Genetic correlation

In multivariate quantitative genetics, a genetic correlation (denoted ${\displaystyle r_{g}}$ or ${\displaystyle r_{a}}$) 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.

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, ${\displaystyle r_{g}=0.75}$, and phenotypic correlation of r=0.45 the bivariate heritability would be ${\displaystyle {\sqrt {0.60}}\cdot 0.75\cdot {\sqrt {0.23}}=0.28}$, 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 ${\displaystyle r_{g}=0.62}$ 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.

—  Charles Darwin, The Origin of Species , 1859

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 ${\displaystyle \Sigma }$ is a genetic covariance matrix and ${\displaystyle D={\sqrt {\operatorname {diag} (\Sigma )}}}$, then the correlation matrix is ${\displaystyle D^{-1}\Sigma D^{-1}}$. For a given genetic covariance ${\displaystyle \operatorname {cov} _{g}}$ between two traits, one with genetic variance ${\displaystyle V_{g1}}$ and the other with genetic variance ${\displaystyle V_{g2}}$, the genetic correlation is computed in the same way as the correlation coefficient ${\displaystyle r_{g}={\frac {\operatorname {cov} _{g}}{\sqrt {V_{g1}V_{g2}}}}}$.

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 ${\displaystyle r_{g}}$ is ${\displaystyle \sigma (r_{g})={\frac {1-r_{g}^{2}}{\sqrt {2}}}\cdot {\sqrt {\frac {\sigma (h_{x}^{2})\cdot \sigma (h_{y}^{2})}{h_{x}^{2}\cdot h_{y}^{2}}}}}$. ^[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:

	Height	Weight
Height	36	36
Weight	36	117

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

	Height	Weight
Height	1
Weight	.55	1

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

• Gene-environment correlation
• Heritability of intelligence; g factor (psychometrics)
• Cognitive epidemiology
• Lothian birth-cohort studies
• Mendelian randomization

