Since only
P can be observed or measured directly, heritability must be estimated from the similarities observed in subjects varying in their level of genetic or environmental similarity. The
statistical analyses required to estimate the
genetic and
environmental components of variance depend on the sample characteristics. Briefly, better estimates are obtained using data from individuals with widely varying levels of genetic relationship - such as
twins, siblings, parents and offspring, rather than from more distantly related (and therefore less similar) subjects. The
standard error for heritability estimates is improved with large sample sizes. In non-human populations it is often possible to collect information in a controlled way. For example, among farm animals it is easy to arrange for a bull to produce offspring from a large number of cows and to control environments. Such
experimental control is generally not possible when gathering human data, relying on naturally occurring relationships and environments. In classical quantitative genetics, there were two schools of thought regarding estimation of heritability. One
school of thought was developed by
Sewall Wright at
The University of Chicago, and further popularized by
C. C. Li (
University of Chicago) and
J. L. Lush (
Iowa State University). It is based on the analysis of correlations and, by extension, regression.
Path Analysis was developed by
Sewall Wright as a way of estimating heritability. The second was originally developed by
R. A. Fisher and expanded at
The University of Edinburgh,
Iowa State University, and
North Carolina State University, as well as other schools. It is based on the
analysis of variance of breeding studies, using the intraclass correlation of relatives. Various methods of estimating components of variance (and, hence, heritability) from
ANOVA are used in these analyses. Today, heritability can be estimated from general pedigrees using
linear mixed models and from
genomic relatedness estimated from genetic markers. Studies of human heritability often utilize adoption study designs, often with
identical twins who have been separated early in life and raised in different environments. Such individuals have identical genotypes and can be used to separate the effects of genotype and environment. A limit of this design is the common prenatal environment and the relatively low numbers of twins reared apart. A second and more common design is the
twin study in which the similarity of identical and fraternal twins is used to estimate heritability. These studies can be limited by the fact that identical twins are
not completely genetically identical, potentially resulting in an underestimation of heritability. In
observational studies, or because of evocative effects (where a genome evokes environments by its effect on them), G and E may covary:
gene environment correlation. Depending on the methods used to estimate heritability, correlations between genetic factors and shared or non-shared environments may or may not be confounded with heritability.
Regression/correlation methods of estimation The first school of estimation uses regression and correlation to estimate heritability.
Comparison of close relatives In the comparison of relatives, we find that in general, :h^2 = \frac{b}{r} = \frac{t}{r} where
r can be thought of as the
coefficient of relatedness,
b is the coefficient of regression and
t is the coefficient of correlation.
Parent-offspring regression 's (1889) data set. Heritability may be estimated by comparing parent and offspring traits (as in Fig. 2). The slope of the line (0.713) approximates the heritability of the trait when offspring values are regressed against the average trait in the parents. If only one parent's value is used then heritability is twice the slope. (This is the source of the term "
regression," since the offspring values always tend to
regress to the mean value for the population,
i.e., the slope is always less than one). This regression effect also underlies the
DeFries–Fulker method for analyzing twins selected for one member being affected.
Sibling comparison A basic approach to heritability can be taken using full-Sib designs: comparing similarity between siblings who share both a biological mother and a father. When there is only additive gene action, this sibling phenotypic correlation is an index of
familiarity – the sum of half the additive genetic variance plus full effect of the common environment. It thus places an upper limit on additive heritability of twice the full-Sib phenotypic correlation. Half-Sib designs compare phenotypic traits of siblings that share one parent with other sibling groups.
Twin studies Heritability for traits in humans is most frequently estimated by comparing resemblances between twins. "The advantage of twin studies, is that the total variance can be split up into genetic, shared or common environmental, and unique environmental components, enabling an accurate estimation of heritability". Fraternal or dizygotic (DZ) twins on average share half their genes (assuming there is no
assortative mating for the trait), and so identical or monozygotic (MZ) twins on average are twice as genetically similar as DZ twins. A crude estimate of heritability, then, is approximately twice the difference in
correlation between MZ and DZ twins, i.e.
