Rare and Common Variants: Twenty arguments

Abstract

Genome-wide association studies have greatly improved our understanding of the genetic basis of disease risk. The fact that they tend not to identify more than a fraction of the specific causal loci has led to divergence of opinion over whether most of the variance is hidden as numerous rare variants of large effect, or common variants of very small effect. Here I review 20 arguments for and against each of these models of the genetic basis of complex traits, and conclude that both classes of effect can be reconciled readily.

Soon after the ascension of genome-wide association studies (GWAS) as the pre-eminent tool for discovering polymorphic genes that influence disease susceptibility and quantitative traits, the field of genetics developed three major outlooks on the architecture of complex traits. When GWAS began the field was dominated by the simple common disease-common variant (CD-CV) hypothesis^1–4 has been refuted in light of the so-called ‘missing heritability problem’, namely the observation that loci detected by GWAS almost without exception explain a small minority of the inferred genetic variance^5,6: it is simply not the case that a few dozen loci of moderate effect and intermediate frequency each explain several percent of disease risk in a population, as is typically observed in crosses or pedigrees. Since then, the genetic component has been attributed instead to one of three causes: a large number of small-effect common variants across the entire allele frequency spectrum (the infinitesimal model)^7,8, a large number of large-effect rare variants (the rare allele model)⁹, or some combination of genotypic, environmental and epigenetic interactions (the broad-sense heritability model)^10,11. Figure 1 shows the expected distribution of genome-wide association profiles under each of these three models and the CD-CV model.

Figure 1. Different expected signatures from GWAS for four models of disease.

Each plot shows the approximate expected distribution of SNP effects for a modest study of 2,000 cases and controls. The Y-axis is the percent of the variance for a trait or disease liability in the population explained by each SNP (note that standard Manhattan plots typically show the significance instead, represented as the negative log10 of the p-value) and the X-axis is the location of tens of thousands of SNPs along the chromosome. In the common disease-common variant (CD-CV) model, a small number of moderate effect loci would produce very strong signals, each of which explains several percent of the genetic variance. Note the expanded scale of the y-axis here relative to the other plots. In the rare allele model, causal variant effects (yellow dots) may be large in a few individuals but are not common enough to explain much variance or result in genome-wide significance. The infinitesimal model by contrast does produce some significant peaks due to small effects of common variants, and in each case several SNPs within an LD-block associate with the trait. Finally, it can be argued that if associations are only seen in some environments (green and orange signals, bottom right), then in a mixed population the overall effect will be reduced at such loci (arrowheads), and fewer associations will be detected, explaining less of the variance.

GWAS are neither powered nor designed to detect variation under any of these models on a consistent basis, so there is as yet insufficient empirical data to resolve the debate. In all likelihood, each of the three genetic architectures contributes, possibly to different degrees, to different diseases or traits. However, since the heritability of risk is generally estimated as narrow sense variance, interaction effects should be considered secondary to the main effects of common and rare variants. The purpose of this article is therefore to review 20 arguments that support or refute the infinitesimal and rare allele models. This is not a comprehensive survey, but rather an overview of five arguments in favour and five arguments against each of these two models, drawn from theory and data from diverse categories of disease. Table 1 lists each of the arguments, roughly according to their relative strength.

Table 1.

The 20 Arguments

For Rare Alleles

Evolutionary theory predicts that disease alleles should be rare.

Empirical population genetic data shows that deleterious variants are rare.

Rare copy number variants contribute to several complex psychological disorders.

Many rare familial disorders are due to rare alleles of large effect.

Synthetic associations may explain common variant effects.

Con Rare Alleles

Simulation of GWAS is not consistent with rare variant explanations.

GWAS associations are consistent across populations.

Sibling recurrence rates are greater than postulated rare variant effect sizes.

Epidemiological transitions cannot be attributed to rare variants.

Rare variants do not obviously have additive effects.

For Common Alleles

GWAS has successfully identified thousands of common variants.

Model organism research supports common variant contributions to complex phenotypes.

Variation in endophenotypes is almost certainly due to common variants.

The infinitesimal model is standard quantitative genetic theory.

Common variants collectively capture the majority of the genetic variance in GWAS.

Con Common Alleles

What accounts for the missing heritability?

Demographic phenomena suggest more than a simple common variant model.

The QTL paradox.

Absence of blending inheritance.

Very few common variants for disease have been functionally validated.

The Models

Infinitesimal model: many variants of small effect

By infinitesimal model, I mean the proposition that common variants are among the major source of genetic variance for disease susceptibility and continuous traits, where hundreds or thousands of loci contribute in each case. The loci detected by GWAS are merely the largest effect sizes drawn from a Poisson or similar distribution. If half a dozen common variants explain 10% of risk in the population, the remainder is attributable to a myriad of variants that each explain considerably less than 1% and have genotype relative risks less than 1.1¹². Figure 2a shows that affected individuals will tend to carry a slight excess of risk variants, since the overall distribution of the number of risk alleles per affected individual is skewed relative to unaffecteds. If these follow the same distribution of allele frequencies as neutral variation, then they will include a large number of rare variants as well. Ultimately, every gene contributes to every trait, but with effect sizes so small that it would take samples greater than the population size of the species to detect them. In practice, as shown by the massive meta-analyses of GWAS for height and body mass index (BMI)^13,14, each involving several hundred thousand people, it is unlikely that more than a few hundred loci will ever be confirmed for most diseases, and these will not necessarily explain even half of the genetic variance. The term infinitesimal borrows from the initial formulation of quantitative genetic theory by RA Fisher⁷. Here it simply signifies the idea that the heritability is not so much missing, as hidden beneath the significance thresholds used to define risk alleles with high confidence¹⁵.