References

1. Falconer, Ch. 19
2. Lynch, M. and Walsh, B. (1998) Genetics and Analysis of Quantitative Traits, Sinauer,Ch21, "Correlations Between Characters", "Ch25, Threshold Characters" ISBN   9780878934812
3. Neale & Maes (1996), Methodology for genetics studies of twins and families Archived 2017-03-27 at the Wayback Machine (6th ed.). Dordrecht, The Netherlands: Kluwer.
4. Plomin et al., p. 123
5. Martin, N. G.; Eaves, L. J. (1977). "The genetical analysis of covariance structure" (PDF). Heredity. 38 (1): 79–95. doi: 10.1038/hdy.1977.9 . PMID   268313. S2CID   12600152. Archived from the original (PDF) on 2016-10-25.
6. Eaves, L. J.; Last, K. A.; Young, P. A.; Martin, N. G. (1978). "Model-fitting approaches to the analysis of human behaviour". Heredity. 41 (3): 249–320. doi: 10.1038/hdy.1978.101 . PMID   370072. S2CID   302717.
7. Loehlin & Vandenberg (1968) "Genetic and environmental components in the covariation of cognitive abilities: An additive model", in Progress in Human Behaviour Genetics, ed. S. G. Vandenberg, pp. 261–278. Johns Hopkins, Baltimore.
8. Purcell, S.; Sham, P. (2002). "Variance components models for gene-environment interaction in quantitative trait locus linkage analysis". Twin Research. 5 (6): 572–6. doi: 10.1375/136905202762342035 . PMID   12573188.
9. Kohler, H. P.; Behrman, J. R.; Schnittker, J. (2011). "Social Science Methods for Twins Data: Integrating Causality, Endowments and Heritability". Biodemography and Social Biology. 57 (1): 88–141. doi:10.1080/19485565.2011.580619. PMC   3158495 . PMID   21845929.
10. Bulik-Sullivan, Brendan; Finucane, Hilary K.; Anttila, Verneri; Gusev, Alexander; Day, Felix R.; Loh, Po-Ru; Duncan, Laramie; Perry, John R. B.; Patterson, Nick; Robinson, Elise B.; Daly, Mark J. (November 2015). "An atlas of genetic correlations across human diseases and traits". Nature Genetics. 47 (11): 1236–1241. doi:10.1038/ng.3406. PMC   4797329 . PMID   26414676.
11. Ning, Zheng; Pawitan, Yudi; Shen, Xia (August 2020). "High-definition likelihood inference of genetic correlations across human complex traits" (PDF). Nature Genetics. 52 (8): 859–864. doi:10.1038/s41588-020-0653-y. hdl: 10616/47311 . PMID   32601477. S2CID   220260262.
12. Wagner, G. P.; Zhang, J. (2011). "The pleiotropic structure of the genotype-phenotype map: The evolvability of complex organisms" (PDF). Nature Reviews. Genetics. 12 (3): 204–13. doi:10.1038/nrg2949. PMID   21331091. S2CID   8612268.^{[ dead link ]}
13. Cheverud, James M. (1988). "A Comparison of Genetic and Phenotypic Correlations". Evolution. 42 (5): 958–968. doi:10.2307/2408911. JSTOR   2408911. PMID   28581166.
14. Krapohl, E.; Euesden, J.; Zabaneh, D.; Pingault, J. B.; Rimfeld, K.; von Stumm, S.; Dale, P. S.; Breen, G.; O'Reilly, P. F.; Plomin, R. (2016). "Phenome-wide analysis of genome-wide polygenic scores" (PDF). Molecular Psychiatry. 21 (9): 1188–93. doi:10.1038/mp.2015.126. PMC   4767701 . PMID   26303664. Archived from the original (PDF) on 2017-02-02. Retrieved 2016-10-24.
