Genetic correlation

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In multivariate quantitative genetics, a genetic correlation (denoted or ) is the proportion of variance that two traits share due to genetic causes, [1] [2] [3] the correlation between the genetic influences on a trait and the genetic influences on a different trait [4] [5] [6] [7] [8] [9] estimating the degree of pleiotropy or causal overlap. A genetic correlation of 0 implies that the genetic effects on one trait are independent of the other, while a correlation of 1 implies that all of the genetic influences on the two traits are identical. The bivariate genetic correlation can be generalized to inferring genetic latent variable factors across > 2 traits using factor analysis. Genetic correlation models were introduced into behavioral genetics in the 1970s–1980s.

Contents

Genetic correlations have applications in validation of genome-wide association study (GWAS) results, breeding, prediction of traits, and discovering the etiology of traits & diseases.

They can be estimated using individual-level data from twin studies and molecular genetics, or even with GWAS summary statistics. [10] [11] Genetic correlations have been found to be common in non-human genetics [12] and to be broadly similar to their respective phenotypic correlations, [13] and also found extensively in human traits, dubbed the 'phenome'. [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

This finding of widespread pleiotropy has implications for artificial selection in agriculture, interpretation of phenotypic correlations, social inequality, [25] attempts to use Mendelian randomization in causal inference, [26] [27] [28] [29] the understanding of the biological origins of complex traits, and the design of GWASes.

A genetic correlation is to be contrasted with environmental correlation between the environments affecting two traits (e.g. if poor nutrition in a household caused both lower IQ and height); a genetic correlation between two traits can contribute to the observed (phenotypic) correlation between two traits, but genetic correlations can also be opposite observed phenotypic correlations if the environment correlation is sufficiently strong in the other direction, perhaps due to tradeoffs or specialization. [30] [31] The observation that genetic correlations usually mirror phenotypic correlations is known as "Cheverud's Conjecture" [32] and has been confirmed in animals [33] [34] and humans, and showed they are of similar sizes; [35] for example, in the UK Biobank, of 118 continuous human traits, only 29% of their intercorrelations have opposite signs, [23] and a later analysis of 17 high-quality UKBB traits reported correlation near-unity. [36]

Interpretation

Genetic correlations are not the same as heritability, as it is about the overlap between the two sets of influences and not their absolute magnitude; two traits could be both highly heritable but not be genetically correlated or have small heritabilities and be completely correlated (as long as the heritabilities are non-zero).

For example, consider two traits – dark skin and black hair. These two traits may individually have a very high heritability (most of the population-level variation in the trait due to genetic differences, or in simpler terms, genetics contributes significantly to these two traits), however, they may still have a very low genetic correlation if, for instance, these two traits were being controlled by different, non-overlapping, non-linked genetic loci.

A genetic correlation between two traits will tend to produce phenotypic correlations – e.g. the genetic correlation between intelligence and SES [16] or education and family SES [37] implies that intelligence/SES will also correlate phenotypically. The phenotypic correlation will be limited by the degree of genetic correlation and also by the heritability of each trait. The expected phenotypic correlation is the bivariate heritability' and can be calculated as the square roots of the heritabilities multiplied by the genetic correlation. (Using a Plomin example, [38] for two traits with heritabilities of 0.60 & 0.23, , and phenotypic correlation of r=0.45 the bivariate heritability would be , so of the observed phenotypic correlation, 0.28/0.45 = 62% of it is due to correlative genetic effects, which is to say nothing of trait mutability in and of itself.)

