Breeder equation

The breeder equation ( english breeder's equation ) describes the expected phenotypic difference between parents and their children, taking into account hereditary factors. It is fundamental in quantitative genetics . It was introduced in 1937 by geneticist Jay Lush in his book Animal Breeding Plans .

the equation

${\displaystyle R=h^{2}\cdot S}$

${\displaystyle R}$: phenotypic difference between parents and children : heritability , proportion of the examined property inherited from the children : difference between parents and their relatives
${\displaystyle h^{2}}$
${\displaystyle S}$

If several properties are to be investigated, the Lande's equation, which is derived from the breeder's equation, is used.

example

About half of intelligence is hereditary, and Alice and Bob are related to an average IQ of 100. Alice and Bob mate. Alice has an IQ of 110 and Bob has an IQ of 130. How smart will your child be?

${\displaystyle h^{2}=0{,}5}$
${\displaystyle {\bar {q}}_{\text{Eltern}}={\frac {q_{\text{Alice}}+q_{\text{Bob}}}{2}}={\frac {110+130}{2}}=120}$
${\displaystyle S={\bar {q}}_{\text{Eltern}}-q_{\text{Verwandtschaft}}=120-100=20}$
${\displaystyle R=h^{2}\cdot S=0{,}5\cdot 20=10}$
${\displaystyle q_{\text{Kind}}={\bar {q}}_{\text{Eltern}}-R=120-10=110}$

On average, Alice and Bob's child would have an IQ of around 110. Exceptions prove the rule.

That's because his parents' intelligence is the result of both hereditary and non-hereditary factors. The latter lead to a regression to the average value (regression to the mean) of the examined property (IQ 100 in this example). Regression does not mean reduction, but adaptation: The breeder equation would e.g. B. also allow a below-average intelligent couple to produce above-average intelligent children on average.

Problems

The breeding equation does not reliably predict the evolution of wild animal populations. In addition, its result can contradict that of the Price equation if phenotypic and genetic properties are not in the same relationship to the fitness of a living being.

swell

• ThePEG - Equation of the Month: The Breeder's Equation
• The multivariate breeder's equation: Evolution in Structured Populations: University of Vermont

Individual evidence

1. ↑ Jay Lush: Animal Breeding Plans . 1st edition. Collegiate Press, Iowa 1937, chap. 12 (English).
2. ↑ Michael B. Morrissey et al: The danger of applying the breeder's equation in observational studies of natural populations . In: Journal of Evolutionary Biology . tape 23 , no. 11 , November 2010, p. 2277–2288 , doi : 10.1111 / j.1420-9101.2010.02084.x (English).