15. Hagenaars, S. P.; Harris, S. E.; Davies, G.; Hill, W. D.; Liewald, D C M.; Ritchie, S. J.; Marioni, R. E.; Fawns-Ritchie, C.; Cullen, B.; Malik, R.; Worrall, B. B.; Sudlow, C L M.; Wardlaw, J. M.; Gallacher, J.; Pell, J.; McIntosh, A. M.; Smith, D. J.; Gale, C. R.; Deary, I. J.; Gale, C. R.; Deary, I. J. (2016). "Shared genetic aetiology between cognitive functions and physical and mental health in UK Biobank (N=112 151) and 24 GWAS consortia". Molecular Psychiatry. 21 (11): 1624–1632. doi:10.1038/mp.2015.225. PMC   5078856 . PMID   26809841.
16. Hill, W. D.; Hagenaars, S. P.; Marioni, R. E.; Harris, S. E.; Liewald DCM; Davies, G.; Okbay, A.; McIntosh, A. M.; Gale, C. R.; Deary, I. J. (2016). "Molecular genetic contributions to social deprivation and household income in UK Biobank (n=112,151)". Current Biology. 26 (22): 3083–3089. doi:10.1016/j.cub.2016.09.035. PMC   5130721 . PMID   27818178.
17. Zheng, Jie; Erzurumluoglu, A. Mesut; Elsworth, Benjamin L.; Kemp, John P.; Howe, Laurence; Haycock, Philip C.; Hemani, Gibran; Tansey, Katherine; Laurin, Charles; Pourcain, Beate St.; Warrington, Nicole M.; Finucane, Hilary K.; Price, Alkes L.; Bulik-Sullivan, Brendan K.; Anttila, Verneri; Paternoster, Lavinia; Gaunt, Tom R.; Evans, David M.; Neale, Benjamin M.; Neale, B. M. (2017). "LD Hub: A centralized database and web interface to perform LD score regression that maximizes the potential of summary level GWAS data for SNP heritability and genetic correlation analysis". Bioinformatics. 33 (2): 272–279. doi:10.1093/bioinformatics/btw613. PMC   5542030 . PMID   27663502.
18. Sivakumaran, Shanya; Agakov, Felix; Theodoratou, Evropi; Prendergast, James G.; Zgaga, Lina; Manolio, Teri; Rudan, Igor; McKeigue, Paul; Wilson, James F.; Campbell, Harry (2011). "Abundant pleiotropy in human complex diseases and traits". The American Journal of Human Genetics. 89 (5): 607–618. doi: 10.1016/j.ajhg.2011.10.004 . PMC   3213397 . PMID   22077970.
19. Solovieff, N.; Cotsapas, C.; Lee, P. H.; Purcell, S. M.; Smoller, J. W. (2013). "Pleiotropy in complex traits: challenges and strategies". Nature Reviews. Genetics. 14 (7): 483–495. doi:10.1038/nrg3461. PMC   4104202 . PMID   23752797.
20. Cotsapas, Chris; Voight, Benjamin F.; Rossin, Elizabeth; Lage, Kasper; Neale, Benjamin M.; Wallace, Chris; Abecasis, Gonçalo R.; Barrett, Jeffrey C.; Behrens, Timothy; Cho, Judy; De Jager, Philip L.; Elder, James T.; Graham, Robert R.; Gregersen, Peter; Klareskog, Lars; Siminovitch, Katherine A.; Van Heel, David A.; Wijmenga, Cisca; Worthington, Jane; Todd, John A.; Hafler, David A.; Rich, Stephen S.; Daly, Mark J.; FOCiS Network of Consortia (2011). "Pervasive sharing of genetic effects in autoimmune disease". PLOS Genetics. 7 (8): e1002254. doi: 10.1371/journal.pgen.1002254 . PMC   3154137 . PMID   21852963.
21. Chambers, J. C.; Zhang, W.; Sehmi, J.; Li, X.; Wass, M. N.; Van Der Harst, P.; Holm, H.; Sanna, S.; Kavousi, M.; Baumeister, S. E.; Coin, L. J.; Deng, G.; Gieger, C.; Heard-Costa, N. L.; Hottenga, J. J.; Kühnel, B.; Kumar, V.; Lagou, V.; Liang, L.; Luan, J.; Vidal, P. M.; Leach, I. M.; O'Reilly, P. F.; Peden, J. F.; Rahmioglu, N.; Soininen, P.; Speliotes, E. K.; Yuan, X.; Thorleifsson, G.; et al. (2011). "Genome-wide association study identifies loci influencing concentrations of liver enzymes in plasma". Nature Genetics. 43 (11): 1131–1138. doi:10.1038/ng.970. PMC   3482372 . PMID   22001757.