Figure 2. Expected distribution of Risk Variants.

(a) The approximate frequency distribution of risk alleles in cases (blue) and controls (red) under the infinitesimal model for a disease with high heritability and 10% prevalence. For this particular parameterization I assumed 200 loci with risk allele frequencies from 0.1 to 0.9, but skewed toward lower frequencies. Each risk allele is assumed to increase the probability of disease additively by 1.04 relative to the overall risk of 10%. The frequency distribution in cases is skewed to the right, but note that the median number of risk alleles in affected individuals is only slightly greater than in unaffecteds. (b) An approximate frequency distribution of risk allele frequencies under a multiplicative rare allele model for a disease with high heritability and 1% prevalence. This parameterization assumes 100 loci, each with a risk allele frequency of 1%, such that each risk allele increases the probability of disease 2.5 fold over a background risk of 0.2%. The vast majority of unaffecteds carry at least one allele (the yellow bar show the expected number of individuals without any risk alleles). The inset shows the same figure on the log scale, emphasizing how relative risk increases with the number of variants carried. Note that the measured per allele GRR across the population in the presence of 100 other alleles is ~1.15, much smaller than the 2.5 fold multiplicative risk due to a single variant. For higher risks (say 5-fold) and 100 alleles, the frequencies must be very rare (~0.1%) for a disease prevalence of 1%, and affecteds will only carry one or two risk alleles.

Rare allele model: many rare alleles of large effect

The alternative view is that most of the variance for certain complex diseases is due to relatively highly penetrant rare variants, the allele frequency of which is typically less than 1%, most of which are recently derived alleles in the human population. Under this model, expressivity may be modified by other loci or the environment^16,17, but the notion is that the rare susceptibility genotype is largely responsible for disease. The rare allele model generally refers to dominant effects, due either to haploinsufficient or gain of function alleles, where risk is elevated 2-fold or more over background. Under these conditions, penetrance need not be anywhere near 100%. In fact, as shown in Figure 2b, the vast majority of unaffected individuals are expected to carry one or more risk alleles. The notion is that a disease such as schizophrenia is actually a collection of hundreds, or possibly even thousands, of similar conditions attributable to rare variants at individual loci¹⁸. If each of these variants explains most of the risk in just a handful of people, their effects will not explain enough of the variance in a total population to be detected by standard GWAS procedures. The total number of loci that may contribute to any disease is a function of the baseline disease incidence, the number of rare variants per locus, and the genotypic relative risk (GRR, namely, effect size). For a disease with a high heritability of 80%, theory indicates that the number of contributing loci can range from over 500 with GRR of just 2 and one very rare variant per locus, to just a dozen loci with GRR of 5 and allele frequencies of 1% or if the disease is relatively common¹⁹.

Broad-sense heritability model: non-additive GxG and GxE interactions, and epigenetic effects

The broad-sense heritability model posits that additive contributions of common variants and large effects of rare variants are insufficient to explain the missing heritability. Proponents of this model point to a long history of detection of genotype-by-genotype interactions (epistasis) and genotype-by-environment interactions (G×E) in model organism quantitative genetic research^20,21, and note the increasing number of studies documenting epigenetic effects²², notably parent-of-origin genetic contributions^23,24 and inheritance of DNA methylation patterns²⁵. The notion here is that since GWAS only measure the average effects of alleles across thousands of individuals, they are incapable of capturing heterogeneity of effect sizes at the family level that would be the hallmark of these broader components of the genetic architecture. Although broad-sense heritability is not considered further in this article (but see Box 1), I do not disregard its potential contribution. Rather, my purpose here is to contrast the two narrow sense models, as resolution of their contributions lays the foundation for consideration of other genetic mechanisms.

Box 1. Broad Sense Heritability Models.

Phenotypic variance is traditionally decomposed into genetic and environmental components, and heritability is defined as the ratio of the genetic to the total phenotypic variance, in a population⁸. The genetic component of phenotypic variance can be further decomposed into additive, dominance, and interaction effects. The additive component is the average effect of substituting one allele for the other, irrespective of whether dominance is present, namely whether the heterozygotes are closer in phenotype to one class of homozygote.

‘Broad sense heritability’ refers to the genetic effect including non-additive components, such as genotype-by-genotype interactions, also known as epistasis, genotype-by-environment interactions (G×E), and epigenetics. Epigenetics refers to the impact of chromatin modification on the effect of a genotype through DNA methylation, alteration of the histone code and, some would argue, microRNA expression.

Genome-wide association studies (GWAS) are not generally powered to detect epistasis or G×E¹²¹, and they are not designed to detect epigenetic influences¹²² (although recent sampling designs to detect parent-of-origin associations do provide evidence for them²³). There are two major obstacles to detecting epistasis: very large samples are required to find sufficient individuals of each genotype combination to accurately measure small effects, and the number of comparisons scales exponentially with the number of interactions so the testing burden is enormous. Additionally, epistatic effects are generally thought to be likely to be small relative to main effects, and the GWAS literature provides few examples of departure from additivity. Similarly, there is as yet little evidence for environmental modification of genotype effects: a recent example relating to the protective effect of coffee consumption and Parkinson’s disease risk provides an exception¹⁰⁸. One of the difficulties may be that the environment is difficult to define and measure, and it may be unique individual exposures that are more important than exposures shared by thousands of people.

