7 Estimating Breeding Values

Learning Objectives

By the end of this chapter, you will be able to:

Estimate breeding values using simple methods (own performance, pedigree index, progeny average)
Explain why contemporary groups must be accounted for
Describe the purpose and advantages of BLUP
Interpret EBVs and their accuracies
Understand why EBVs can change over time as new data arrive

7.1 Introduction

[Content to be developed: True Breeding Value (TBV) is unknown, but we can estimate it (EBV) from available information. This chapter covers methods from simple to sophisticated.]

7.2 The Challenge: TBV is Unknown

[Content to be developed: We want to rank animals by TBV, but we can only observe phenotypes. We must estimate TBV from phenotypes, pedigrees, and genomic data.]

7.3 Simple Estimation Methods

[Content to be developed: Basic approaches to estimating breeding values.]

7.3.1 Method 1: Own Performance

[Content to be developed:]

\[ \hat{BV} = h^2 (P - \mu) \]

Where P is the individual’s phenotype and μ is the population mean.

Accuracy: $r = \sqrt{h^2}$

Example: If h² = 0.36 and a pig weighs 100 kg while the mean is 90 kg, then EBV = 0.36 × (100 - 90) = 3.6 kg.

7.3.2 Method 2: Pedigree Index (Midparent BV)

[Content to be developed:]

\[ \hat{BV}_{offspring} = \frac{1}{2} (EBV_{sire} + EBV_{dam}) \]

Accuracy: $r = \sqrt{\frac{h^2}{2}}$ (assuming parent EBVs are true BVs)

Used for young animals without own records.

7.3.3 Method 3: Progeny Average

[Content to be developed:]

\[ \hat{BV}_{parent} = 2 \times (\bar{P}_{progeny} - \mu) \]

(Multiplied by 2 because progeny get half their genes from each parent)

Accuracy: Increases with number of progeny. For n progeny: $r = \sqrt{\frac{n h^2}{4 + (n-1) h^2}}$

7.3.4 Limitations of Simple Methods

[Content to be developed:]

Don’t account for contemporary group effects (environmental differences)
Don’t properly weight information sources by their accuracy
Don’t use all relatives simultaneously (e.g., sibs, grandparents)

7.4 Contemporary Groups

[Content to be developed: Animals must be compared within the same environment.]

7.4.1 Definition

[Content to be developed: A contemporary group is a set of animals raised in the same environment and time period.]

7.4.2 Examples

[Content to be developed:]

Dairy: Herd-year-season
Beef: Ranch-year-season, weaning group
Swine: Farm-batch, pen (for within-farm comparisons)
Poultry: House-batch, cage-row

7.4.3 Why Contemporary Groups Matter

[Content to be developed: Without adjustment for environmental differences, animals in better environments appear genetically superior (false positive selection).]

7.4.4 Adjusting for Contemporary Groups

[Content to be developed: Subtract contemporary group mean before estimating BV.]

\[ \hat{BV} = h^2 (P - \mu_{CG}) \]

Where μ_CG is the contemporary group mean.

7.5 Best Linear Unbiased Prediction (BLUP)

[Content to be developed: The modern standard for estimating breeding values.]

7.5.1 What is BLUP?

[Content to be developed:]

Best: Minimizes prediction error variance
Linear: Linear function of the data
Unbiased: Expected value equals true BV
Prediction: For random effects (breeding values, not fixed effects like contemporary groups)

7.5.2 Why BLUP?

[Content to be developed:]

Uses all information: Own records, parents, progeny, sibs, and more distant relatives
Accounts for fixed effects: Contemporary groups and other systematic environmental effects
Optimal weighting: Information sources weighted by their accuracy
Shrinkage: EBVs shrink toward the population mean when information is sparse

7.5.3 BLUP Concepts (High-Level)

[Content to be developed: No mixed model equations (MME) at this level. Focus on concepts.]

Animals with more information → EBVs closer to TBV
Animals with less information → EBVs closer to parent average or population mean
Relationships among animals are accounted for
BLUP simultaneously solves for contemporary group effects and breeding values

7.5.4 BLUP in Practice

[Content to be developed: Most commercial breeding programs use BLUP or its extensions (genomic BLUP, single-step GBLUP).]

7.6 Understanding EBVs

[Content to be developed: How to interpret estimated breeding values.]

7.6.1 EBV as a Deviation from the Base

[Content to be developed: EBVs are expressed as deviations from a base population (often set to zero mean in a specific year).]