22. Hemani, Gibran; Bowden, Jack; Haycock, Philip; Zheng, Jie; Davis, Oliver; Flach, Peter; Gaunt, Tom; Smith, George Davey (2017). "Automating Mendelian randomization through machine learning to construct a putative causal map of the human phenome". doi:10.1101/173682. S2CID   8865889.{{cite journal}}: Cite journal requires |journal= (help)
23. Canela-Xandri, Oriol; Rawlik, Konrad; Tenesa, Albert (2018). "An atlas of genetic associations in UK Biobank". Nature Genetics. 50 (11): 1593–1599. doi:10.1038/s41588-018-0248-z. PMC   6707814 . PMID   30349118.
24. Socrates, Adam; Bond, Tom; Karhunen, Ville; Auvinen, Juha; Rietveld, Cornelius A.; Veijola, Juha; Jarvelin, Marjo-Riitta; o'Reilly, Paul F. (2017). "Polygenic risk scores applied to a single cohort reveal pleiotropy among hundreds of human phenotypes". doi:10.1101/203257. S2CID   90474334.{{cite journal}}: Cite journal requires |journal= (help)
25. Mõttus, René; Marioni, Riccardo; Deary, Ian J. (2017). "Markers of Psychological Differences and Social and Health Inequalities: Possible Genetic and Phenotypic Overlaps". Journal of Personality. 85 (1): 104–117. doi: 10.1111/jopy.12220 . hdl: 20.500.11820/6ea2bc27-6ce8-4cab-8efa-17a19437941c . PMID   26292196.
26. Burgess, S.; Butterworth, A. S.; Thompson, J. R. (2016). "Beyond Mendelian randomization: how to interpret evidence of shared genetic predictors". Journal of Clinical Epidemiology. 69: 208–216. doi:10.1016/j.jclinepi.2015.08.001. PMC   4687951 . PMID   26291580.
27. Hagenaars, Saskia P.; Gale, Catharine R.; Deary, Ian J.; Harris, Sarah E. (2017). "Cognitive ability and physical health: A Mendelian randomization study". Scientific Reports. 7 (1): 2651. Bibcode:2017NatSR...7.2651H. doi:10.1038/s41598-017-02837-3. PMC   5453939 . PMID   28572633.
28. Bowden, J.; Davey Smith, G.; Burgess, S. (2015). "Mendelian randomization with invalid instruments: Effect estimation and bias detection through Egger regression". International Journal of Epidemiology. 44 (2): 512–525. doi:10.1093/ije/dyv080. PMC   4469799 . PMID   26050253.
29. Verbanck, Marie; Chen, Chia-Yen; Neale, Benjamin; Do, Ron (2018). "Detection of widespread horizontal pleiotropy in causal relationships inferred from Mendelian randomization between complex traits and diseases". Nature Genetics. 50 (5): 693–698. doi:10.1038/s41588-018-0099-7. PMC   6083837 . PMID   29686387.
30. Falconer, p. 315 cites the example of chicken size and egg laying: chickens grown large for genetic reasons lay later, fewer, and larger eggs, while chickens grown large for environmental reasons lay quicker and more but normal sized eggs; Table 19.1 on p. 316 also provides examples of opposite-signed phenotypic & genetic correlations: fleece-weight/length-of-wool & fleece weight/body-weight in sheep, and body-weight/egg-timing & body-weight/egg-production in chicken. One consequence of the negative chicken correlations was that, despite moderate heritabilities and a positive phenotypic correlation, selection had begun to fail to yield any improvements (p. 329) according to "Genetic slippage in response to selection for multiple objectives", Dickerson 1955.
31. Kruuk, Loeske E. B.; Slate, Jon; Pemberton, Josephine M.; Brotherstone, Sue; Guinness, Fiona; Clutton-Brock, Tim (2002). "Antler Size in Red Deer: Heritability and Selection but No Evolution". Evolution. 56 (8): 1683–95. doi:10.1111/j.0014-3820.2002.tb01480.x. PMID   12353761. S2CID   33699313.