Cause

Genetic correlations can arise due to: [19]

  1. linkage disequilibrium (two neighboring genes tend to be inherited together, each affecting a different trait)
  2. biological pleiotropy (a single gene having multiple otherwise unrelated biological effects, or shared regulation of multiple genes [39] )
  3. mediated pleiotropy (a gene affects trait X and trait X affects trait Y).
  4. biases: population stratification such as ancestry or assortative mating (sometimes called "gametic phase disequilibrium"), spurious stratification such as ascertainment bias/self-selection [40] or Berkson's paradox, or misclassification of diagnoses

Uses

Causes of changes in traits

Genetic correlations are scientifically useful because genetic correlations can be analyzed over time within an individual longitudinally [41] (e.g. intelligence is stable over a lifetime, due to the same genetic influences – childhood genetically correlates with old age [42] ), or across diagnoses, allowing discovery of whether different genes influence a trait over a lifetime (typically, they do not [4] ), whether different genes influence a trait in different populations due to differing local environments, whether there is disease heterogeneity across times or places or sex (particularly in psychiatric diagnoses there is uncertainty whether 1 country's 'autism' or 'schizophrenia' is the same as another's or whether diagnostic categories have shifted over time/place leading to different levels of ascertainment bias), and to what degree traits like autoimmune or psychiatric disorders or cognitive functioning meaningfully cluster due sharing a biological basis and genetic architecture. This can be an important constraint on conceptualizations of the two traits: traits which seem different phenotypically but which share a common genetic basis require an explanation for how these genes can influence both traits.

Boosting GWASes

Genetic correlations can be used in GWASes by using polygenic scores or genome-wide hits for one (often more easily measured) trait to increase the prior probability of variants for a second trait; for example, since intelligence and years of education are highly genetically correlated, a GWAS for education will inherently also be a GWAS for intelligence and be able to predict variance in intelligence as well [43] and the strongest SNP candidates can be used to increase the statistical power of a smaller GWAS, [44] a combined analysis on the latent trait done where each measured genetically-correlated trait helps reduce measurement error and boosts the GWAS's power considerably (e.g. Krapohl et al. 2017, using elastic net and multiple polygenic scores, improving intelligence prediction from 3.6% of variance to 4.8%; [45] Hill et al. 2017b [46] uses MTAG [47] to combine 3 g-loaded traits of education, household income, and a cognitive test score to find 107 hits & doubles predictive power of intelligence) or one could do a GWAS for multiple traits jointly. [48] [49]

Genetic correlations can also quantify the contribution of correlations <1 across datasets which might create a false "missing heritability", by estimating the extent to which differing measurement methods, ancestral influences, or environments create only partially overlapping sets of relevant genetic variants. [50]

Breeding

Hairless dogs have imperfect teeth; long-haired and coarse-haired animals are apt to have, as is asserted, long or many horns; pigeons with feathered feet have skin between their outer toes; pigeons with short beaks have small feet, and those with long beaks large feet. Hence if man goes on selecting, and thus augmenting any peculiarity, he will almost certainly modify unintentionally other parts of the structure, owing to the mysterious laws of correlation.

Genetic correlations are also useful in applied contexts such as plant/animal breeding by allowing substitution of more easily measured but highly genetically correlated characteristics (particularly in the case of sex-linked or binary traits under the liability-threshold model, where differences in the phenotype can rarely be observed but another highly correlated measure, perhaps an endophenotype, is available in all individuals), compensating for different environments than the breeding was carried out in, making more accurate predictions of breeding value using the multivariate breeder's equation as compared to predictions based on the univariate breeder's equation using only per-trait heritability & assuming independence of traits, and avoiding unexpected consequences by taking into consideration that artificial selection for/against trait X will also increase/decrease all traits which positively/negatively correlate with X. [51] [52] [53] [54] [55] The limits to selection set by the inter-correlation of traits, and the possibility for genetic correlations to change over long-term breeding programs, lead to Haldane's dilemma limiting the intensity of selection and thus progress.

Breeding experiments on genetically correlated traits can measure the extent to which correlated traits are inherently developmentally linked & response is constrained, and which can be dissociated. [56] Some traits, such as the size of eyespots on the butterfly Bicyclus anynana can be dissociated in breeding, [57] but other pairs, such as eyespot colors, have resisted efforts. [58]

Mathematical definition

Given a genetic covariance matrix, the genetic correlation is computed by standardizing this, i.e., by converting the covariance matrix to a correlation matrix. Generally, if is a genetic covariance matrix and , then the correlation matrix is . For a given genetic covariance between two traits, one with genetic variance and the other with genetic variance , the genetic correlation is computed in the same way as the correlation coefficient .

