically informed (e.g., subgingival pathogen colonization and "complex" traits). Heritability (i.e., variance explained; h²) was calculated using Visscher's Genome-wide Complex Trait Analysis (GCTA), using a random-effects mixed linear model and restricted maximum likelihood (REML) regression adjusting for ancestry (10 principal components), age, and sex. Heritability estimates were modest for clinical traits-NT = 0.11 (se = 0.07), severe chronic periodontitis (CDC/AAP) = 0.22 (se = 0.19), WW17 Stage 4 vs. 1/2 = 0.15 (se = 0.11). "High gingival index" and "high red complex colonization" had h² > 0.50, while a periodontal complex trait defined by high IL-1β GCF expression and Aggregatibacter actinomycetemcomitans subgingival colonization had the highest h² = 0.72 (se = 0.32). Our results indicate that all GWAS SNPs explain modest levels of the observed variance in clinical oral and dental measures. Subgingival bacterial colonization and complex phenotypes encompassing both bacterial colonization and local inflammatory response had the highest heritability, suggesting that these biologically informed traits capture aspects of the disease process and are promising targets for genomics investigations, according to the notion of precision oral health.

Estimation of metabolic syndrome heritability in three large populations including full pedigree and genomic information

Metabolic syndrome is a complex human disorder characterized by a cluster of conditions (increased blood pressure, hyperglycemia, excessive body fat around the waist, and abnormal cholesterol or triglyceride levels). Any of these conditions increases the risk of serious disorders such as diabetes or cardiovascular disease. Currently, the degree of genetic regulation of this syndrome is under debate and partially unknown. The principal aim of this study was to estimate the genetic component and the common environmental effects in different populations using full pedigree and genomic information. We used three large populations (Gubbio, ARIC, and Ogliastra cohorts) to estimate the heritability of metabolic syndrome. Due to both pedigree and genotyped data, different approaches were applied to summarize relatedness conditions. Linear mixed models (LLM) using average information restricted maximum likelihood (AIREML) algorithm were applied to partition the variances and estimate heritability (h²) and common sib-household effect (c²). Globally, results obtained from pedigree information showed a significant heritability (h²: 0.286 and 0.271 in Gubbio and Ogliastra, respectively), whereas a lower, but still significant heritability was found using SNPs data ([Formula: see text]: 0.167 and 0.254 in ARIC and Ogliastra). The remaining heritability between h² and [Formula: see text] ranged between 0.031 and 0.237. Finally, the common environmental c² in Gubbio and Ogliastra were also significant accounting for about 11% of the phenotypic variance. Availability of different kinds of populations and data helped us to better understand what happened when heritability of metabolic syndrome is estimated and account for different possible confounding. Furthermore, the opportunity of comparing different results provided more precise and less biased estimation of heritability.

The causal influence of brain size on human intelligence: Evidence from within-family phenotypic associations and GWAS modeling

There exists a moderate correlation between MRI-measured brain size and the general factor of IQ performance (g), but the question of whether the association reflects a theoretically important causal relationship or spurious confounding remains somewhat open. Previous small studies (n < 100) looking for the persistence of this correlation within families failed to find a tendency for the sibling with the larger brain to obtain a higher test score. We studied the within-family relationship between brain volume and intelligence in the much larger sample provided by the Human Connectome Project (n = 1,022) and found a highly significant correlation (disattenuated ρ = 0.18, p < .001). We replicated this result in the Minnesota Center for Twin and Family Research (n = 2,698), finding a highly significant within-family correlation between head circumference and intelligence (disattenuated ρ = 0.19, p < .001). We also employed novel methods of causal inference relying on summary statistics from genome-wide association studies (GWAS) of head size (n ≈ 10,000) and measures of cognition (257,000 < n < 767,000). Using bivariate LD Score regression, we found a genetic correlation between intracranial volume (ICV) and years of education (EduYears) of 0.41 (p < .001). Using the Latent Causal Variable method, we found a genetic causality proportion of 0.72 (p < .001); thus the genetic correlation arises from an asymmetric pattern, extending to sub-significant loci, of genetic variants associated with ICV also being associated with EduYears but many genetic variants associated with EduYears not being associated with ICV. This is the pattern of genetic results expected from a causal effect of brain size on intelligence. These findings give reason to take up the hypothesis that the dramatic increase in brain volume over the course of human evolution has been the result of natural selection favoring general intelligence.

Genome-wide association studies on the phyllosphere microbiome: Embracing complexity in host-microbe interactions

Environmental sequencing shows that plants harbor complex communities of microbes that vary across environments. However, many approaches for mapping plant genetic variation to microbe-related traits were developed in the relatively simple context of binary host-microbe interactions under controlled conditions. Recent advances in sequencing and statistics make genome-wide association studies (GWAS) an increasingly promising approach for identifying the plant genetic variation associated with microbes in a community context. This review discusses early efforts on GWAS of the plant phyllosphere microbiome and the outlook for future studies based on human microbiome GWAS. A workflow for GWAS of the phyllosphere microbiome is then presented, with particular attention to how perspectives on the mechanisms, evolution and environmental dependence of plant-microbe interactions will influence the choice of traits to be mapped.