32. Cheverud, James M. (1988). "A comparison of genetic and phenotypic correlations". Evolution. 42 (5): 958–968. doi: 10.1111/j.1558-5646.1988.tb02514.x . PMID   28581166. S2CID   21190284.
33. Roff, Derek A. (1995). "The estimation of genetic correlations from phenotypic correlations – a test of Cheverud's conjecture". Heredity. 74 (5): 481–490. doi: 10.1038/hdy.1995.68 . S2CID   32644733.
34. Kruuk, Loeske E.B.; Slate, Jon; Wilson, Alastair J. (2008). "New answers for old questions: The evolutionary quantitative genetics of wild animal populations" (PDF). Annual Review of Ecology, Evolution, and Systematics. 39: 525–548. doi:10.1146/annurev.ecolsys.39.110707.173542. S2CID   86659038. Archived from the original (PDF) on 2019-07-21.
35. Dochtermann, Ned A. (2011). "Testing Cheverud's conjecture for behavioral correlations and behavioral syndromes". Evolution. 65 (6): 1814–1820. doi: 10.1111/j.1558-5646.2011.01264.x . PMID   21644966. S2CID   21760916.
36. Sodini, Sebastian M.; Kemper, Kathryn E.; Wray, Naomi R.; Trzaskowski, Maciej (2018). "Comparison of Genotypic and Phenotypic Correlations: Cheverud's Conjecture in Humans". Genetics. 209 (3): 941–948. doi: 10.1534/genetics.117.300630 . PMC   6028255 . PMID   29739817. S2CID   13668940.
37. Krapohl, E.; Plomin, R. (2016). "Genetic link between family socioeconomic status and children's educational achievement estimated from genome-wide SNPS". Molecular Psychiatry. 21 (3): 437–443. doi:10.1038/mp.2015.2. PMC   4486001 . PMID   25754083.
38. Plomin et al., p. 397
39. Tong, Pin; Monahan, Jack; Prendergast, James G. D. (2017). "Shared regulatory sites are abundant in the human genome and shed light on genome evolution and disease pleiotropy". PLOS Genetics. 13 (3): e1006673. doi: 10.1371/journal.pgen.1006673 . PMC   5365138 . PMID   28282383.
40. Munafò, Marcus R.; Tilling, Kate; Taylor, Amy E.; Evans, David M.; Davey Smith, George (2018). "Collider scope: When selection bias can substantially influence observed associations". International Journal of Epidemiology. 47 (1): 226–235. doi:10.1093/ije/dyx206. PMC   5837306 . PMID   29040562.
41. Hewitt, J. K.; Eaves, L. J.; Neale, M. C.; Meyer, J. M. (1988). "Resolving causes of developmental continuity or "tracking." I. Longitudinal twin studies during growth". Behavior Genetics. 18 (2): 133–51. doi:10.1007/BF01067836. PMID   3377729. S2CID   41253666.
42. Deary, I. J.; Yang, J.; Davies, G.; Harris, S. E.; Tenesa, A.; Liewald, D.; Luciano, M.; Lopez, L. M.; Gow, A. J.; Corley, J.; Redmond, P.; Fox, H. C.; Rowe, S. J.; Haggarty, P.; McNeill, G.; Goddard, M. E.; Porteous, D. J.; Whalley, L. J.; Starr, J. M.; Visscher, P. M. (2012). "Genetic contributions to stability and change in intelligence from childhood to old age" (PDF). Nature. 482 (7384): 212–5. Bibcode:2012Natur.482..212D. doi:10.1038/nature10781. hdl: 20.500.11820/4d760b66-7022-43c8-8688-4dc62f6d7659 . PMID   22258510. S2CID   4427683.