7.6.2 Comparing Animals

[Content to be developed: Use the difference between EBVs, not absolute values.]

Example: Bull A has EBV = +500 kg for milk, Bull B has EBV = +300 kg. Bull A is expected to produce daughters that give 200 kg more milk than Bull B’s daughters (on average).

7.6.3 EBVs Change Over Time

[Content to be developed: As new data arrive (own records, progeny, genomic info), EBVs are re-estimated. Animals can be re-ranked.]

7.6.4 EBVs for Young vs. Old Animals

[Content to be developed:]

Young: Based on pedigree (parents) and possibly genomics → lower accuracy
Old: Based on own records, progeny, pedigree → higher accuracy

7.7 Accuracy of EBVs (Reliability)

[Content to be developed: Measure of confidence in the EBV.]

7.7.1 Definition

[Content to be developed:]

\[ \text{Reliability} = r^2 = \text{cor}^2(EBV, TBV) \]

Range: 0 to 1.

7.7.2 Interpreting Reliability

[Content to be developed:]

r² = 0.90: EBV is very close to TBV (highly confident)
r² = 0.50: EBV is moderately accurate (moderate confidence)
r² = 0.20: EBV is still close to parent average (low confidence)

7.7.3 Factors Affecting Reliability

[Content to be developed:]

Heritability
Number of own records
Number of progeny records
Genomic information
Number and relationship of relatives with records

7.7.4 Using Reliability in Selection Decisions

[Content to be developed: Animals with high EBV but low reliability have more uncertainty. Consider both EBV and reliability when making selection decisions.]

7.8 R Demonstration: Simple BV Estimation

[Content to be developed:]

# Example: Estimate BV from own performance
h2 <- 0.30
phenotype <- 95  # kg
pop_mean <- 90   # kg

EBV_own <- h2 * (phenotype - pop_mean)
cat("EBV from own performance:", EBV_own, "kg\n")

accuracy_own <- sqrt(h2)
cat("Accuracy:", round(accuracy_own, 3), "\n")

# Example: Midparent BV
EBV_sire <- 8
EBV_dam <- 6
EBV_offspring <- (EBV_sire + EBV_dam) / 2
cat("EBV from pedigree (midparent):", EBV_offspring, "kg\n")

# Example: Progeny average
progeny_mean <- 92
n_progeny <- 20
EBV_parent <- 2 * (progeny_mean - pop_mean)
cat("EBV from progeny average:", EBV_parent, "kg\n")

# Accuracy from progeny
r_progeny <- sqrt((n_progeny * h2) / (4 + (n_progeny - 1) * h2))
cat("Accuracy from", n_progeny, "progeny:", round(r_progeny, 3), "\n")

7.9 Examples Across Species

[Content to be developed: Real-world EBV systems.]

7.9.1 Dairy Cattle: Net Merit Index

[Content to be developed: EBVs for milk, fat, protein, fertility, health, longevity. Combined into a single index (Net Merit).]

7.9.2 Beef Cattle: EPDs

[Content to be developed: Expected Progeny Differences for birth weight, weaning weight, yearling weight, carcass traits.]

7.9.3 Swine: EBVs for Growth and Reproduction

[Content to be developed: EBVs for average daily gain, backfat, feed efficiency, litter size.]

7.9.4 Poultry: EBVs in Breeding Lines

[Content to be developed: EBVs for body weight, feed efficiency, egg production, egg quality (layers).]

7.10 Summary

[Content to be developed.]

7.10.1 Key Points

True Breeding Value (TBV) is unknown but can be estimated (EBV)
Simple methods: own performance, pedigree index, progeny average
Contemporary groups must be accounted for to avoid environmental confounding
BLUP is the modern standard: uses all information, accounts for fixed effects, optimal weighting
EBVs are expressed as deviations from a base population
Accuracy (reliability) measures confidence in EBV
EBVs can change over time as new data arrive

7.11 Practice Problems

[Problems to be developed]

A heifer has a weaning weight of 240 kg. The contemporary group mean is 230 kg, and h² = 0.25. Estimate her breeding value.
Bull A has 100 progeny with a mean weaning weight of 235 kg. The population mean is 230 kg, and h² = 0.25. Estimate the bull’s breeding value and accuracy.
Explain why an animal’s EBV can change from one genetic evaluation to the next.