A particular class of genetic interaction that has yet to attract full attention is deleterious intergenic compound heterozygosity, namely interactions between multiple rare variants that lead to disease. Whether and how often such interactions extend to heterozygous combinations of alleles has considerable implications for the potential of broad sense heritability to be a major component of disease susceptibility. If hundreds of mutations each at a frequency of less than 1% all affect a particular disease, then many more people will be doubly or triply heterozygous for various combinations, than are homozygous for any one variant. It is not known how often heterozygotes that individually do not associate with disease would be deleterious in combination. Synthetic genetic interaction screens in yeast^123,124 have demonstrated that thousands of combinations of individually viable mutations can jointly be lethal, and similar examples have been documented in Drosophila melanogaster and Caenorhabditis elegans^125,126.

Arguments in favour of the rare allele model

Evolutionary theory predicts that disease alleles should be rare

Perhaps the strongest argument for the rare allele model comes from evolutionary theory. Since disease is deleterious to fitness, variants that promote disease should be selected against, and hence disease-promoting variants should not be common^3,26,27. The existence of disease-promoting variants reflects the balance between mutation creating new susceptibility variants, and selection preventing them from drifting into the population^2,28. Mutation rates are sufficiently large that purifying selection cannot remove all deleterious variants, and those that have a modest effect on fitness (for example, if they influence late-onset diseases ²⁹) may rise to allele frequencies of 1% or occasionally more, particularly if the effect is recessive. But selection is sufficiently efficient that even a fitness reduction of a fraction of a percent will keep allele frequencies from reaching common levels. The argument has been made that relaxed selection in modern humans may favor the accumulation of deleterious rare alleles, greatly increasing the prevalence of disease hundreds of generations into the future³⁰.

Empirical population genetic data shows that deleterious variants are rare

It has been appreciated for some time that the distribution of minor allele frequencies (MAFs) is strongly skewed towards an excess of rare variants: over a third of all polymorphisms have frequencies below 5%³¹. Multiple factors contribute to this skewed distribution, but the finding from whole-exome sequence data that non-synonymous substitutions are even more significantly skewed towards low frequencies almost certainly reflects the operation of purifying selection^32–34. As a class, amino acid substitutions appear to be deleterious. It need not follow that the reduction in fitness is due to promotion of chronic disease, and the observation does not equate to saying that all rare non-synonymous variants are deleterious. However, the finding is consistent with the theory that selection keeps fitness-reducing alleles at a large proportion of genes at low frequency³⁵. It remains to be seen whether the same is true of regulatory polymorphisms^36,37, since (despite the considerable technological achievements of the ENCODE project, http://www.genome.gov/10005107) we still lack efficient procedures for identifying enhancers and other regulatory regions that polymorphisms could disrupt³⁸.

Many rare familial disorders are due to rare alleles of large effect

These are not restricted to conditions such as Cystic Fibrosis and Muscular Dystrophy that are solely due to rare, high penetrance Mendelian mutations. There are numerous chronic conditions that have familial analogs: well-known examples include rare variants promoting atherosclerosis through hypercholesterolemia³⁹, the lesions responsible for Maturity Onset Diabetes of the Young (MODY)⁴⁰, and the BRCA1 and BRCA2 breast cancer susceptibility mutations⁴¹. In fact, perusal of the Online Mendelian Inheritance in Man (OMIM) database provides examples of near-Mendelian cases of many relatively common disorders⁴². Probably the most comprehensive survey of this model is the demonstration that half of the cases of X-linked mental retardation can be ascribed to rare protein-coding mutations, which were discovered by comprehensive sequencing of X-chromosomal exons⁴³. There is thus extensive precedent for rare variants contributing substantially to special cases of complex disease, including risk of infection⁴⁴.

Rare copy number variants contribute to several complex psychological disorders

Copy number variants (CNV) are either hemizygous deletions or local duplications that result in 3 or even 4 copies of a locus⁴⁵. Five percent of cases of schizophrenia and of autism have each been attributed to CNVs at fewer than a half dozen genomic locations^46–48. These effects are less highly penetrant than Mendelian mutations, implying modification by the genetic background. There is no evidence to support the hypothesis that rare single nucleotide variants at the same loci are the major source of genetic variance⁹, but ongoing deep sequencing studies will quantify such effects. In the case of the ciliopathies, there is evidence from functional assays that rare variants can both promote and modify the severity of disease⁴⁹. It is thus incontrovertible that rare variants contribute to disease risk, and that identification of such alleles is a powerful mode of genetic analysis. The question is whether they can account for more than a minor fraction of complex disease risk.

Synthetic associations may explain common variant effects

‘Synthetic association’ describes the situation where the association of a common variant with a disease is actually due to linkage disequilibrium between the common variant and several disease-promoting rare variants that happen to segregate on the same haplotype⁵⁰. Thus, a common variant present in 20% of cases that mathematically explains one percent of disease susceptibility may actually simply report the activity of two or three rare variants that each substantially elevate risk in one or two percent of the cases. Until this year rare variants been excluded from the major whole genome genotyping platforms, so there has been no way to systematically document their contribution. Synthetic association is not expected to account for most of the missing heritability^{19, 51}, but this type of effect must always be considered as an explanation for apparent common-variant effects⁵².