Computing the genetic correlation

Genetic correlations require a genetically informative sample. They can be estimated in breeding experiments on two traits of known heritability and selecting on one trait to measure the change in the other trait (allowing inferring the genetic correlation), family/adoption/twin studies (analyzed using SEMs or DeFries–Fulker extremes analysis), molecular estimation of relatedness such as GCTA, [59] methods employing polygenic scores like HDL (High-Definition Likelihood), [11] LD score regression, [17] [60] BOLT-REML, [61] CPBayes, [62] or HESS, [63] comparison of genome-wide SNP hits in GWASes (as a loose lower bound), and phenotypic correlations of populations with at least some related individuals. [64]

As with estimating SNP heritability and genetic correlation, the better computational scaling & the ability to estimate using only established summary association statistics is a particular advantage for HDL [11] and LD score regression over competing methods. Combined with the increasing availability of GWAS summary statistics or polygenic scores from datasets like the UK Biobank, such summary-level methods have led to an explosion of genetic correlation research since 2015.[ citation needed ]

The methods are related to Haseman–Elston regression & PCGC regression. [65] Such methods are typically genome-wide, but it is also possible to estimate genetic correlations for specific variants or genome regions. [66]

One way to consider it is using trait X in twin 1 to predict trait Y in twin 2 for monozygotic and dizygotic twins (i.e. using twin 1's IQ to predict twin 2's brain volume); if this cross-correlation is larger for the more genetically-similar monozygotic twins than for the dizygotic twins, the similarity indicates that the traits are not genetically independent and there is some common genetics influencing both IQ and brain volume. (Statistical power can be boosted by using siblings as well. [67] )

Genetic correlations are affected by methodological concerns; underestimation of heritability, such as due to assortative mating, will lead to overestimates of longitudinal genetic correlation, [68] and moderate levels of misdiagnoses can create pseudo correlations. [69]

As they are affected by heritabilities of both traits, genetic correlations have low statistical power, especially in the presence of measurement errors biasing heritability downwards, because "estimates of genetic correlations are usually subject to rather large sampling errors and therefore seldom very precise": the standard error of an estimate is . [70] (Larger genetic correlations & heritabilities will be estimated more precisely. [71] ) However, inclusion of genetic correlations in an analysis of a pleiotropic trait can boost power for the same reason that multivariate regressions are more powerful than separate univariate regressions. [72]

Twin methods have the advantage of being usable without detailed biological data, with human genetic correlations calculated as far back as the 1970s and animal/plant genetic correlations calculated in the 1930s, and require sample sizes in the hundreds for being well-powered, but they have the disadvantage of making assumptions which have been criticized, and in the case of rare traits like anorexia nervosa it may be difficult to find enough twins with a diagnosis to make meaningful cross-twin comparisons, and can only be estimated with access to the twin data; molecular genetic methods like GCTA or LD score regression have the advantage of not requiring specific degrees of relatedness and so can easily study rare traits using case-control designs, which also reduces the number of assumptions they rely on, but those methods could not be run until recently, require large sample sizes in the thousands or hundreds of thousands (to obtain precise SNP heritability estimates, see the standard error formula), may require individual-level genetic data (in the case of GCTA but not LD score regression).

More concretely, if two traits, say height and weight have the following additive genetic variance-covariance matrix:

HeightWeight
Height3636
Weight36117

Then the genetic correlation is .55, as seen is the standardized matrix below:

HeightWeight
Height1
Weight.551

In practice, structural equation modeling applications such as Mx or OpenMx (and before that, historically, LISREL [73] ) are used to calculate both the genetic covariance matrix and its standardized form. In R, cov2cor() will standardize the matrix.

Typically, published reports will provide genetic variance components that have been standardized as a proportion of total variance (for instance in an ACE twin study model standardised as a proportion of V-total = A+C+E). In this case, the metric for computing the genetic covariance (the variance within the genetic covariance matrix) is lost (because of the standardizing process), so you cannot readily estimate the genetic correlation of two traits from such published models. Multivariate models (such as the Cholesky decomposition [ better source needed ]) will, however, allow the viewer to see shared genetic effects (as opposed to the genetic correlation) by following path rules. It is important therefore to provide the unstandardised path coefficients in publications.