7.12 Further Reading

[References to be added]

Mrode: Linear Models for the Prediction of Animal Breeding Values
Breed association EPD/EBV documentation (e.g., Angus, Holstein)

# Estimating Breeding Values {#sec-breeding-values} <div class="learning-objectives"> ### Learning Objectives {.unnumbered} By the end of this chapter, you will be able to: 1. Estimate breeding values using simple methods (own performance, pedigree index, progeny average) 2. Explain why contemporary groups must be accounted for 3. Describe the purpose and advantages of BLUP 4. Interpret EBVs and their accuracies 5. Understand why EBVs can change over time as new data arrive </div> ```{r} #| echo: false #| message: false #| warning: false # Load required packages library(tidyverse) library(knitr) # Set default theme for plots theme_set(theme_minimal(base_size = 12)) ``` ## Introduction [Content to be developed: True Breeding Value (TBV) is unknown, but we can estimate it (EBV) from available information. This chapter covers methods from simple to sophisticated.] ## The Challenge: TBV is Unknown [Content to be developed: We want to rank animals by TBV, but we can only observe phenotypes. We must estimate TBV from phenotypes, pedigrees, and genomic data.] ## Simple Estimation Methods [Content to be developed: Basic approaches to estimating breeding values.] ### Method 1: Own Performance [Content to be developed:] $$ \hat{BV} = h^2 (P - \mu) $$ Where P is the individual's phenotype and μ is the population mean. **Accuracy**: $r = \sqrt{h^2}$ **Example**: If h² = 0.36 and a pig weighs 100 kg while the mean is 90 kg, then EBV = 0.36 × (100 - 90) = 3.6 kg. ### Method 2: Pedigree Index (Midparent BV) [Content to be developed:] $$ \hat{BV}_{offspring} = \frac{1}{2} (EBV_{sire} + EBV_{dam}) $$ **Accuracy**: $r = \sqrt{\frac{h^2}{2}}$ (assuming parent EBVs are true BVs) Used for young animals without own records. ### Method 3: Progeny Average [Content to be developed:] $$ \hat{BV}_{parent} = 2 \times (\bar{P}_{progeny} - \mu) $$ (Multiplied by 2 because progeny get half their genes from each parent) **Accuracy**: Increases with number of progeny. For n progeny: $r = \sqrt{\frac{n h^2}{4 + (n-1) h^2}}$ ### Limitations of Simple Methods [Content to be developed:] - Don't account for contemporary group effects (environmental differences) - Don't properly weight information sources by their accuracy - Don't use all relatives simultaneously (e.g., sibs, grandparents) ## Contemporary Groups [Content to be developed: Animals must be compared within the same environment.] ### Definition [Content to be developed: A contemporary group is a set of animals raised in the same environment and time period.] ### Examples [Content to be developed:] - **Dairy**: Herd-year-season - **Beef**: Ranch-year-season, weaning group - **Swine**: Farm-batch, pen (for within-farm comparisons) - **Poultry**: House-batch, cage-row ### Why Contemporary Groups Matter [Content to be developed: Without adjustment for environmental differences, animals in better environments appear genetically superior (false positive selection).] ### Adjusting for Contemporary Groups [Content to be developed: Subtract contemporary group mean before estimating BV.] $$ \hat{BV} = h^2 (P - \mu_{CG}) $$ Where μ_CG is the contemporary group mean. ## Best Linear Unbiased Prediction (BLUP) [Content to be developed: The modern standard for estimating breeding values.] ### What is BLUP? [Content to be developed:] - **Best**: Minimizes prediction error variance - **Linear**: Linear function of the data - **Unbiased**: Expected value equals true BV - **Prediction**: For random effects (breeding values, not fixed effects like contemporary groups) ### Why BLUP? [Content to be developed:] 1. **Uses all information**: Own records, parents, progeny, sibs, and more distant relatives 2. **Accounts for fixed effects**: Contemporary groups and other systematic environmental effects 3. **Optimal weighting**: Information sources weighted by their accuracy 4. **Shrinkage**: EBVs shrink toward the population mean when information is sparse ### BLUP Concepts (High-Level) [Content to be developed: No mixed model equations (MME) at this level. Focus on concepts.] - Animals with more information → EBVs closer to TBV - Animals with less information → EBVs closer to parent average or population mean - Relationships among animals are accounted for - BLUP simultaneously solves for contemporary group effects and breeding values ### BLUP in Practice [Content