Arguments against the rare allele model

Analysis of GWAS data is not consistent with rare variant explanations

A major argument against rare variants as the predominant source of missing heritability comes from the analysis of allele frequency distributions of GWAS data¹⁹. Rare allele proponents point out that it is difficult to model the true distribution of rare variants, and that they are under-represented on genotyping arrays, which complicates the interpretation. Nevertheless, considerations of linkage disequilibrium using standard quantitative genetic theory¹⁹ place strong constraints on the number of rare variants and their range of effect sizes that would be compatible with them making a major contribution yet remaining undetected in GWAS, as explained in Figure 2. Furthermore, analyses of the distribution of risk allele frequencies across 8 traits argues that if anything minor allele frequencies are skewed to be greater than 0.2, providing strong empirical evidence that rare alleles are not alone responsible⁵³. No-one doubts that some fraction of the total risk for any complex disease is due to rare alleles, but these studies argue that it is not the majority.

Sibling recurrence rates are greater than expected by the postulated effect sizes of rare variants

Heritability of disease is very often inferred from elevated sibling recurrence rates relative to incidence in unrelated individuals. Intuitively, if a disease has a prevalence of 1% in the general population, but 50% of siblings are affected, then the odds are elevated 50-fold in the family, whereas a single segregating rare variant with a 5-fold effect would only be expected to result in disease for 5% of carrier individuals. Sibling recurrence rates are generally much higher than can be attributed to rare variants with the postulated effect sizes¹⁷. If rare variants are contributing then they are doing so in the context of many other genetic variants in the pedigrees, as shown by a recent analysis of schizophrenia genetics⁵⁴. Under multiplicative models, disease may cluster in families due to segregation of multiple rare variants that happen to be brought together in the pedigree. Nevertheless, the rare allele model must not only explain association data in populations, but also fit demographic distributions of disease within and among families, and there is little theory supporting the claim that they can do both^55–57.

Rare variants do not obviously have additive effects

On the face of it, the widely documented additivity of genetic associations is inconsistent either with the dominance of rare variant effects, or the assumption that they interact multiplicatively within individuals to influence disease. However, it turns out that rare variants can easily induce apparently additive effects statistically, because the homozygotes for the tagging variant are twice as likely as the heterozygotes to carry the rare variant. Multiplicative interactions between rare variants cannot be measured in GWAS because of low power, but it will be important to establish mechanistically whether combinations of two or more such mutations increase risk in a linear or synergistic manner^58,59. Compound heterozygosity for two different rare variants at one locus is well documented in diseases such as cystic fibrosis, hemochromatosis and sickle cell syndromes; extension of the concept to include intergenic multiple heterozygosity could represent a large source of genetic variance that is almost impossible to detect with current methods.

Epidemiological transitions cannot be attributed to rare variants

The fourth argument against rare variant effects is a demographic one, namely the changing prevalence of so many chronic diseases in a span of just two or three generations, and/or the known impact of environmental variables on risk. For example, diabetes and heart disease have greatly increased in incidence in India and China in the past 10 years^60,61, an epidemiological transition that at best implies a change in penetrance of genetic effects attributable to any class of variant, rare or common, in the contemporary environment. Schizophrenia, a disease with very high heritability (inferred from twin studies) and for which very few replicated GWAS hits have been identified despite extensive scans, nevertheless shows such demographic influences as whether the parents live in rural or urban areas (disease rates are elevated in children born after migration to cities)⁶². Paternal age effects on psychological disease⁶³ might be attributed to elevated mutation rates in sperm, but other hypotheses are equally compatible with the data, and maternal age effects operate in the opposite direction as younger mothers have higher likelihoods of having affected children⁶⁴. In other words, rare variants alone cannot explain the demographic distribution of disease incidence.

GWAS associations are consistent across populations

An empirical argument against pervasive rare variant effects is that common variants are often consistent across populations — such as between Caucasians and Asians — despite differences in allele frequencies^65,66. If rare variants are recently derived relative to the common variants, then they should be at different frequencies in Caucasians and Asians, and we would expect that they would only induce synthetic common variant associations in one of these populations, or at least would not tend to have the same magnitude of effect. This would be especially true of common variants that differ in frequency between the two populations. Under a mutation-selection balance model, it may be possible for different novel rare variants to have effects in each population, and fine mapping studies sometimes reveal subtle differences in the patterns of association [eg.^67,68. Nevertheless, the simplest interpretation of the consistency of common variant effects is that they are actually due to the common variants themselves or to unobserved common variants in high LD across all populations.

Arguments in favour of the infinitesimal model

The infinitesimal model is standard quantitative genetic theory

Just as evolutionary theory provides a strong argument in favor of rare variants, standard quantitative genetic theory provides ample support for the infinitesimal model^7,8. Whatever the causes of the maintenance of genetic variance may be, the consistent observation is that all diseases have significant heritability, and hence purifying selection has been unable to purge the population of disease-promoting variants². At face value, the existence of dozens of susceptibility alleles for metabolic and immunological diseases with effect sizes that are just not detected for psychological diseases implies a difference in genetic architecture between the two categories of conditions. This may imply different intensities of purifying selection, although other models, including decanalization⁶⁹, are also compatible with the data. Since the majority of the genetic variance remains unexplained, it is a priori just as likely to exist in the form of rare or common alleles, and the fact is that there is nothing about GWAS findings that is inconsistent with the infinitesimal model of many variants of very small effect across the full allele frequency spectrum. This model has served applied quantitative geneticists as well as evolutionary biologists for close to a century, and in a sense can be regarded as the null model that needs to be disproved before it is abandoned.