Exploring the genetic correlations of antisocial behaviour and life history traits

Prior evolutionary theory provided reason to suspect that measures of development and reproduction would be correlated with antisocial behaviours in human and non-human species. Behavioural genetics has revealed that most quantitative traits are heritable, suggesting that these phenotypic correlations may share genetic aetiologies. We use genome-wide association study data to estimate the genetic correlations between various measures of reproductive development (N = 52 776-318 863) and antisocial behaviour (N = 31 968). Our genetic correlation analyses demonstrate that alleles associated with higher reproductive output (number of children ever born, r _g = 0.50, P = 0.0065) were positively correlated with alleles associated with antisocial behaviour, whereas alleles associated with more delayed reproductive onset (age at first birth, r _g = -0.64, P = 0.0008) were negatively associated with alleles linked to antisocial behaviour. Ultimately, these findings coalesce with evolutionary theories suggesting that increased antisocial behaviours may partly represent a faster life history approach, which may be significantly calibrated by genes.

DECLARATION OF INTEREST

None.

Accurate Genomic Prediction of Human Height

We construct genomic predictors for heritable but extremely complex human quantitative traits (height, heel bone density, and educational attainment) using modern methods in high dimensional statistics (i.e., machine learning). The constructed predictors explain, respectively, ∼40, 20, and 9% of total variance for the three traits, in data not used for training. For example, predicted heights correlate ∼0.65 with actual height; actual heights of most individuals in validation samples are within a few centimeters of the prediction. The proportion of variance explained for height is comparable to the estimated common SNP heritability from genome-wide complex trait analysis (GCTA), and seems to be close to its asymptotic value (i.e., as sample size goes to infinity), suggesting that we have captured most of the heritability for SNPs. Thus, our results close the gap between prediction R-squared and common SNP heritability. The ∼20k activated SNPs in our height predictor reveal the genetic architecture of human height, at least for common variants. Our primary dataset is the UK Biobank cohort, comprised of almost 500k individual genotypes with multiple phenotypes. We also use other datasets and SNPs found in earlier genome-wide association studies (GWAS) for out-of-sample validation of our results.

The accuracy of LD Score regression as an estimator of confounding and genetic correlations in genome-wide association studies

To infer that a single-nucleotide polymorphism (SNP) either affects a phenotype or is linkage disequilibrium with a causal site, we must have some assurance that any SNP-phenotype correlation is not the result of confounding with environmental variables that also affect the trait. In this study, we study the properties of linkage disequilibrium (LD) Score regression, a recently developed method for using summary statistics from genome-wide association studies to ensure that confounding does not inflate the number of false positives. We do not treat the effects of genetic variation as a random variable and thus are able to obtain results about the unbiasedness of this method. We demonstrate that LD Score regression can produce estimates of confounding at null SNPs that are unbiased or conservative under fairly general conditions. This robustness holds in the case of the parent genotype affecting the offspring phenotype through some environmental mechanism, despite the resulting correlation over SNPs between LD Scores and the degree of confounding. Additionally, we demonstrate that LD Score regression can produce reasonably robust estimates of the genetic correlation, even when its estimates of the genetic covariance and the two univariate heritabilities are substantially biased.

Statistical properties of simple random-effects models for genetic heritability

Random-effects models are a popular tool for analysing total narrow-sense heritability for quantitative phenotypes, on the basis of large-scale SNP data. Recently, there have been disputes over the validity of conclusions that may be drawn from such analysis. We derive some of the fundamental statistical properties of heritability estimates arising from these models, showing that the bias will generally be small. We show that that the score function may be manipulated into a form that facilitates intelligible interpretations of the results. We go on to use this score function to explore the behavior of the model when certain key assumptions of the model are not satisfied - shared environment, measurement error, and genetic effects that are confined to a small subset of sites. The variance and bias depend crucially on the variance of certain functionals of the singular values of the genotype matrix. A useful baseline is the singular value distribution associated with genotypes that are completely independent - that is, with no linkage and no relatedness - for a given number of individuals and sites. We calculate the corresponding variance and bias for this setting.

