8  Genetic Correlations and Correlated Response

Learning Objectives

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

  1. Define genetic correlation and explain what causes it
  2. Interpret positive, negative, and zero genetic correlations
  3. Calculate correlated response to selection
  4. Explain why antagonistic correlations complicate breeding programs
  5. Provide examples of important genetic correlations in livestock

8.1 Introduction

[Content to be developed: Most breeding programs aim to improve multiple traits. Understanding genetic correlations is essential for predicting how selection on one trait affects other traits.]

8.2 What is Genetic Correlation?

[Content to be developed: Define genetic correlation (r_A).]

8.2.1 Definition

[Content to be developed:]

\[ r_A(X,Y) = \frac{\text{Cov}_A(X, Y)}{\sigma_A(X) \times \sigma_A(Y)} \]

Where:

  • r_A(X,Y) = genetic correlation between traits X and Y
  • Cov_A(X,Y) = additive genetic covariance
  • σ_A(X), σ_A(Y) = additive genetic standard deviations

Range: -1 to +1

8.2.2 Interpreting Genetic Correlations

[Content to be developed:]

  • r_A > 0 (Positive): Selecting for trait X increases trait Y
  • r_A < 0 (Negative, antagonistic): Selecting for trait X decreases trait Y
  • r_A ≈ 0: Traits are genetically independent

8.3 Causes of Genetic Correlations

[Content to be developed: Why are traits genetically correlated?]

8.3.1 Pleiotropy

[Content to be developed: The same genes affect multiple traits. Example: Genes affecting overall growth rate influence multiple body weights (birth, weaning, yearling).]

8.3.2 Linkage Disequilibrium

[Content to be developed: Genes affecting different traits are physically linked on the same chromosome. Creates temporary correlation that can be broken by recombination over generations.]

8.3.3 Distinguishing Pleiotropy from Linkage

[Content to be developed: Pleiotropy is permanent (same gene); linkage is temporary (can be broken). In practice, most genetic correlations arise from pleiotropy.]

8.4 Examples of Genetic Correlations in Livestock

[Content to be developed: Provide species-specific examples.]

8.4.1 Positive (Favorable) Genetic Correlations

[Content to be developed:]

  • Carcass traits: Loin depth and % lean (r_A ≈ +0.6)
  • Body weights at different ages: Weaning weight and yearling weight (r_A ≈ +0.7)
  • Milk components: Fat yield and protein yield (r_A ≈ +0.7-0.8)

8.4.2 Positive (Unfavorable) Genetic Correlations

[Content to be developed:]

  • Swine backfat and growth rate: Selecting for faster growth increases backfat (r_A ≈ +0.2 to +0.4)
  • Broiler growth and leg problems: Faster growth associated with leg soundness issues (r_A ≈ +0.3 to +0.5)

8.4.3 Negative (Antagonistic) Genetic Correlations

[Content to be developed:]

  • Dairy: Milk yield and fertility (r_A ≈ -0.2 to -0.4)
  • Dairy: Milk yield and body condition score (r_A ≈ -0.3 to -0.5)
  • Layers: Egg production and egg weight (r_A ≈ -0.2 to -0.4)
  • Swine: Litter size and piglet birth weight (r_A ≈ -0.2 to -0.3)

8.4.4 Near-Zero Genetic Correlations

[Content to be developed:]

  • Beef: Marbling and lean growth (r_A ≈ 0 to -0.1)
  • Traits affecting different physiological systems

8.5 Correlated Response to Selection

[Content to be developed: How selection on trait X causes change in trait Y.]

8.5.1 Equation for Correlated Response

[Content to be developed:]

\[ CR_Y = i \times r_X \times r_A(X,Y) \times \sigma_A(Y) \times \frac{1}{L} \]

Where:

  • CR_Y = correlated response in trait Y (per year)
  • i = selection intensity on trait X
  • r_X = accuracy of selection on trait X
  • r_A(X,Y) = genetic correlation between X and Y
  • σ_A(Y) = additive genetic SD of trait Y
  • L = generation interval

8.5.2 Interpreting Correlated Response

[Content to be developed:]

  • If r_A is positive, CR_Y is positive (Y increases when selecting for X)
  • If r_A is negative, CR_Y is negative (Y decreases when selecting for X)
  • Magnitude depends on r_A and genetic variation in Y

8.5.3 Example: Dairy Milk Yield and Fertility

[Content to be developed:]

If we select for increased milk yield:

  • Direct response: Milk increases (desired)
  • Correlated response: Fertility declines (undesired, because r_A ≈ -0.3)

This creates the need for multi-trait selection (Chapter 9).