Common variants collectively capture the majority of the genetic variance in GWAS

Direct empirical support for the infinitesimal model comes from genomic variance analyses^{70, 71}. Animal breeders have been using ‘genomic selection’ methods with great success for the past decade⁷², basing their selection of sires and dams on the overall predicted breeding value determined from the full set of genomic markers that capture variation distributed throughout the genome. Similarly in humans, by taking all nominally significant SNPs rather than just the GWAS significant ones, it is possible to capture much more of the genetic variance than is explained by the highly significant loci^73,74 (see Box 2). A multivariate version of this approach, implemented by regression of phenotypic similarity on genetic relatedness, also implies that common variants capture the majority of the genetic variants⁷¹. Furthermore, partitioning of the genetic variance on a chromosome-by-chromosome basis, for a diverse set of traits, shows that the proportion of variance explained is consistently proportional to chromosome length^75,76. Variance is distributed along all of the chromosomes, and is therefore attributable to hundreds of loci. Since common variants are used for the partitioning it is most parsimonious to conclude that they are responsible, and simulations of rare variants so distributed capture much less of the variance.

Box 2. Association Tests in Unrelated Individuals.

Genome-wide association studies (GWAS) generally start with comprehensive SNP-wise evaluation of the significance of the correlation between genotype and trait. For the most part, it is assumed that genotypic effects are ordered, namely that the heterozygotes will have intermediate risk or trait values.

As millions of tests are performed, the results must be adjusted to control for false positives, (usually using the conservative Bonferroni correction¹²⁷), resulting in the standard GWAS threshold of 5×10⁻⁸. The significance of the test statistic is then plotted against SNP position along the chromosome (see Figure 1). For the most part, genotyped SNPs are thought to ‘tag’ the actual causal variant, so efforts are made to estimate (‘impute’) as many genotypes in the region of a GWAS hit as possible¹²⁸, increasing the chances that the common causal variant is represented or that the effects of less common ones are better captured. Due to improved methods for imputation, most minor alleles down to 5% frequency can now be inferred with high accuracy, if the reference panel is appropriately matched for population structure¹²⁹. Rare variants, particularly those at a frequency of less than 1%, need to be sequenced directly.

Although association tests are reasonably powered to detect common variants that have a genotypic relative risk of 1.2 or more in meta-analyses that include tens of thousands of individuals, detecting the effects of single rare variant remains problematic. Various score statistics are being developed that evaluate pools of rare variants in a part of a gene, or group of related genes, for over-representation in cases or controls¹¹⁹. These can be conditioned on prior estimation of the likelihood that a nucleotide substitution is deleterious. Functional tests are used increasingly to validate candidate causal polymorphisms.

Two additional strategies have been proposed to overcome the very high false negative rate in GWAS that results from adoption of the strict GWAS threshold. One is to generate a weighted sum of the contributions of all variants beyond nominal statistical thresholds observed in a discovery sample, and then ask whether it is predictive of risk or phenotype in a second sample⁵³. In several instances where SNP-wise GWAS has uncovered few loci, this approach has provided clear evidence for polygenic risk, but it must be recognized that the high variance in estimation of effects results in noisy scores that, although highly significant in the replication sample, only capture over an order of magnitude less of the variance and are far from predictive. See⁷⁴ for another related strategy. The second approach is to evaluate all SNPs simultaneously by multiple regression, or the elegant equivalent of regressing the similarity between individuals on their overall genetic similarity⁷¹, which gives rise to an estimate of the genetic variance explained by all SNPs. Partitioning of the genome into chromosome-sized units [75], or smaller, allows for estimation of the contribution of each region of the genome to the genotypic variance.

Variation in endophenotypes is almost certainly due to common variants

Threshold-dependent models⁷⁷ postulate that disease is more likely to arise in individuals who have extreme values of underlying endophenotypes^78,79. In many cases, causal common variants associated with a continuous endophenotype have been associated with disease [eg^80–82], and in some cases these have been confirmed by in vitro biochemical assays for structural and regulatory effects [eg^83–85]. eQTL analysis shows that gene expression and splicing are heavily influenced by common variants, possibly for the majority of transcripts^86–88. To ignore these data is to deny that such transcriptional and metabolic variation is relevant to disease. It is of course possible that disease represents a discrete phase shift (in gene expression profiles, for example) that takes the organism outside the normal range of continuous variation. Thus, tumor samples have discrete transcriptome profile differences^89,90, and it is not obvious that the normal variability is relevant to pathology. Similarly, at least some cortex samples from autistic brains converge on a common transcriptional profile⁹¹. By contrast, various blood disorders have been shown to correlate with extreme values for the major vectors of modules of gene expression⁹². More research on the relationship between endophenotypes and disease is needed, but most observers would consider it implausible that natural variation in physiology is irrelevant to variation in disease susceptibility, and would maintain that common variants are most likely responsible for continuously distributed physiological variation.

