In charlotte-ngs/lbgfs2020: Livestock Breeding and Genomics (Fall 2020)

knitr::opts_chunk$set(echo = FALSE, results = "asis")
knitr::knit_hooks$set(hook_convert_odg = rmdhelp::hook_convert_odg)

So far ...

• Prediction of breeding values based on regression approach
• Usage of single class of information
  • own performance on the same trait
  • repeated measures
  • offspring records

$\rightarrow$ How to combine different sources of information

Desired Scenario

#rmdhelp::use_odg_graphic(ps_path = "odg/desiredscenario.odg")
knitr::include_graphics(path = "odg/desiredscenario.png")

Two Approaches

1. Selection Index Theory and

2. Best Linear Unbiased Prediction (BLUP)

3. Same genetic model

4. Main difference in how identifiable environment is corrected for
5. Start with 1. then move to 2.
6. Nowadays 2. is most widely used method

Differentiate between

• true breeding value: measures genetic potential, but cannot be observed
• predicted breeding value: use information, such as phenotypic observations to predict true breeding value as accurate as possible

Three objectives of predicted breeding values

1. selection criterion for parents of next generation
2. prediction of true breeding value as early as possible
3. predicted breeding values affect price of semen and breeding animals

Selection Index Method

#rmdhelp::use_odg_graphic(ps_path = "odg/selectionmethod.odg")
knitr::include_graphics(path = "odg/selectionmethod.png")

What is the Selection Index

• Combine all available information
• Assign single number $I$ to each animal
• Rank animals according to $I$
• Use ranking as selection criterion
• Weights $b_t$ for each information
• Determine weights $b$ - How To? Follows

Aggregate Genotype

• Want to improve more than just one trait
• How to select animals?

#rmdhelp::use_odg_graphic(ps_path = "odg/aggregategenotype.odg")
knitr::include_graphics(path = "odg/aggregategenotype.png")

Selection Methods

• Tandem selection: First improve only trait 1, then improve only trait 2
• Independent selection boundaries: select for trait 1, among selected look at trait 2
• Combine traits into aggregate genotype $H$

\begin{equation} H = w_1 a_1 + w_2 a_2 + \cdots + w_m a_m = w^T a \notag \end{equation}

\begin{tabular}{lll} where & $a$ & vector of true breeding values \ & $w$ & vector of economic values \end{tabular}

Economic Values

• Change in profit when trait changes
• How does the profit change when animals
  • are healthier or
  • produce more or
  • reduce environmental impact

Change in Profit

#rmdhelp::use_odg_graphic(ps_path = "odg/changeinprofit.odg")
knitr::include_graphics(path = "odg/changeinprofit.png")

Selection Index Construction

• Index Construction means: finding unknown vector of weights $b$ in $I$
• Objective: $I$ has to approximate $H$ as good as possible
• Criterion:

\begin{equation} E(H-I)^2 \rightarrow \text{ min} \notag \end{equation}

• Result: Index normal equations

\begin{equation} Pb = Gw \notag \end{equation}

Solution

• Compute $b$ from index normal equation

\begin{align} Pb &= Gw \notag \ P^{-1}Pb &= P^{-1}Gw \notag \ b &= P^{-1}Gw \notag \end{align}

• Accuracy of index $I$

\begin{equation} r_{HI} = \frac{cov(H,I)}{\sigma_H \sigma_I} = \frac{\sigma_I}{\sigma_H} \notag \end{equation}

charlotte-ngs/lbgfs2020 documentation built on Dec. 20, 2020, 5:39 p.m.