8.6 Why Genetic Correlations Complicate Breeding

[Content to be developed: Antagonistic correlations prevent simultaneous improvement of all traits.]

8.6.1 Trade-offs

[Content to be developed: Can’t maximize all traits at once if correlations are negative. Must balance improvements.]

8.6.2 Need for Multi-Trait Selection

[Content to be developed: Selection indices (Chapter 9) account for genetic correlations and economic weights to optimize overall genetic merit.]

8.7 R Demonstration: Simulating Genetic Correlations

[Content to be developed:]

# Simulate two traits with genetic correlation
library(MASS)
set.seed(123)

n <- 1000
r_A <- -0.4  # Negative genetic correlation
sigma_A_X <- 5
sigma_A_Y <- 3
sigma_E <- 8

# Genetic covariance matrix
Sigma_A <- matrix(c(sigma_A_X^2, r_A * sigma_A_X * sigma_A_Y,
                    r_A * sigma_A_X * sigma_A_Y, sigma_A_Y^2), nrow = 2)

# Simulate breeding values
BV <- mvrnorm(n, mu = c(0, 0), Sigma = Sigma_A)
colnames(BV) <- c("BV_X", "BV_Y")

# Add environmental effects
E_X <- rnorm(n, 0, sigma_E)
E_Y <- rnorm(n, 0, sigma_E)

# Phenotypes
P_X <- BV[, "BV_X"] + E_X
P_Y <- BV[, "BV_Y"] + E_Y

# Plot
data.frame(BV_X = BV[, "BV_X"], BV_Y = BV[, "BV_Y"]) %>%
  ggplot(aes(x = BV_X, y = BV_Y)) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", color = "red") +
  labs(title = paste("Genetic Correlation r_A =", r_A),
       x = "Breeding Value for Trait X",
       y = "Breeding Value for Trait Y") +
  theme_minimal()

# Calculate correlation
cor_genetic <- cor(BV[, "BV_X"], BV[, "BV_Y"])
cat("Simulated genetic correlation:", round(cor_genetic, 3), "\n")

8.8 R Demonstration: Correlated Response

[Content to be developed:]

# Calculate correlated response
i <- 1.76         # Selection intensity (top 10%)
r_X <- 0.60       # Accuracy of selection on trait X
r_A_XY <- -0.35   # Genetic correlation between X and Y
sigma_A_Y <- 4    # Genetic SD of trait Y
L <- 2            # Generation interval (years)

CR_Y <- (i * r_X * r_A_XY * sigma_A_Y) / L
cat("Correlated response in trait Y:", round(CR_Y, 2), "per year\n")
cat("Note: Negative CR means trait Y declines when selecting for increased trait X\n")

8.9 Summary

[Content to be developed.]

8.9.1 Key Points

  • Genetic correlation (r_A) measures the degree to which two traits share genetic influences
  • Caused by pleiotropy (same genes) or linkage (genes on same chromosome)
  • Positive r_A: traits improve together
  • Negative r_A: improving one trait worsens the other (antagonistic)
  • Correlated response is the change in trait Y when selecting on trait X
  • Antagonistic correlations require multi-trait selection methods (Chapter 9)

8.10 Practice Problems

[Problems to be developed]

  1. Traits X and Y have r_A = +0.60. If you select for increased trait X, what happens to trait Y? Explain.

  2. Milk yield and fertility in dairy cattle have r_A ≈ -0.30. Calculate the correlated response in fertility (in genetic SD units) if: i = 2.0, r_X = 0.70, σ_A(fertility) = 0.5, L = 4 years.

  3. Explain why genetic correlations caused by pleiotropy are more permanent than those caused by linkage.

  4. A breeder selects only for increased milk yield and ignores fertility. Over 10 years, fertility declines substantially. Explain why this happened and what should be done differently.

8.11 Further Reading

[References to be added]

  • Published genetic parameters for livestock traits
  • Papers on antagonistic correlations in dairy, swine, poultry