Model organism research supports common variant contributions to complex phenotypes

In model organism research, both pedigree analyses and genetic crosses in which linkage mapping is used to localize QTL almost always lead to the identification of multiple variants influencing the quantitative trait of interest²⁰. This is as true of threshold-dependent characters and cryptic variation⁹³ as it is of continuous variation. Furthermore, the phenomenon of transgressive segregation in mapping populations of mice and flies established from eight founder strains provides strong empirical support for the existence of common polygenes^94–96. The overwhelming evidence from classical quantitative genetics is that traits are regulated by many loci with a wide range of effect sizes. A counterargument is that in any cross or pedigree, there is no information about the frequency of contributing QTL alleles in the population, so some fraction of the mapped factors are likely to be rare variants – and if the parents were selected from a base population, possibly most are unusual rare variants, including mutations that were unconsciously selected in the laboratory. In the past year, re-sequencing of evolved outbred populations of Drosophila melanogaster has provided strong support for selection on thousands of variants being responsible for changes in the highly complex traits of body size and fecundity^97,98.

GWAS has successfully identified thousands of common variants⁹⁹

While there has been a very public focus on the failure of GWAS to find the missing heritability^5,6, the simplest explanation for this is that the expectations were based on unrealistic prior assumption of effect sizes. Once it is accepted that most alleles are associated with relative risks less than 1.2, it becomes clear that hundreds of thousands of individuals are required to identify more than a few dozen loci than explain more than 20% of the variance. In fact, sample sizes can be extrapolated from the range of variant effects in initial discovery samples¹², and in the case of height, the GIANT consortium (http://www.broadinstitute.org/collaboration/giant/) confirmed the inferences from 30,000 individuals¹⁰⁰ when they jumped to 180,000, finding an additional 180 or so loci¹⁴. Simply put, the data is generally consistent with the infinitesimal model to a first approximation, even where variants are yet to be identified. It is the common variant of moderate effect version of the CD-CV model that needs to be discarded.

Arguments against the infinitesimal model

The QTL paradox

Where are all of the QTL that are so consistently detected in pedigrees and in experimental crosses, when we transition to outbred populations? Why is it that 10 loci can each explain 5% of the genetic variance and most of the heritability in a cross between two strains, but in no case has GWAS yet found more than one locus with an effect size that large? Two explanations can be forwarded immediately: first, the QTL are actually rare variants that only contribute in that cross, and so are precisely the rare variants predicted by the rare allele theory; or second, each cross captures just a small fraction of the genetic variance in a population, so QTL with relatively large effects in one cross will be expected to be diluted in their contribution relative to other QTL when measured in the entire population. In many cases as well, the effect size estimated in the cross will be an overestimate due to the Beavis effect/winner’s curse^101,102, while in an unknown proportion of cases, QTL will turn out to be due to multiple linked variants that coarse mapping fails to resolve into individual SNPs¹⁰³. Nevertheless, there remains a general paradox that GWAS has found so few variants of moderate effect.

Absence of blending inheritance

A more pointed argument against the infinitesimal nature of effects is that it predicts less granularity in the distribution of risk and phenotypic trait variation than is often observed, though I am not aware of a quantitative assessment of this claim. In the infinitesimal model, disease risk ought to blend smoothly when unrelated people have children. The larger the number of alleles affecting a trait, the lower the among-individual variance should be under random mating since most individuals will share similar numbers of risk alleles. However, disease incidence and complex phenotypes generally cluster in families. A possible resolution of this conundrum is that the observed clustering of disease in families could be explained by stochastic variation in the number of susceptibility alleles: if two people happen to have more than the average number of small variants, so will their children. Furthermore, homophily, the tendency for couples to pair on the basis of shared attributes (including sub-clinical disease indicators), will tend to enrich for variants that promote those attributes¹⁰⁴. Granularity of traits is difficult to document, but facial features provide a good example of a suite of traits that do not simply follow either blending or Mendelian inheritance¹⁰⁵. Certain features such as the shape of the nose, location of the cheek bones, or curve of the lips, run strongly in families, appearing in distant relatives in patterns that are suggestive of large genetic effects. If such clustering is also true of endophenotypes then the infinitesimal model will be incomplete.

Demographic phenomena suggest more than a simple common variant model

As with the rare allele model, infinitesimal effects are also not consistent with a wide range of demographic effects that are indicative of GxE interactions and complex genetic interactions. Prime among these are (i) the pervasiveness of differences in disease risk between geographic areas that are not obviously explained by genetic differentiation, (ii) increasing burden of complex disease in the span of one or two generations (both of these phenomena are obvious upon browsing the CDC website at http://www/cdc/gov for incidence data), and (iii) conditioning of the risk for one disease on another disease in the same individual^106,107. This does not counter the existence of thousands of small effect loci affecting each trait or disease risk profile, but it suggests that the narrow-sense genetic effects alone are unlikely to be sufficient explanation. It must be noted that there is very little evidence from GWAS for either GxE or GxG interactions¹⁰⁸, but such effects could be mild at the level of individual associations and be below the power of detection.

Very few common variants for disease have been functionally validated

A technical argument against all common variant models is that association alone is insufficient evidence of function: correlation is not causation. Very few of the thousands of GWAS significant associations have been shown using molecular genetics, biochemistry or biophysics to be the actual risk variant^{38, 109}. In this context, prudence suggests an open mind in each individual case as to whether the variant, another common variant in LD, or a series of less common variants of large effect synthetically associated may be responsible. The case of protection against anemia in chronic hepatitis C, where the initial GWAS discovery clearly captures two less common causal coding variants at the ITPA locus, is a good example¹¹⁰.

What accounts for the missing heritability?