Partitioning Phenotypic Variance Due to Parent-of-Origin Effects Using Genomic Relatedness Matrices

We propose a new method, G-REMLadp, to estimate the phenotypic variance explained by parent-of-origin effects (POEs) across the genome. Our method uses restricted maximum likelihood analysis of genome-wide genetic relatedness matrices based on individuals' phased genotypes. Genome-wide SNP data from parent child duos or trios is required to obtain relatedness matrices indexing the parental origin of offspring alleles, as well as offspring phenotype data to partition the trait variation into variance components. To calibrate the power of G-REMLadp to detect non-null POEs when they are present, we provide an analytic approximation derived from Haseman-Elston regression. We also used simulated data to quantify the power and Type I Error rates of G-REMLadp, as well as the sensitivity of its variance component estimates to violations of underlying assumptions. We subsequently applied G-REMLadp to 36 phenotypes in a sample of individuals from the Avon Longitudinal Study of Parents and Children (ALSPAC). We found that the method does not seem to be inherently biased in estimating variance due to POEs, and that substantial correlation between parental genotypes is necessary to generate biased estimates. Our empirical results, power calculations and simulations indicate that sample sizes over 10000 unrelated parent-offspring duos will be necessary to detect POEs explaining < 10% of the variance with moderate power. We conclude that POEs tagged by our genetic relationship matrices are unlikely to explain large proportions of the phenotypic variance (i.e. > 15%) for the 36 traits that we have examined.

SOME USES OF MODELS OF QUANTITATIVE GENETIC SELECTION IN SOCIAL SCIENCE

The theory of selection of quantitative traits is widely used in evolutionary biology, agriculture and other related fields. The fundamental model known as the breeder’s equation is simple, robust over short time scales, and it is often possible to estimate plausible parameters. In this paper it is suggested that the results of this model provide useful yardsticks for the description of social traits and the evaluation of transmission models. The differences on a standard personality test between samples of Old Order Amish and Indiana rural young men from the same county and the decline of homicide in Medieval Europe are used as illustrative examples of the overall approach. It is shown that the decline of homicide is unremarkable under a threshold model while the differences between rural Amish and non-Amish young men are too large to be a plausible outcome of simple genetic selection in which assortative mating by affiliation is equivalent to truncation selection.

On the reconciliation of missing heritability for genome-wide association studies

The definition of heritability has been unique and clear, but its estimation and estimates vary across studies. Linear mixed model (LMM) and Haseman-Elston (HE) regression analyses are commonly used for estimating heritability from genome-wide association data. This study provides an analytical resolution that can be used to reconcile the differences between LMM and HE in the estimation of heritability given the genetic architecture, which is responsible for these differences. The genetic architecture was classified into three forms via thought experiments: (i) coupling genetic architecture that the quantitative trait loci (QTLs) in the linkage disequilibrium (LD) had a positive covariance; (ii) repulsion genetic architecture that the QTLs in the LD had a negative covariance; (iii) and neutral genetic architecture that the QTLs in the LD had a covariance with a summation of zero. The neutral genetic architecture is so far most embraced, whereas the coupling and the repulsion genetic architecture have not been well investigated. For a quantitative trait under the coupling genetic architecture, HE overestimated the heritability and LMM underestimated the heritability; under the repulsion genetic architecture, HE underestimated but LMM overestimated the heritability for a quantitative trait. These two methods gave identical results under the neutral genetic architecture. A general analytical result for the statistic estimated under HE is given regardless of genetic architecture. In contrast, the performance of LMM remained elusive, such as further depended on the ratio between the sample size and the number of markers, but LMM converged to HE with increased sample size.

Application of linear mixed models to study genetic stability of height and body mass index across countries and time

Background: It is now possible to estimate genetic correlations between two independent samples when there is no overlapping phenotypic information. We applied the latest bivariate genomic methods to children in the UK and older adults in Sweden to ask two questions. Are the same variants driving individual differences in anthropometric traits in these two populations, and are these variants as important in childhood as they are later in life?

Methods: A sample of 3152 11-year-old children in the UK was compared with a sample of 6813 adults with an average age of 65 in Sweden. Genotypes were imputed from 1000 genomes with combined 9 767 136 single nucleotide polymorphisms meeting quality control criteria in both samples. Two cross-sample GCTA-GREML analyses and linkage disequilibrium (LD) score regressions were conducted to assess genetic correlations across more than 50 years: child versus adult height and child versus adult body mass index (BMI). Consistency of effects was tested using the recently proposed polygenic scoring method.

Results: For height, GCTA-GREML and LD score indicated strong genetic stability between children and adults, 0.58 (0.16) and 1.335 (1.09), respectively. For BMI, both methods produced similarly strong estimates of genetic stability 0.75 (0.26) and 0.855 (0.49), respectively. In height, adult polygenic score explained 60% of genetic variance in childhood and 10% of variance in BMI.

Conclusions: Here we replicated and extended previous findings of longitudinal genetic stability in anthropometric traits to cross-cultural dimensions, and showed that for height but not BMI these variants are as important in childhood as they are in adulthood.