43. Rietveld, C. A.; Medland, S. E.; Derringer, J.; Yang, J.; Esko, T.; Martin, N. W.; Westra, H. J.; Shakhbazov, K.; Abdellaoui, A.; Agrawal, A.; Albrecht, E.; Alizadeh, B. Z.; Amin, N.; Barnard, J.; Baumeister, S. E.; Benke, K. S.; Bielak, L. F.; Boatman, J. A.; Boyle, P. A.; Davies, G.; De Leeuw, C.; Eklund, N.; Evans, D. S.; Ferhmann, R.; Fischer, K.; Gieger, C.; Gjessing, H. K.; Hägg, S.; Harris, J. R.; et al. (2013). "GWAS of 126,559 individuals identifies genetic variants associated with educational attainment". Science. 340 (6139): 1467–1471. Bibcode:2013Sci...340.1467R. doi:10.1126/science.1235488. PMC   3751588 . PMID   23722424.
44. Rietveld, C. A.; Esko, T.; Davies, G.; Pers, T. H.; Turley, P.; Benyamin, B.; Chabris, C. F.; Emilsson, V.; Johnson, A. D.; Lee, J. J.; Leeuw, C. d.; Marioni, R. E.; Medland, S. E.; Miller, M. B.; Rostapshova, O.; Van Der Lee, S. J.; Vinkhuyzen, A. A. E.; Amin, N.; Conley, D.; Derringer, J.; Van Duijn, C. M.; Fehrmann, R.; Franke, L.; Glaeser, E. L.; Hansell, N. K.; Hayward, C.; Iacono, W. G.; Ibrahim-Verbaas, C.; Jaddoe, V.; et al. (2014). "Common genetic variants associated with cognitive performance identified using the proxy-phenotype method". Proceedings of the National Academy of Sciences. 111 (38): 13790–13794. Bibcode:2014PNAS..11113790R. doi: 10.1073/pnas.1404623111 . PMC   4183313 . PMID   25201988.
45. Krapohl, E.; Patel, H.; Newhouse, S.; Curtis, C. J.; von Stumm, S.; Dale, P. S.; Zabaneh, D.; Breen, G.; O'Reilly, P. F.; Plomin, R. (2018). "Multi-polygenic score approach to trait prediction". Molecular Psychiatry. 23 (5): 1368–1374. doi:10.1038/mp.2017.163. PMC   5681246 . PMID   28785111.
46. Hill, W. D.; Marioni, R. E.; Maghzian, O.; Ritchie, S. J.; Hagenaars, S. P.; McIntosh, A. M.; Gale, C. R.; Davies, G.; Deary, I. J. (2019). "A combined analysis of genetically correlated traits identifies 187 loci and a role for neurogenesis and myelination in intelligence". Molecular Psychiatry. 24 (2): 169–181. doi:10.1038/s41380-017-0001-5. PMC   6344370 . PMID   29326435.
47. Turley, Patrick; Walters, Raymond K.; Maghzian, Omeed; Okbay, Aysu; Lee, James J.; Fontana, Mark Alan; Nguyen-Viet, Tuan Anh; Wedow, Robbee; Zacher, Meghan; Furlotte, Nicholas A.; Magnusson, Patrik; Oskarsson, Sven; Johannesson, Magnus; Visscher, Peter M.; Laibson, David; Cesarini, David; Neale, Benjamin M.; Benjamin, Daniel J. (2018). "Multi-trait analysis of genome-wide association summary statistics using MTAG". Nature Genetics. 50 (2): 229–237. doi:10.1038/s41588-017-0009-4. PMC   5805593 . PMID   29292387.
48. Andreassen, Ole A.; Thompson, Wesley K.; Schork, Andrew J.; Ripke, Stephan; Mattingsdal, Morten; Kelsoe, John R.; Kendler, Kenneth S.; O'Donovan, Michael C.; Rujescu, Dan; Werge, Thomas; Sklar, Pamela; Roddey, J. Cooper; Chen, Chi-Hua; McEvoy, Linda; Desikan, Rahul S.; Djurovic, Srdjan; Dale, Anders M.; Djurovic, S.; Dale, A. M. (2013). "Improved Detection of Common Variants Associated with Schizophrenia and Bipolar Disorder Using Pleiotropy-Informed Conditional False Discovery Rate". PLOS Genetics. 9 (4): e1003455. doi: 10.1371/journal.pgen.1003455 . PMC   3636100 . PMID   23637625.
49. Porter, Heather F.; o'Reilly, Paul F. (2017). "Multivariate simulation framework reveals performance of multi-trait GWAS methods". Scientific Reports. 7: 38837. Bibcode:2017NatSR...738837P. doi:10.1038/srep38837. PMC   5347376 . PMID   28287610.
