# User Contributed Dictionary

### Noun

- The condition of being inherited
- In the context of "countable|genetics": The ratio of the genetic variance of a population to its phenotypic variance; i.e. the proportion of variability that is genetic in origin

# Extensive Definition

In genetics, Heritability is the
proportion of phenotypic
variation in a population that is attributable to genetic variation among
individuals. Variation among individuals may be due to genetic
and/or environmental factors. Heritability analyses estimate the
relative contributions of differences in genetic and non-genetic
factors to the total phenotypic variance in a population.

## Definition

Consider a statistical
model for describing some particular phenotype:

- Phenotype (P) = Genotype (G) + Environment (E).

- Var(P) = Var(G) + Var(E) + 2 Cov(G,E).

- H^2 = \frac .

The parameter H2 is the broad-sense heritability
and reflects all possible genetic contributions to a population's
phenotypic variance. Included are effects due to allelic variation
(additive variance), dominance
variation or which act epistatically
(multi-genic interactions), as well as maternal
and paternal effects, where individuals are directly affected of
their parents' phenotype (such as with milk production in
mammals).

These additional terms can be included in genetic
models. For example, the simplest genetic model involves a single
locus with two alleles that effect some quantitative phenotype, as
shown by + in Figure 1. We can calculate the linear regression of
phenotype on the number of B alleles (0, 1, or 2), which is shown
as the Linear Effect line. For any genotype, BiBj, the expected
phenotype can then be written as the sum of the overall mean, a
linear effect, and a dominance deviation:

- P_ = \mu + \alpha_i + \alpha_j + d_ = Population mean + Additive Effect (a_=\alpha_i+\alpha_j) + Dominance Deviation (d_).

The additive genetic variance is the weighted
average of the squares of the additive effects:

- Var(A) = f(bb)a^2_+f(Bb)a^2_+f(BB)a^2_,

where f(bb)a_+f(Bb)a_+f(BB)a_ = 0.

There is a similar relationship for variance of
dominance deviations:

- Var(D) = f(bb)d^2_+f(Bb)d^2_+f(BB)d^2_,

where f(bb)d_+f(Bb)d_+f(BB)d_ = 0.

Narrow-sense heritability is defined as

- h^2 = \frac

and quantifies only the portion of the phenotypic
variation that is additive (allelic) by nature (note upper case H2
for broad sense, lower case h2 for narrow sense). When interested
in improving livestock via artificial selection, for example,
knowing the narrow-sense heritability of the trait of interest will
allow predicting how much the mean of the trait will increase in
the next generation as a function of how much the mean of the
selected parents differs from the mean of the population from which
the selected parents were chosen. The observed response to
selection leads to an estimate of the narrow-sense heritability
(called realized heritability).

## Estimating heritability

Estimating heritability is not a simple process, since only P can be observed or measured directly. Measuring the genetic and environmental variance requires various sophisticated statistical methods. These methods give better estimates when using data from closely related individuals - such as brothers, sisters, parents and offspring, rather than from more distantly related ones. The standard error for heritability estimates are generally very poor unless the dataset is large.Calculating the strength of selection, S (the
difference in mean trait between the population as a whole and the
selected parents of the next generation, also called the selection
differential ) and response to selection R (the difference in
offspring and whole parental generation mean trait) in an
artificial selection experiment will allow calculation of realized
heritability as the response to selection relative to the strength
of selection, h2=R/S as in Fig. 3.

### Comparison of close relatives

In the comparison of relatives, we find that in general,h^2 = \frac = \frac where r can be thought of as
the
coefficient of relatedness, b is the coefficient of regression
and t the coefficient of correlation.

#### Parent-offspring regression

Heritability may be estimated by comparing parent
and offspring traits (as In Fig. 4). The slope of the line (0.57)
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. (note
that 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).

#### Full-sib comparison

Full-sib designs compare phenotypic traits of siblings that share a mother and a father with other sibling groups. The estimate of the sibling phenotypic correlation is an index on familiality which is equal to half the additive genetic variance plus the common environment variance when there is only additive gene action.#### Half-sib comparison

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 (Fig. 2 & 5). Identical twins (MZ twins) are twice as genetically similar as fraternal twins (DZ twins) and so heritability is approximately twice the difference in correlation between MZ and DZ twins, 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 degee to which DZ twins share the same genes, c2=DZ-1/2h2. Unique environmental variance, e2, reflects the degree to which identical twins raised together are dissimilar, e2=1-r(MZ).The classical twin study has
been severely criticized
and is used less and less frequently nowadays.