to be developed: Most commercial breeding programs use BLUP or its extensions (genomic BLUP, single-step GBLUP).] ## Understanding EBVs [Content to be developed: How to interpret estimated breeding values.] ### EBV as a Deviation from the Base [Content to be developed: EBVs are expressed as deviations from a base population (often set to zero mean in a specific year).] ### Comparing Animals [Content to be developed: Use the difference between EBVs, not absolute values.] **Example**: Bull A has EBV = +500 kg for milk, Bull B has EBV = +300 kg. Bull A is expected to produce daughters that give 200 kg more milk than Bull B's daughters (on average). ### EBVs Change Over Time [Content to be developed: As new data arrive (own records, progeny, genomic info), EBVs are re-estimated. Animals can be re-ranked.] ### EBVs for Young vs. Old Animals [Content to be developed:] - **Young**: Based on pedigree (parents) and possibly genomics → lower accuracy - **Old**: Based on own records, progeny, pedigree → higher accuracy ## Accuracy of EBVs (Reliability) [Content to be developed: Measure of confidence in the EBV.] ### Definition [Content to be developed:] $$ \text{Reliability} = r^2 = \text{cor}^2(EBV, TBV) $$ Range: 0 to 1. ### Interpreting Reliability [Content to be developed:] - **r² = 0.90**: EBV is very close to TBV (highly confident) - **r² = 0.50**: EBV is moderately accurate (moderate confidence) - **r² = 0.20**: EBV is still close to parent average (low confidence) ### Factors Affecting Reliability [Content to be developed:] 1. Heritability 2. Number of own records 3. Number of progeny records 4. Genomic information 5. Number and relationship of relatives with records ### Using Reliability in Selection Decisions [Content to be developed: Animals with high EBV but low reliability have more uncertainty. Consider both EBV and reliability when making selection decisions.] ## R Demonstration: Simple BV Estimation [Content to be developed:] ```{r} #| echo: true #| eval: false # Example: Estimate BV from own performance h2 <- 0.30 phenotype <- 95 # kg pop_mean <- 90 # kg EBV_own <- h2 * (phenotype - pop_mean) cat("EBV from own performance:", EBV_own, "kg\n") accuracy_own <- sqrt(h2) cat("Accuracy:", round(accuracy_own, 3), "\n") # Example: Midparent BV EBV_sire <- 8 EBV_dam <- 6 EBV_offspring <- (EBV_sire + EBV_dam) / 2 cat("EBV from pedigree (midparent):", EBV_offspring, "kg\n") # Example: Progeny average progeny_mean <- 92 n_progeny <- 20 EBV_parent <- 2 * (progeny_mean - pop_mean) cat("EBV from progeny average:", EBV_parent, "kg\n") # Accuracy from progeny r_progeny <- sqrt((n_progeny * h2) / (4 + (n_progeny - 1) * h2)) cat("Accuracy from", n_progeny, "progeny:", round(r_progeny, 3), "\n") ``` ## Examples Across Species [Content to be developed: Real-world EBV systems.] ### Dairy Cattle: Net Merit Index [Content to be developed: EBVs for milk, fat, protein, fertility, health, longevity. Combined into a single index (Net Merit).] ### Beef Cattle: EPDs [Content to be developed: Expected Progeny Differences for birth weight, weaning weight, yearling weight, carcass traits.] ### Swine: EBVs for Growth and Reproduction [Content to be developed: EBVs for average daily gain, backfat, feed efficiency, litter size.] ### Poultry: EBVs in Breeding Lines [Content to be developed: EBVs for body weight, feed efficiency, egg production, egg quality (layers).] ## Summary [Content to be developed.] ### Key Points - True Breeding Value (TBV) is unknown but can be estimated (EBV) - Simple methods: own performance, pedigree index, progeny average - Contemporary groups must be accounted for to avoid environmental confounding - BLUP is the modern standard: uses all information, accounts for fixed effects, optimal weighting - EBVs are expressed as deviations from a base population - Accuracy (reliability) measures confidence in EBV - EBVs can change over time as new data arrive ## Practice Problems [Problems to be developed] 1. A heifer has a weaning weight of 240 kg. The contemporary group mean is 230 kg, and h² = 0.25. Estimate her breeding value. 2. Bull A has 100 progeny with a mean weaning weight of 235 kg. The population mean is 230 kg, and h² = 0.25. Estimate the bull's breeding value and accuracy. 3. Explain why an animal's EBV can change from one genetic evaluation to the next. ## Further Reading [References to be added] - Mrode: Linear Models for the Prediction of Animal Breeding Values - Breed association EPD/EBV documentation (e.g., Angus, Holstein)