See also

Related Research Articles

<span class="mw-page-title-main">Heritability</span> Estimation of effect of genetic variation on phenotypic variation of a trait

Heritability is a statistic used in the fields of breeding and genetics that estimates the degree of variation in a phenotypic trait in a population that is due to genetic variation between individuals in that population. The concept of heritability can be expressed in the form of the following question: "What is the proportion of the variation in a given trait within a population that is not explained by the environment or random chance?"

Twin studies are studies conducted on identical or fraternal twins. They aim to reveal the importance of environmental and genetic influences for traits, phenotypes, and disorders. Twin research is considered a key tool in behavioral genetics and in related fields, from biology to psychology. Twin studies are part of the broader methodology used in behavior genetics, which uses all data that are genetically informative – siblings studies, adoption studies, pedigree, etc. These studies have been used to track traits ranging from personal behavior to the presentation of severe mental illnesses such as schizophrenia.

A quantitative trait locus (QTL) is a locus that correlates with variation of a quantitative trait in the phenotype of a population of organisms. QTLs are mapped by identifying which molecular markers correlate with an observed trait. This is often an early step in identifying the actual genes that cause the trait variation.

<span class="mw-page-title-main">Pleiotropy</span> Influence of a single gene on multiple phenotypic traits

Pleiotropy occurs when one gene influences two or more seemingly unrelated phenotypic traits. Such a gene that exhibits multiple phenotypic expression is called a pleiotropic gene. Mutation in a pleiotropic gene may have an effect on several traits simultaneously, due to the gene coding for a product used by a myriad of cells or different targets that have the same signaling function.

Research on the heritability of IQ inquires into the degree of variation in IQ within a population that is due to genetic variation between individuals in that population. There has been significant controversy in the academic community about the heritability of IQ since research on the issue began in the late nineteenth century. Intelligence in the normal range is a polygenic trait, meaning that it is influenced by more than one gene, and in the case of intelligence at least 500 genes. Further, explaining the similarity in IQ of closely related persons requires careful study because environmental factors may be correlated with genetic factors.

Heritability is the proportion of variance caused by genetic factors of a specific trait in a population. Falconer's formula is a mathematical formula that is used in twin studies to estimate the relative contribution of genetic vs. environmental factors to variation in a particular trait based on the difference between twin correlations. Statistical models for heritability commonly include an error that will absorb phenotypic variation that cannot be described by genetics when analyzed. These are unique subject-specific influences on a trait. Falconer's formula was first proposed by the Scottish geneticist Douglas Falconer.

<span class="mw-page-title-main">Genome-wide association study</span> Study of genetic variants in different individuals

In genomics, a genome-wide association study, is an observational study of a genome-wide set of genetic variants in different individuals to see if any variant is associated with a trait. GWA studies typically focus on associations between single-nucleotide polymorphisms (SNPs) and traits like major human diseases, but can equally be applied to any other genetic variants and any other organisms.

Gene–environment correlation is said to occur when exposure to environmental conditions depends on an individual's genotype.

Behavioural genetics, also referred to as behaviour genetics, is a field of scientific research that uses genetic methods to investigate the nature and origins of individual differences in behaviour. While the name "behavioural genetics" connotes a focus on genetic influences, the field broadly investigates the extent to which genetic and environmental factors influence individual differences, and the development of research designs that can remove the confounding of genes and environment. Behavioural genetics was founded as a scientific discipline by Francis Galton in the late 19th century, only to be discredited through association with eugenics movements before and during World War II. In the latter half of the 20th century, the field saw renewed prominence with research on inheritance of behaviour and mental illness in humans, as well as research on genetically informative model organisms through selective breeding and crosses. In the late 20th and early 21st centuries, technological advances in molecular genetics made it possible to measure and modify the genome directly. This led to major advances in model organism research and in human studies, leading to new scientific discoveries.