### Large, complex pedigrees

## 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 (1957 [1969]). Considering only the most basic of genetic models, we can look at the quantitative contribution of a single locus with genotype Gi asy_i = \mu + g_i + e

where

g_i is the effect of genotype Gi

and e is the environmental effect.

Consider an experiment with a group of sires and
their progeny from random dams. Since the progeny get half of their
genes from the father and half from their (random) mother, the
progeny equation is

z_i = \mu + \fracg_i + e

#### Intraclass correlations

Consider the experiment above. We have two groups of progeny we can compare. The first is comparing the various progeny for an individual sire (called within sire group). The variance will include terms for genetic variance (since they did not all get the same genotype) and environmental variance. This is thought of as an error term.The second group of progeny are comparisons of
means of half sibs with each other (called among sire group). In
addition to the error term as in the within sire groups, we have an
addition term due to the differences among different means of half
sibs. The intraclass correlation is

- corr(z,z') = corr(\mu + \fracg + e, \mu + \fracg + e') = \fracV_g ,

#### The ANOVA

In an experiment with n sires and r progeny per sire, we can calculate the following ANOVA, using V_g as the genetic variance and V_e as the environmental variance:The \fracV_g term is the intraclass correlation
among half sibs. We can easily calculate H^2 = \frac = \frac. The
Expected Mean Square is calculated from the relationship of the
individuals (progeny within a sire are all half-sibs, for example),
and an understanding of intraclass correlations.

### 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_ = \mu + \alpha_i + \alpha_j + d_ + e,

where

\alpha_i is the additive effect of the ith
allele, \alpha_j is the additive effect of the jth allele, d_ 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.

### Larger models

When a large, complex pedigree is available for estimating heritability, the most efficient use of the data is in a restricted maximum likelihood (REML) model. The raw data will usually have three or more datapoints 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 timepoints 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 http://www-personal.une.edu.au/~bkinghor/pedigree.htm,
and analysed with programs such as ASReml, VCE http://vce.tzv.fal.de/index.pl
or WOMBAT http://agbu.une.edu.au/~kmeyer/wombat.html.

## Response to Selection

In selective breeding of plants and animals, the
expected response to selection can be estimated by the following
equation:

R = h2S

In this equation, the Response to Selection (R)
is defined as the realized average difference between the parent
generation and the next generation. The Selection Differential (S)
is defined as the average difference between the parent generation
and the selected parents.

For example, imagine that a plant breeder is
involved in a selective breeding project with the aim of increasing
the number of kernels per ear of corn. For the sake of argument,
let us assume that the average ear of corn in the parent generation
has 100 kernels. Let us also assume that the selected parents
produce corn with an average of 120 kernels per ear. If h2 equals
0.5, then the next generation will produce corn with an average of
0.5(120-100) = 10 additional kernels per ear. Therefore, the total
number of kernels per ear of corn will equal, on average,
110.

## External links

## References

### Notes

### Further reading

- Falconer, D. S. & Mackay TFC (1996). Introduction to Quantitative Genetics. Fourth edition. Addison Wesley Longman, Harlow, Essex, UK
- Gillespie, G. H. (1997). Population Genetics: A Concise Guide. Johns Hopkins University Press.
- Joseph, J. (2004). The Gene Illusion: Genetic Research in Psychiatry and Psychology Under the Microscope.New York: Algora. (2003 United Kingdom Edition by PCCS Books) (Chapter 5 contains a critique of the heritability concept)
- Joseph, J. (2006). Missing Gene: Psychiatry, Heredity, and the Fruitless Search for Genes.New York: Algora.
- Kempthorne, O (1957 [1969]) An Introduction to Genetic Statistics. John Wiley. Reprinted, 1969 by Iowa State University Press.
- Lynch, M. & Walsh, B. 1997. Genetics and Analysis of Quantitative Traits. Sinauer Associates. ISBN 0-87893-481-2.
- Malécot, G. 1948. Les Mathématiques de l'Hérédité. Masson, Paris.
- Wahlsten, D. (1994) The intelligence of heritability. Canadian Psychology 35, 244-258.

heritability in German: Heritabilität

heritability in Spanish: Heredabilidad

heritability in French: Héritabilité

heritability in Russian: Наследуемость
(генетика)

heritability in Serbian: Херитабилност

heritability in Finnish:
Heritabiliteetti