Uncovering the Genetic Architectures of Quantitative Traits

The aim of a genome-wide association study (GWAS) is to identify loci in the human genome affecting a phenotype of interest. This review summarizes some recent work on conceptual and methodological aspects of GWAS. The average effect of gene substitution at a given causal site in the genome is the key estimand in GWAS, and we argue for its fundamental importance. Implicit in the definition of average effect is a linear model relating genotype to phenotype. The fraction of the phenotypic variance ascribable to polymorphic sites with nonzero average effects in this linear model is called the heritability, and we describe methods for estimating this quantity from GWAS data. Finally, we show that the theory of compressed sensing can be used to provide a sharp estimate of the sample size required to identify essentially all sites contributing to the heritability of a given phenotype.

Misspecification in Mixed-Model-Based Association Analysis

Additive genetic variance in natural populations is commonly estimated using mixed models, in which the covariance of the genetic effects is modeled by a genetic similarity matrix derived from a dense set of markers. An important but usually implicit assumption is that the presence of any nonadditive genetic effect increases only the residual variance and does not affect estimates of additive genetic variance. Here we show that this is true only for panels of unrelated individuals. In the case that there is genetic relatedness, the combination of population structure and epistatic interactions can lead to inflated estimates of additive genetic variance.

The genetics of early-onset bipolar disorder: A systematic review

BACKGROUND

Early-onset bipolar disorder has been associated with a significantly worse prognosis than late-onset BD and has been hypothesized to be a genetically homogenous subset of BD. A sizeable number of studies have investigated early-onset BD through linkage-analyses, candidate-gene association studies, genome-wide association studies (GWAS), and analyses of copy number variants (CNVs), but this literature has not yet been reviewed.

METHODS

A systematic review was conducted using the PubMed database on articles published online before January 15, 2015 and after 1990. Separate searches were made for linkage studies, candidate gene-association studies, GWAS, and studies on CNVs.

RESULTS

Seventy-three studies were included in our review. There is a lack of robust positive findings on the genetics of early-onset BD in any major molecular genetics method.

LIMITATIONS

Early-onset populations were quite small in some studies. Variance in study methods hindered efforts to interpret results or conduct meta-analysis.

CONCLUSIONS

The field is still at an early phase for research on early-onset BD. The largely null findings mirror the results of most genetics research on BD. Although most studies were underpowered, the null findings could mean that early-onset BD may not be as genetically homogenous as has been hypothesized or even that early-onset BD does not differ genetically from adult-onset BD. Nevertheless, clinically the probabilistic developmental risk trajectories associated with early-onset that may not be primarily genetically determined continued to warrant scrutiny. Future research should dramatically expand sample sizes, use atheoretical research methods like GWAS, and standardize methods.

The Fourth Law of Behavior Genetics

Behavior genetics is the study of the relationship between genetic variation and psychological traits. Turkheimer (2000) proposed "Three Laws of Behavior Genetics" based on empirical regularities observed in studies of twins and other kinships. On the basis of molecular studies that have measured DNA variation directly, we propose a Fourth Law of Behavior Genetics: "A typical human behavioral trait is associated with very many genetic variants, each of which accounts for a very small percentage of the behavioral variability." This law explains several consistent patterns in the results of gene discovery studies, including the failure of candidate gene studies to robustly replicate, the need for genome-wide association studies (and why such studies have a much stronger replication record), and the crucial importance of extremely large samples in these endeavors. We review the evidence in favor of the Fourth Law and discuss its implications for the design and interpretation of gene-behavior research.

Applying compressed sensing to genome-wide association studies

Background

The aim of a genome-wide association study (GWAS) is to isolate DNA markers for variants affecting phenotypes of interest. This is constrained by the fact that the number of markers often far exceeds the number of samples. Compressed sensing (CS) is a body of theory regarding signal recovery when the number of predictor variables (i.e., genotyped markers) exceeds the sample size. Its applicability to GWAS has not been investigated.

Results

Using CS theory, we show that all markers with nonzero coefficients can be identified (selected) using an efficient algorithm, provided that they are sufficiently few in number (sparse) relative to sample size. For heritability equal to one (h² = 1), there is a sharp phase transition from poor performance to complete selection as the sample size is increased. For heritability below one, complete selection still occurs, but the transition is smoothed. We find for h² ∼ 0.5 that a sample size of approximately thirty times the number of markers with nonzero coefficients is sufficient for full selection. This boundary is only weakly dependent on the number of genotyped markers.

Conclusion

Practical measures of signal recovery are robust to linkage disequilibrium between a true causal variant and markers residing in the same genomic region. Given a limited sample size, it is possible to discover a phase transition by increasing the penalization; in this case a subset of the support may be recovered. Applying this approach to the GWAS analysis of height, we show that 70-100% of the selected markers are strongly correlated with height-associated markers identified by the GIANT Consortium.