Chapter 24.4, Problem 41AQP

Summary Introduction

To determine:

The characteristic that would respond best to selection among body weight, tenderness, and fat content in beef cattle.

Introduction:

Response to selection is denoted by the “R”. It determines the extent to which a trait subjected to selection changes in a generation. It is calculated as the product of narrow-sense heritability and selection differential. Mathematically, it can be expressed as follows:

$\text{R}=h^2\times \text{S}$

Here, R is the response to selection.

$h^2$ is the narrow-sense heritability.

S is the selection differential.

Explanation of Solution

To determine the characteristic that would respond best to selection, narrow-sense heritabilities of each trait should be calculated. The trait having highest narrow-sense heritability would have a highest response to selection as there is a direct relation between narrow-sense heritability and response to selection.

Narrow-sense heritability is denoted by the symbol h². It represents the proportion of phenotypic variance occurred due to one of the components (additive genetic variance) of genetic variance. Narrow-sense heritability is mathematically expressed as:

$h^2=\frac{V_A}{V_P}$

Here, h² is the narrow-sense heritability.

V_A is the additive genetic variance.

V_P is the genetic variance.

There are three components of phenotypic variance, which are used in its calculation. These components are genetic variance, environmental variance, and genetic-environmental variance. Furthermore, genetic variance also has three components; additive genetic variance, dominance genetic variance, and gene interaction variance. Mathematically, it can be expressed as follows:

$\begin{array}{l}{h}^2=\frac{V_A}{V_G+V_E+V_{GE}}\\ h^2=\frac{V_A}{V_A+V_D+V_I+V_E+V_{GE}}\end{array}$

Narrow-sense heritabilities of among body weight, tenderness, and fat content in beef cattle are as follows:

1. Narrow-sense heritability for body weight.

$\begin{array}{l}{h}^2=\frac{V_A}{V_A+V_D+V_I+V_E+V_{GE}}\\ h^2=\frac{22}{22+10+3+42+0}\\ h^2=\frac{22}{77}\\ h^2=0.29\end{array}$

2. Narrow-sense heritability for tenderness.

$\begin{array}{l}{h}^2=\frac{V_A}{V_A+V_D+V_I+V_E+V_{GE}}\\ h^2=\frac{12}{12+5+2+8+1}\\ h^2=\frac{12}{28}\\ h^2=0.43\end{array}$

3. Narrow-sense heritability for fat content.

$\begin{array}{l}{h}^2=\frac{V_A}{V_A+V_D+V_I+V_E+V_{GE}}\\ h^2=\frac{45}{45+25+8+64+0}\\ h^2=\frac{45}{142}\\ h^2=0.32\end{array}$

The highest narrow-sense heritability is of tenderness, which is 0.43. So, the characteristic that would respond best to selection is tenderness.

Conclusion

Tenderness would respond best to selection among body weight, tenderness, and fat content in beef cattle.