Finally, there is the argument that there truly is missing heritability in GWAS studies. It is little appreciated that GWAS do not actually measure heritability (the ratio of genetic to total phenotypic variance in a population) but rather they measure just the genetic variance. Missing heritability is inferred with respect to heritability estimates that generally derive from family studies, where ironically direct estimates of the genetic contribution are lacking. Consequently, it is difficult to actually estimate how much of the variance GWAS-captured variants should explain in outbred populations. However, in the case of height, where heritability is as high as 80%, over 50% of the phenotype can be attributed to common variants using the mixed linear modeling approach⁷¹, and after adjustment for allele frequency skews and incomplete LD, essentially the entire genetic contribution has been ascribed to genotypic variation. Yet the same methods applied to BMI do not capture much more than half of the expected genotypic variance, and it is not clear that they are as efficient for schizophrenia, arthritis or intelligence^75,76. In these cases, it can be argued that the infinitesimal model does not capture the full range of genetic variance, and that there is a true missing heritability problem that will need to be addressed with rare alleles and broad sense heritability components that were introduced in Box 1.

Conclusion

The true debate over the source of genetic variation for disease is not one of “is it rare or common variants”, or even of “how much does each class contribute”, but rather “how do they work together” ¹¹¹. An interesting thought experiment is to ask whether a population of individuals who are only polymorphic for common variants differ in their common disease risk; or conversely whether rare variants are sufficient to explain the observed distribution of risk in the absence of common variants. The result of both experiments is likely to be negative, but the challenge is to devise strategies to test the hypotheses.

Empirically, there is ample support for both class of effect. As of June 2011, the NHGRI GWAS catalog lists 1,449 genome-wide significant associations with 237 traits and diseases, spread across all chromosome except the Y⁹⁹. Some of these may be due to LD with rare variants, but parsimony suggests most are common variant effects. MutDB¹¹²(http://mutdb.org/) contains a much larger number of rare coding variants that are either associated with disease or predicted to be damaging. As more individuals are sequenced, many of these appear in healthy controls, but it must be recognized that even large effect alleles are subject to background modification and incomplete penetrance. Initial resequencing of genes identified by GWAS¹¹³ has produced mixed results: only 1 of 63 genes in an initial screen for inflammatory bowel disease found evidence for rare variant effects (and these were protective¹¹⁴, but see also¹¹⁵), whereas a significant excess of rare coding variants was found in 4 genes for hypertriglyceridemia¹¹⁶. Considerable resolution of the burden of deleterious rare variants will no doubt emerge in the next few years as whole exome and genome sequencing ramps up^117,118. Interpretation will be complicated by the natural tendency to under-report negative results, by difficult statistical issues¹¹⁹, as well as the problem of how to define regulatory effects.

The typical resolution of the observation that disease is categorical (people are either cases or controls) yet genetic contributions are complex, is that disease is generally a threshold-dependent response superimposed over a continuous liability¹²⁰. This interpretation actually provides a straightforward framework for integrating rare and common variant effects (Figure 4). Liability is quite likely to be established by the additive and infinitesimal contributions of hundreds of polymorphisms, each regulating a series of biochemical traits that impinge on the phenotype: metabolite abundance, gene expression, and hormone levels, for example. Disease arises either in individuals at the extremes of the liability scale who move beyond the threshold, or in individuals close to the threshold who are pushed into adversity through environmental and behavioral agents, or because they carry one or more rare variants. On this model, the rare variant can either increase or decrease function, and whether or not it associates with disease will be conditional on the background liability. The notion that even rare variants have variable penetrance thus blurs the distinction between infinitesimal and major-effect models of disease susceptibility.

Figure 4. Joint effects of rare and common variants.

A straight forward reconciliation of the effects of rare and common variants supposes that pervasive common variation influences the expression and activity of genes in pathways, establishing the background liability to disease that is then further modified by rare variants with larger effects. In this hypothetical example of central metabolism, standing variation results in some individuals having lower flux than others (left versus right; colored boxes imply enzyme activity differences from low, red, to high, green), but according to standard biochemical theory¹³⁰, systems evolve such that most variation is accommodated within the healthy range. The impact of a rare variant that knocks out one copy of the enzyme indicated with the cross is conditional on this liability, pushing the individual on the left beyond the disease threshold, while the individual on the right can accommodate the mutation given higher activity elsewhere in glycolysis.

Figure 3. Inconsistency between GWAS results and rare variant expectations.

(A) The frequency distribution of risk allele frequencies (light red) for 414 common variant associations with 17 diseases is only slightly skewed toward lower frequency variants. By contrast, simulations, in this case assuming up to 9 rare causal variants inducing the common variant association with SNPs at the same frequency as observed on common genotyping platforms (light green bars) result in a marked left-skew with a peak for common variants whose frequency is less than 10%. (The skew is even stronger if only a single causal variant is responsible). The observed data is thus not immediately consistent with the rare variant model. (B) Part of the problem with synthetic associations is that they would explain too much heritability if they were pervasively responsible for common variant effects. This is due to the relationship between allele frequency, maximum possible LD, and the amount of variance explained [19]. The plot shows the expected odds ratio due to a rare variant of the indicated frequency (from 0.5% to 2%) if it increases the odds ratio at a common SNP (with which it is in maximum possible LD) 1.1-fold. Intermediate effect sizes (2<OR<5) require combined causal variant frequencies in excess of 1%. As the number of rare variants increases, the likelihood that they are in high LD with the common variant also drops, further reducing the probability that they can explain observed common variant association. Suppose a disease has a prevalence of 1%. Then 10 causal variants each at a frequency of 1% would result in 20% of people carrying a causal variant. If the penetrance is 5% then 1% of people would have the disease, and these 10 variants would completely explain the genetic risk. Similarly if 100 causal variants were each at 0.1% frequency, it would take ~10 such variants to induce each single common variant association with an observed OR of 1.1. If large GWAS detect dozens of such common loci, and they were actually due to LD with rare variants, then the heritability would be explained several times over. Alternatively, if hundreds of very rare causal variants are not in LD with common variants, we do not expect to see GWAS significant associations. Data from¹⁹.

