A Numerical Example

To illustrate how this works, let's examine the simple example in Table 1.

Table 1: A simple example to illustrate response to selection in a quantitative trait.

Genotype	$A_1A_1$	$A_1A_2$	$A_2A_2$
Phenotype	1.303	1.249	0.948

Given these phenotypes, $p = 0.25$, and $V_p = 0.16$, it follows that ${\bar x} = 1.08$ and $h^2_N = 0.1342$. Suppose the mean phenotype after selection is 1.544. What will the phenotype be among the newly born progeny?

$$\begin{eqnarray*} S &=& \bar x^* - \bar x \\ &=& 1.544 - 1.08 \\ &=& 0.46... ...&=& \bar x + \Delta\bar x \\ &=& 1.08 + 0.06 \\ &=& 1.14 \end{eqnarray*}$$