Editing Heritability (section)

== Response to selection ==
[[File:Response to selection.jpg|200px|right|thumbnail|Figure 4. Strength of selection (S) and response to selection (R) in an artificial selection experiment, ''h''<sup>2</sup>=R/S.]]

In [[selective breeding]] of plants and animals, the expected response to selection of a trait with known narrow-sense heritability <math> (h^2) </math> can be estimated using the ''breeder's equation'':<ref>{{cite book | vauthors = Plomin R, DeFries JC, McClearn GE, McGuffin P | title = Behavioral Genetics: A Primer. | edition = 2nd | location = New York | publisher = W.H. Freeman | year = 2017 | isbn = 978-0-7167-2056-0 | url = https://archive.org/details/behavioralgeneti0000plom_s9m8 }}</ref>

:<math> R = h^2 S </math>

In this equation, the Response to Selection (R) is defined as the realized average difference between the parent generation and the next generation, and the Selection Differential (S) is defined as the average difference between the parent generation and the selected parents.<ref name = "Kempthorne_1957" />{{rp|1957}}<ref>{{cite book | vauthors = Falconer DS, Mackay TF |title=Introduction to quantitative genetics |date=1998 |publisher=Longman |location=Essex |isbn=978-0-582-24302-6 |edition=4th |url=https://archive.org/details/introductiontoqu00falc }}</ref>

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 h<sup>2</sup> 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.

Observing the response to selection in an artificial selection experiment will allow calculation of realized heritability as in Fig. 4.

Heritability in the above equation is equal to the ratio <math>\mathrm{Var}(A)/\mathrm{Var}(P)</math> only if the genotype and the environmental noise follow [[Gaussian distributions]].