Genetic Correlation

In multivariate quantitative genetics, a genetic correlation (denoted $r_g$ or $r_a$) is the proportion of variance that two traits share due to genetic causes, the correlation between the genetic influences on a trait and the genetic influences on a different trait Plomin et al., p. 123 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.

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. Genetic correlations have been found to be common in non-human genetics and to be broadly similar to their respective phenotypic correlations, and also found extensively in human traits, dubbed the 'phenome'.

This finding of widespread pleiotropy has implications for artificial selection in agriculture, interpretation of phenotypic correlations, social inequality, attempts to use Mendelian randomization in causal inference, 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. The observation that genetic correlations usually mirror phenotypic correlations is known as "Cheverud's Conjecture" and has been confirmed in animals and humans, and showed they are of similar sizes; for example, in the UK Biobank, of 118 continuous human traits, only 29% of their intercorrelations have opposite signs, and a later analysis of 17 high-quality UKBB traits reported correlation near-unity.

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 or education and family SES 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, for two traits with heritabilities of 0.60 & 0.23, $r_g=0.75$, and phenotypic correlation of ''r''=0.45 the bivariate heritability would be $\sqrt \cdot 0.75 \cdot \sqrt = 0.28$, so of the observed phenotypic correlation, 0.28/0.45 = 62% of it is due to genetics.)

Cause

Genetic correlations can arise due to:

# linkage disequilibrium (two neighboring genes tend to be inherited together, each affecting a different trait)
# biological pleiotropy (a single gene having multiple otherwise unrelated biological effects, or shared regulation of multiple genes)
# mediated pleiotropy (a gene causes trait ''X'' and trait ''X'' causes trait ''Y'').
# biases: population stratification such as ancestry or assortative mating (sometimes called "gametic phase disequilibrium"), spurious stratification such as ascertainment bias/self-selection 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 (e.g. intelligence is stable over a lifetime, due to the same genetic influences – childhood genetically correlates $r_g=0.62$ with old age), or across studies or populations or ethnic groups/races , or across diagnoses, allowing discovery of whether different genes influence a trait over a lifetime (typically, they do not), 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 (for example, reading & mathematics disability genetically correlate, consistent with the Generalist Genes Hypothesis, and these genetic correlations explain the observed phenotypic correlations or 'co-morbidity'; IQ and specific measures of cognitive performance such as verbal, spatial, and memory tasks, reaction time, long-term memory, executive function etc. all show high genetic correlations as do neuroanatomical measurements , and the correlations may increase with age, with implications for the etiology & nature of intelligence). 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 and the strongest SNP candidates can be used to increase the statistical power of a smaller GWAS, 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%; Hill et al. 2017b uses MTAG 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.

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.

Breeding

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''. 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. Some traits, such as the size of eyespots on the butterfly ''Bicyclus anynana

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