Falconer's formula H2=2(r(MZ)-r(DZ)). The effect of shared environment,
c2, contributes to similarity between siblings due to the commonality of the environment they are raised in. Shared environment is approximated by the DZ correlation minus half heritability, which is the degree to which DZ twins share the same genes,
c2 = r(DZ) - 1/2
h2. Unique environmental variance,
e2, reflects the degree to which identical twins raised together are dissimilar,
e2=1-r(MZ).
Analysis of variance methods of estimation The second set of methods of estimation of heritability involves ANOVA and estimation of variance components.
Basic model We use the basic discussion of Kempthorne.
Model with additive and dominance terms For a model with additive and dominance terms, but not others, the equation for a single locus is :y_{ij} = \mu + \alpha_i + \alpha_j + d_{ij} + e, where \alpha_i is the additive effect of the ith allele, \alpha_j is the additive effect of the jth allele, d_{ij} is the dominance deviation for the ijth genotype, and e is the environment. Experiments can be run with a similar setup to the one given in Table 1. Using different relationship groups, we can evaluate different intraclass correlations. Using V_a as the additive genetic variance and V_d as the dominance deviation variance, intraclass correlations become
linear functions of these parameters. In general, :Intraclass correlation = r V_a + \theta V_d, where r and \theta are found as r = P[
alleles drawn at random from the relationship pair are
identical by descent], and \theta = P[
genotypes drawn at random from the relationship pair are
identical by descent]. Some common relationships and their coefficients are given in Table 2.
Linear mixed models A wide variety of approaches using linear mixed models have been reported in literature. Via these methods, phenotypic variance is partitioned into genetic, environmental and experimental design variances to estimate heritability. Environmental variance can be explicitly modeled by studying individuals across a broad range of environments, although inference of genetic variance from phenotypic and environmental variance may lead to underestimation of heritability due to the challenge of capturing the full range of environmental influence affecting a trait. Other methods for calculating heritability use data from
genome-wide association studies to estimate the influence on a trait by genetic factors, which is reflected by the rate and influence of putatively associated genetic loci (usually
single-nucleotide polymorphisms) on the trait. This can lead to underestimation of heritability, however. This discrepancy is referred to as "missing heritability" and reflects the challenge of accurately modeling both genetic and environmental variance in heritability models. When a large, complex pedigree or another aforementioned type of data is available, heritability and other quantitative genetic parameters can be estimated by
restricted maximum likelihood (REML) or
Bayesian methods. The
raw data will usually have three or more data points for each individual: a code for the sire, a code for the dam and one or several trait values. Different trait values may be for different traits or for different time points of measurement. The currently popular methodology relies on high degrees of certainty over the identities of the sire and dam; it is not common to treat the sire identity probabilistically. This is not usually a problem, since the methodology is rarely applied to wild populations (although it has been used for several wild ungulate and bird populations), and sires are invariably known with a very high degree of certainty in breeding programmes. There are also algorithms that account for uncertain paternity. The pedigrees can be viewed using programs such as Pedigree Viewer and analyzed with programs such as
ASReml, VCE [https://web.archive.org/web/20070312053650/http://vce.tzv.fal.de/index.pl, WOMBAT MCMCglmm within the R environment [https://www.rdocumentation.org/packages/MCMCglmm/versions/2.29/topics/MCMCglmm-package or the
BLUPF90 family of programs . Pedigree models are helpful for untangling confounds such as
reverse causality,
maternal effects such as the
prenatal environment, and confounding of
genetic dominance, shared environment, and maternal gene effects.
Genomic heritability When genome-wide genotype data and phenotypes from large population samples are available, one can estimate the relationships between individuals based on their genotypes and use a linear mixed model to estimate the variance explained by the genetic markers. This gives a genomic heritability estimate based on the variance captured by common genetic variants. There are multiple methods that make different adjustments for allele frequency and
linkage disequilibrium. Particularly, the method called High-Definition Likelihood (HDL) can estimate genomic heritability using only GWAS summary statistics, making it easier to incorporate large sample size available in various GWAS meta-analysis. == Response to selection ==