50. De Vlaming, Ronald; Okbay, Aysu; Rietveld, Cornelius A.; Johannesson, Magnus; Magnusson, Patrik K. E.; Uitterlinden, André G.; Van Rooij, Frank J. A.; Hofman, Albert; Groenen, Patrick J. F.; Thurik, A. Roy; Koellinger, Philipp D. (2017). "Meta-GWAS Accuracy and Power (MetaGAP) Calculator Shows that Hiding Heritability is Partially Due to Imperfect Genetic Correlations across Studies". PLOS Genetics. 13 (1): e1006495. doi: 10.1371/journal.pgen.1006495 . PMC   5240919 . PMID   28095416.
51. Hazel, L. N. (1943). "The Genetic Basis for Constructing Selection Indexes". Genetics. 28 (6): 476–490. doi:10.1093/genetics/28.6.476. PMC   1209225 . PMID   17247099.
52. Rae, A. L. (1951) "The Importance of Genetic Correlations in Selection"
53. Hazel, L. N.; Lush, JAY L. (1942). "The Efficiency of Three Methods of Selection" (PDF). Journal of Heredity. 33 (11): 393–399. doi:10.1093/oxfordjournals.jhered.a105102.
54. Lerner, M. (1950) Population genetics and animal improvement: as illustrated by the inheritance of egg production. New York: Cambridge Univ. Press
55. Falconer, pp. 324–329
56. Conner, Jeffrey K. (2012). "Quantitative Genetic Approaches to Evolutionary Constraint: How Useful?". Evolution. 66 (11): 3313–3320. doi: 10.1111/j.1558-5646.2012.01794.x . PMID   23106699. S2CID   15933304.
57. Beldade, Patrícia; Koops, Kees; Brakefield, Paul M. (2002). "Developmental constraints versus flexibility in morphological evolution" (PDF). Nature. 416 (6883): 844–847. Bibcode:2002Natur.416..844B. doi:10.1038/416844a. PMID   11976682. S2CID   4382085.
58. Allen, Cerisse E.; Beldade, Patrícia; Zwaan, Bas J.; Brakefield, Paul M. (2008). "Differences in the selection response of serially repeated color pattern characters: Standing variation, development, and evolution". BMC Evolutionary Biology. 8 (1): 94. Bibcode:2008BMCEE...8...94A. doi: 10.1186/1471-2148-8-94 . PMC   2322975 . PMID   18366752.
59. Lee, S.H.; Yang, J.; Goddard, M.E.; Visscher, P.M.; Wray, N.R. (2012). "Estimation of pleiotropy between complex diseases using single-nucleotide polymorphism-derived genomic relationships and restricted maximum likelihood". Bioinformatics. 28 (19): 2540–2542. doi:10.1093/bioinformatics/bts474. PMC   3463125 . PMID   22843982.
60. Bulik-Sullivan, B. K.; Loh, P. R.; Finucane, H.; Ripke, S.; Yang, J.; Schizophrenia Working Group of the Psychiatric Genomics Consortium; Patterson, N.; Daly, M. J.; Price, A. L.; Neale, B. M. (2015). "LD Score regression distinguishes confounding from polygenicity in genome-wide association studies". Nature Genetics. 47 (3): 291–295. doi:10.1038/ng.3211. PMC   4495769 . PMID   25642630.
61. Loh, Po-Ru; Bhatia, Gaurav; Gusev, Alexander; Finucane, Hilary K.; Bulik-Sullivan, Brendan K.; Pollack, Samuela J.; Psychiatric Genomics Consortium, Schizophrenia Working Group; De Candia, Teresa R.; Lee, Sang Hong; Wray, Naomi R.; Kendler, Kenneth S.; O'Donovan, Michael C.; Neale, Benjamin M.; Patterson, Nick; Price, Alkes L. (2015). "Contrasting regional architectures of schizophrenia and other complex diseases using fast variance components analysis". doi:10.1101/016527. S2CID   196690764.{{cite journal}}: Cite journal requires |journal= (help)