Online Summary.

For the past couple of years, discussion of the so-called “missing heritability problem” has focused attention on the failure of genome-wide association studies (GWAS) to discover more than a minor fraction of the genetic variance for complex traits and disease susceptibility. However, it now appears that the problem is largely a result of the small contribution of most variants, either because the variants are too rare to contribute population-wide, or because the effect sizes of common variants are in general very small. This review presents five arguments for, and five against, each of these two models, and concludes that while the infinitesimal model is essentially correct, rare alleles of large effect almost certainly also make an essential contribution to risk of disease. Some of the more important arguments are:

• Standard evolutionary and quantitative genetic theory both provide strong expectations for rare and common variant contributions

• There is increasingly solid empirical evidence for both classes of contribution

• Neither model can yet be said to provide compelling explanations for epidemiological transitions and other demographic phenomena including familial clustering and sibling resemblance

• Mechanistic explanations for additive within-locus, and multiplicative between-locus, effects are ultimately desired to complement purely statistical description of effects

• On either model, the majority of healthy individuals carry disease-associated alleles

• While common variants may establish the background liability to many complex diseases, environmental and rare variant perturbations will often provide the extra impetus that pushe an individual over the disease threshold.

Glossary

Common disease-common variant (CD-CV) hypothesis

The model that complex disease is largely attributable to a moderate number of common variants, each of which explain several percent of the risk in a population

Genetic variance

The contribution of genotypic differences among individuals to phenotypic variation

Heritability

The proportion of the phenotypic variance in a population that is due to genotypic differences among individuals

Narrow sense variance

The additive component of the genetic variance, namely the average effect of substituting one allele for another at a locus

Genotype relative risk

The ratio of the risk of disease between individuals with and without the genotype. A ratio of 1.1 equates to a 10% increase in risk

Penetrance

The proportion of individuals with a mutation or risk variant who have the disease

Expressivity

The severity of the disease in individuals who have the risk variant and disease; Genotype-by-genotype interactions (epistasis)¸ Refers to the situation in which the effect of one genotype is conditional on genotypes at one or more other unlinked loci

Genotype-by-environment (G×E) interactions

Refers to the situation in which the effect of the genotype is conditional on the environment, which may include abiotic (temperature), biotic (viral exposure), and cultural/behavioral influences

Parent-of-origin genetic contributions

Genetic effects that are only seen when the allele is transmitted either from the mother or from the father

Purifying selection

Selection against genetic variants that reduce fitness, generally keeps deleterious alleles at a low frequency or removes them from the population

ENCODE

Encyclopedia of DNA Elements

Chronic disease

Medical conditions that develop slowly and persist, generally with a strong genetic component

Ciliopathy

A class of diseases due to disruption of the cilium, a cellular organelle

Linkage disequilibrium

Non-random association between genotypes, generally discussed in relation to loci that are closely located on a chromosome, for example within a gene

Haplotype

A set of alleles that commonly segregate together, defined as regions of extended linkage disequilibrium, which in humans is often up to 100kb in length

Mutation-selection balance

An evolutionary model that accounts for the maintenance of genetic variation as a balance between mutation generating variance, and purifying selection removing it

Decanalization

The notion that genetic systems evolved to be buffered, but that large effect mutations or environmental change can overcome this buffering, increasing the genetic variance

Genomic selection

The use of genetic markers spread throughout the genome to select individuals with desired predicted breeding values

Predicted breeding value

The estimated phenotype of progeny of individuals that have a particular genotype

Threshold-dependent model

A model that postulates that individuals who exceed some threshold value of a continuous physiological characteristic (‘liability’), have or are at high risk for disease

Endophenotypes

Intermediate physiological or psychological traits, such as metabolite and transcript abundance, or a specific neuronal function

eQTL analysis

Studies of the association between genotypes and gene expression (transcript abundance), leading to the detection of expression quantitative trait loci, or eQTL

Cryptic variation

Genetic variation whose effects are only seen under perturbed conditions, such as in the presence a particular mutation or environmental exposure

Transgressive segregation

The appearance of traits in the offspring that are more extreme than observed in either parent

Beavis effect/winner’s curse

The observation that the effect sizes estimated in a discovery sample tend to be over-estimates of the true effect sizes since they typically receive the benefit of sampling variance in the same direction as the true effect, in order to exceed strict genome-wide significance levels

Biography

Autobiographical Statement

Greg Gibson recently moved to the Georgia Institute of Technology where he is using integrative genomics approaches to study the evolution of disease susceptibility and its implications for predictive health. He received his Ph.D. and postdoctoral training in Drosophila melanogaster developmental genetics, and developed his interest in evolutionary quantitative genetics for the most part while on the faculty at North Carolina State University. He has combined gene expression profiling and candidate gene association studies to elucidate the molecular basis of variation for complex traits, with a particular focus on cryptic variation and genotype-by-environment interactions.