The missing heritability problem refers to the difference between heritability estimates from genetic data and heritability estimates from twin and family data across many physical and mental traits, including diseases, behaviors, and other phenotypes. This is a problem that has significant implications for medicine, since a person's susceptibility to disease may depend more on the combined effect of all the genes in the background than on the disease genes in the foreground, or the role of genes may have been severely overestimated.

Predictive genomics is at the intersection of multiple disciplines: predictive medicine, personal genomics and translational bioinformatics. Specifically, predictive genomics deals with the future phenotypic outcomes via prediction in areas such as complex multifactorial diseases in humans. To date, the success of predictive genomics has been dependent on the genetic framework underlying these applications, typically explored in genome-wide association (GWA) studies. The identification of associated single-nucleotide polymorphisms underpin GWA studies in complex diseases that have ranged from Type 2 Diabetes (T2D), Age-related macular degeneration (AMD) and Crohn's disease.

Genome-wide complex trait analysis (GCTA) Genome-based restricted maximum likelihood (GREML) is a statistical method for heritability estimation in genetics, which quantifies the total additive contribution of a set of genetic variants to a trait. GCTA is typically applied to common single nucleotide polymorphisms (SNPs) on a genotyping array and thus termed "chip" or "SNP" heritability.

A human disease modifier gene is a modifier gene that alters expression of a human gene at another locus that in turn causes a genetic disease. Whereas medical genetics has tended to distinguish between monogenic traits, governed by simple, Mendelian inheritance, and quantitative traits, with cumulative, multifactorial causes, increasing evidence suggests that human diseases exist on a continuous spectrum between the two.

<span class="mw-page-title-main">Polygenic score</span> Numerical score aimed at predicting a trait based on variation in multiple genetic loci

In genetics, a polygenic score (PGS) is a number that summarizes the estimated effect of many genetic variants on an individual's phenotype. The PGS is also called the polygenic index (PGI) or genome-wide score; in the context of disease risk, it is called a polygenic risk score or genetic risk score. The score reflects an individual's estimated genetic predisposition for a given trait and can be used as a predictor for that trait. It gives an estimate of how likely an individual is to have a given trait based only on genetics, without taking environmental factors into account; and it is typically calculated as a weighted sum of trait-associated alleles.

<span class="mw-page-title-main">Family resemblance (anthropology)</span> Physical and psychological similarities shared between close relatives

Family resemblance refers to physical similarities shared between close relatives, especially between parents and children and between siblings. In psychology, the similarities of personality are also observed.

<span class="mw-page-title-main">Complex traits</span>

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In evolutionary biology, developmental bias refers to the production against or towards certain ontogenetic trajectories which ultimately influence the direction and outcome of evolutionary change by affecting the rates, magnitudes, directions and limits of trait evolution. Historically, the term was synonymous with developmental constraint, however, the latter has been more recently interpreted as referring solely to the negative role of development in evolution.

In statistical genetics, linkage disequilibrium score regression is a technique that aims to quantify the separate contributions of polygenic effects and various confounding factors, such as population stratification, based on summary statistics from genome-wide association studies (GWASs). The approach involves using regression analysis to examine the relationship between linkage disequilibrium scores and the test statistics of the single-nucleotide polymorphisms (SNPs) from the GWAS. Here, the "linkage disequilibrium score" for a SNP "is the sum of LD r2 measured with all other SNPs".

The Omnigenic Model, first proposed by Evan A. Boyle, Yang I. Li, and Jonathan K. Pritchard, describes a hypothesis regarding the heritability of complex traits. Expanding beyond polygenes, the authors propose that all genes expressed within a cell affect the expression of a given trait. In addition, the model states that the peripheral genes, ones that do not have a direct impact on expression, explain more heritability of traits than core genes, ones that have a direct impact on expression. The process that the authors propose that facilitates this effect is called “network pleiotropy”, in which peripheral genes can affect core genes, not by having a direct effect, but rather by virtue of being mediated within the same cell.

Personality traits are patterns of thoughts, feelings and behaviors that reflect the tendency to respond in certain ways under certain circumstances.

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