Genome-wide complex trait analysis
Genome-wide complex trait analysis (GCTA) Genome-based restricted maximum likelihood (GREML) is a statistical method for variance component estimation in genetics which quantifies the total narrow-sense (additive) contribution to a trait's heritability of a particular subset of genetic variants (typically limited to SNPs with MAF >1%, hence terms such as "chip heritability"/"SNP heritability"). This is done by directly quantifying the chance genetic similarity of unrelated individuals and comparing it to their measured similarity on a trait; if two unrelated individuals are relatively similar genetically and also have similar trait measurements, then  the measured genetics are likely to causally influence that trait, and the correlation can to some degree tell how much. This can be illustrated by plotting the squared pairwise trait differences between individuals against their estimated degree of relatedness. The GCTA framework can be applied in a variety of settings. For example, it can be used to examine changes in heritability over aging and development. It can also be extended to analyse bivariate genetic correlations between traits. There is an ongoing debate about whether GCTA generates reliable or stable estimates of heritability when used on current SNP data. The method  is based on the outdated and false dichotomy of genes versus the environment. It also suffers from serious methodological weaknesses, such as susceptibility to population stratification. GCTA heritability estimates are useful because they provide lower bounds for the genetic contributions to traits such as intelligence without relying on the assumptions used in twin studies and other family and pedigree studies, thereby corroborating them and enabling the design of well-powered genome-wide association study (GWAS) designs to find the specific genetic variants involved. For example, a GCTA estimate of 30% SNP heritability is consistent with a larger total genetic heritability  of 70%. However, if the GCTA estimate was ~0%, then that would imply one of three things: a) there is no genetic contribution, b) the genetic contribution is entirely in the form of genetic variants not included, or c) the genetic contribution is entirely in the form of non-additive effects such as epistasis/dominance. Running GCTA on individual chromosomes and regressing the estimated proportion of trait variance explained by each chromosome against that chromosome's length can reveal whether the responsible genetic variants cluster or are distributed evenly across the genome or are sex-linked. Chromosomes can of course  be replaced by more fine-grained or functionally informed subdivisions. Examining genetic correlations can reveal to what extent observed correlations, such as between intelligence and socioeconomic status, are due to the same genetic traits, and in the case of diseases, can indicate shared causal pathways such as can be inferred from the genetic variation jointly associated with schizophrenia and other mental diseases or reduced intelligence. History. Estimation in biology/animal breeding using standard ANOVA/REML methods of variance components such as heritability, shared-environment, maternal effects etc. typically requires individuals of known relatedness such as parent/child; this is often  unavailable or the pedigree data unreliable, leading to inability to apply the methods or requiring strict laboratory control of all breeding (which threatens the external validity of all estimates), and several authors have noted that relatedness could be measured directly from genetic markers (and if individuals were reasonably related, economically few markers would have to be obtained for statistical power), leading Kermit Ritland to propose in 1996 that directly measured pairwise relatedness could be compared to pairwise phenotype measurements (Ritland 1996, "A Marker-based Method for Inferences About Quantitative Inheritance in Natural Populations"). As genome sequencing costs dropped steeply over  the 2000s, acquiring enough markers on enough subjects for reliable estimates using very distantly related individuals became possible. An early application of the method to humans came with Visscher et al. 2006/2007, which used SNP markers to estimate the actual relatedness of siblings and estimate heritability from the direct genetics. In humans, unlike the original animal/plant applications, relatedness is usually known with high confidence in the 'wild population', and the benefit of GCTA is connected more to avoiding assumptions of classic behavioral genetics designs and verifying their results, and partitioning heritability by SNP class and chromosomes. The first use  of GCTA proper in humans was published in 2010, finding 45% of variance in human height can be explained by the included SNPs. (Large GWASes on height have since confirmed the estimate.) The GCTA algorithm was then described and a software implementation published in 2011. It has since been used to study a wide variety of biological, medical, psychiatric, and psychological traits in humans, and inspired many variant approaches. Benefits. Robust heritability. Twin and family studies have long been used to estimate variance explained by particular categories of genetic and environmental causes. Across a wide variety of human traits studied , there is typically minimal shared-environment influence, considerable non-shared environment influence, and a large genetic component (mostly additive), which is on average ~50% and sometimes much higher for some traits such as height or intelligence. However, the twin and family studies have been criticized for their reliance on a number of assumptions that are difficult or impossible to verify, such as the equal environments assumption (that the environments of monozygotic and dizygotic twins are equally similar), that there is no misclassification of zygosity (mistaking identical for fraternal & vice versa), that twins are unrepresentative of the general population, and that  there is no assortative mating. Violations of these assumptions can result in both upwards and downwards bias of the parameter estimates. (This debate & criticism have particularly focused on the heritability of IQ.) The use of SNP or whole-genome data from unrelated subject participants (with participants too related, typically >0.025 or ~fourth cousins levels of similarity, being removed, and several principal components included in the regression to avoid & control for population stratification) bypasses many heritability criticisms: twins are often entirely uninvolved, there are no questions of equal treatment, relatedness is estimated precisely, and the samples are drawn from a  broad variety of subjects. In addition to being more robust to violations of the twin study assumptions, SNP data can be easier to collect since it does not require rare twins and thus also heritability for rare traits can be estimated (with due correction for ascertainment bias). GWAS power. GCTA estimates can be used to resolve the missing heritability problem and design GWASes which will yield genome-wide statistically-significant hits. This is done by comparing the GCTA estimate with the results of smaller GWASes. If a GWAS of n=10k using SNP data fails to turn up any hits, but  the GCTA indicates a high heritability accounted for by SNPs, then that implies that a large number of variants are involved (polygenicity) and thus that much larger GWASes will be required to accurately estimate each SNP's effect and directly account for a fraction of the GCTA heritability. Interpretation. GCTA estimates are often misinterpreted as "the total genetic contribution", and since they are often much less than the twin study estimates, the twin studies are presumed to be biased and the genetic contribution to a particular trait is minor. This is incorrect, as GCTA estimates are lower bounds. A more  correct interpretation would be that: GCTA estimates are the expected amount of variance that could be predicted by an indefinitely large GWAS using a simple additive linear model (without any interactions or higher-order effects) in a particular population at a particular time given the limited selection of SNPs and a trait measured with a particular amount of precision. Hence, there are many ways to exceed GCTA estimates: Implementations. The original "GCTA" software package is the most widely used; its primary functionality covers the GREML estimation of SNP heritability, but includes other functionality: Other implementations and variant algorithms include: Traits . GCTA estimates frequently find estimates 0.1-0.5, consistent with broadsense heritability estimates (with the exception of personality traits, for which theory & current GWAS results suggest non-additive genetics driven by frequency-dependent selection). Traits univariate GCTA has been used on (excluding SNP heritability estimates computed using other algorithms such as LD score regression, and bivariate GCTAs which are listed in genetic correlation) include (point-estimate format: "formula_4(standard error)"):