62. Majumdar, Arunabha; Haldar, Tanushree; Bhattacharya, Sourabh; Witte, John S. (2018). "An efficient Bayesian meta-analysis approach for studying cross-phenotype genetic associations". PLOS Genetics. 14 (2): e1007139. doi: 10.1371/journal.pgen.1007139 . PMC   5825176 . PMID   29432419.
63. Shi, Huwenbo; Kichaev, Gleb; Pasaniuc, Bogdan (2016). "Contrasting the Genetic Architecture of 30 Complex Traits from Summary Association Data". The American Journal of Human Genetics. 99 (1): 139–153. doi:10.1016/j.ajhg.2016.05.013. PMC   5005444 . PMID   27346688.
64. Lynch, Michael (1999). "Estimating genetic correlations in natural populations". Genetical Research. 74 (3): 255–264. doi: 10.1017/s0016672399004243 . PMID   10689802.
65. Golan, David; Lander, Eric S.; Rosset, Saharon (2014). "Measuring missing heritability: Inferring the contribution of common variants". Proceedings of the National Academy of Sciences. 111 (49): E5272–E5281. Bibcode:2014PNAS..111E5272G. doi: 10.1073/pnas.1419064111 . PMC   4267399 . PMID   25422463.
66. Shi, Huwenbo; Mancuso, Nicholas; Spendlove, Sarah; Pasaniuc, Bogdan (2017). "Local Genetic Correlation Gives Insights into the Shared Genetic Architecture of Complex Traits". The American Journal of Human Genetics. 101 (5): 737–751. doi:10.1016/j.ajhg.2017.09.022. PMC   5673668 . PMID   29100087.
67. Posthuma, Daniëlle; Boomsma, Dorret I. (2000). "A Note on the Statistical Power in Extended Twin Designs" (PDF). Behavior Genetics. 30 (2): 147–158. doi:10.1023/A:1001959306025. PMID   10979605. S2CID   14920235. Archived from the original (PDF) on 2016-09-11. Retrieved 2016-10-24.
68. DeFries, J. C., Plomin, Robert, LaBuda, Michele C. (1987). "Genetic Stability of Cognitive Development From Childhood to Adulthood" (PDF). Developmental Psychology. 23 (1): 4–12. doi:10.1037/0012-1649.23.1.4.
69. Wray, Naomi R.; Lee, Sang Hong; Kendler, Kenneth S. (2012). "Impact of diagnostic misclassification on estimation of genetic correlations using genome-wide genotypes". European Journal of Human Genetics. 20 (6): 668–674. doi:10.1038/ejhg.2011.257. PMC   3355255 . PMID   22258521.
70. Falconer, pp. 317–318
71. Schmitt, J. E.; Eyler, L. T.; Giedd, J. N.; Kremen, W. S.; Kendler, K. S.; Neale, M. C. (2007). "Review of twin and family studies on neuroanatomic phenotypes and typical neurodevelopment". Twin Research and Human Genetics. 10 (5): 683–694. doi:10.1375/twin.10.5.683. PMC   4038708 . PMID   17903108.
72. Almasy, L.; Dyer, T. D.; Blangero, J. (1997). "Bivariate quantitative trait linkage analysis: Pleiotropy versus co-incident linkages". Genetic Epidemiology. 14 (6): 953–8. doi:10.1002/(SICI)1098-2272(1997)14:6<953::AID-GEPI65>3.0.CO;2-K. PMID   9433606. S2CID   34841607.
73. Heath, A. C.; Neale, M. C.; Hewitt, J. K.; Eaves, L. J.; Fulker, D. W. (1989). "Testing structural equation models for twin data using LISREL". Behavior Genetics. 19 (1): 9–35. doi:10.1007/BF01065881. PMID   2712816. S2CID   46155044.

Cited sources

• Falconer, Douglas Scott (1960). Introduction to Quantitative Genetics.
• Plomin, Robert; DeFries, John C.; Knopik, Valerie S. and Neiderhiser, Jenae M. (2012). Behavioral Genetics. Worth Publishers. ISBN   978-1-4292-4215-8.

External links

• The G-matrix Online Archived 2016-09-18 at the Wayback Machine