Editing Heritability (section)

====Comparison of close relatives====
In the comparison of relatives, we find that in general,

:<math>h^2 = \frac{b}{r} = \frac{t}{r}</math>

where ''r'' can be thought of as the [[Coefficient of relationship|coefficient of relatedness]], ''b'' is the coefficient of regression and ''t'' is the coefficient of correlation.

=====Parent-offspring regression=====
[[Image:Galton experiment.png|200px|right|thumbnail|Figure 2. [[Francis Galton]]'s (1889) data showing the relationship between offspring height (928 individuals) as a function of mean parent height (205 sets of parents).]]

Heritability may be estimated by comparing parent and offspring traits (as in Fig. 2). 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. (This is the source of the term "[[regression analysis|regression]]," since the offspring values always tend to [[regression toward the mean|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 regression|DeFries–Fulker method]] for analyzing twins selected for one member being affected.<ref>{{cite journal | vauthors = DeFries JC, Fulker DW | title = Multiple regression analysis of twin data | journal = Behavior Genetics | volume = 15 | issue = 5 | pages = 467–73 | date = September 1985 | pmid = 4074272 | doi = 10.1007/BF01066239 | s2cid = 1172312 }}</ref>

=====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.<ref>{{cite book | title = Introduction to Quantitative Genetics | first1 = Douglas S. | last1 = Falconer | first2 = Trudy F. C. | last2 = Mackay | name-list-style = vanc | date = December 1995 | publisher = [[Longman]] | edition = 4th | isbn = 978-0582243026 | url = https://archive.org/details/introductiontoqu00falc }}</ref> 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=====
{{main|Twin study}}

[[Image:Twin-concordances.jpg|300px|thumbnail|Figure 3. Twin concordances for seven psychological traits (sample size shown inside bars), with DZ being fraternal and MZ being identical twins.]]
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".<ref name="pmid18157630">{{cite journal | vauthors = Gielen M, Lindsey PJ, Derom C, Smeets HJ, Souren NY, Paulussen AD, Derom R, Nijhuis JG | title = Modeling genetic and environmental factors to increase heritability and ease the identification of candidate genes for birth weight: a twin study | journal = Behavior Genetics | volume = 38 | issue = 1 | pages = 44–54 | date = January 2008 | pmid = 18157630 | pmc = 2226023 | doi = 10.1007/s10519-007-9170-3 }}</ref> 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]] ''H''<sup>2</sup>=2(r(MZ)-r(DZ)).

The effect of shared environment, ''c''<sup>2</sup>, 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, ''c''<sup>2</sup>=DZ-1/2''h''<sup>2</sup>. Unique environmental variance, ''e''<sup>2</sup>, reflects the degree to which identical twins raised together are dissimilar, ''e''<sup>2</sup>=1-r(MZ).