10 Mating Strategies and Optimum Contribution Selection

Learning Objectives

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

Distinguish selection decisions from mating decisions
Explain why mating strategies matter for managing inbreeding and genetic diversity
Describe different types of mating systems (random, assortative, compensatory)
Understand the concept and purpose of Optimum Contribution Selection (OCS)
Identify software tools used for mating optimization in commercial breeding

10.1 Introduction

[Content to be developed: After selecting which animals become parents (Chapter 7-9), we must decide which parents to mate with each other. Mating decisions affect genetic diversity, inbreeding, and offspring quality.]

10.2 Selection vs. Mating

[Content to be developed: Two distinct decisions.]

10.2.1 Selection: Who Becomes a Parent?

[Content to be developed: Choose animals with highest EBVs or index values.]

10.2.2 Mating: Who Mates with Whom?

[Content to be developed: Allocate matings among selected parents. Affects:]

Inbreeding and genetic diversity
Offspring uniformity vs. variability
Rate of genetic gain (indirectly)

10.3 Types of Mating Systems

[Content to be developed: Different strategies for allocating matings.]

10.3.1 Random Mating

[Content to be developed:]

Mates chosen at random from selected parents
Simple but doesn’t optimize inbreeding or offspring quality
Baseline for comparison

10.3.2 Assortative Mating

[Content to be developed:]

Positive assortative: Mate like to like (high EBV males with high EBV females)

Increases variance in offspring
Can accelerate genetic gain in top tier
Risk of increasing inbreeding

Negative assortative: Mate unlike to unlike (high EBV with low EBV)

Reduces variance in offspring
More uniform offspring quality
Rarely used in practice

10.3.3 Inbreeding Avoidance

[Content to be developed:]

Avoid mating close relatives
Reduces risk of inbreeding depression
Common in all breeding programs

10.4 Mating to Manage Inbreeding

[Content to be developed: Inbreeding is a major concern in closed populations.]

10.4.1 Inbreeding Depression

[Content to be developed: Reduction in performance due to increased homozygosity, especially for fitness traits (reproduction, health, survival).]

10.4.2 Inbreeding Coefficient (F)

[Content to be developed:]

\[ F = \text{Probability that two alleles at a locus are identical by descent} \]

Range: 0 to 1.

10.4.3 Rate of Inbreeding (ΔF)

[Content to be developed:]

\[ \Delta F = \frac{1}{2 N_e} \]

Where N_e is the effective population size.

10.4.4 Minimum Coancestry Mating

[Content to be developed: Pair animals to minimize the average relationship (coancestry) of offspring.]

Helps control inbreeding
Can be computed from pedigree or genomic relationships

10.5 Compensatory Mating

[Content to be developed: Mating to balance strengths and weaknesses.]

10.5.1 Purpose

[Content to be developed: Reduce variation in offspring quality by mating animals with complementary strengths.]

10.5.2 Example: Terminal Sire Systems

[Content to be developed: Mate terminal sires strong in growth and carcass with maternal lines strong in reproduction.]

10.5.3 Limitations

[Content to be developed: Doesn’t change the average breeding value of offspring, just reduces variance.]

10.6 Optimum Contribution Selection (OCS)

[Content to be developed: Modern approach to simultaneously optimize selection and mating.]

10.6.1 Concept

[Content to be developed:]

Traditional approach: Select parents first, then decide matings
OCS approach: Simultaneously decide:
1. How many offspring each animal should produce
2. Which animals to mate together

10.6.2 Objective

[Content to be developed:]

\[ \max \ \text{Genetic merit subject to } \Delta F \leq \text{constraint} \]

Maximize genetic gain while constraining the rate of inbreeding.

10.6.3 How OCS Works

[Content to be developed:]

Calculate EBVs or index values for all candidates
Calculate relationship matrix (pedigree or genomic)
Optimize number of offspring per animal
Allocate specific matings

10.6.4 Benefits of OCS

[Content to be developed:]

Balances short-term genetic gain with long-term genetic diversity
Can use more parents (lower intensity) while maintaining gain
Explicitly controls inbreeding rate
Used by commercial breeding companies

10.6.5 Software for OCS

[Content to be developed:]

MateSel: Developed by AGBU (Australia), widely used in industry
AlphaMate: Research tool
EVA: Used in some breeding programs

10.7 Software Tools for Mating Decisions

[Content to be developed: Industry tools.]

10.7.1 MateSel

[Content to be developed:]

Optimizes mate allocations to maximize index value while constraining inbreeding
Inputs: EBVs, relationships, mating constraints
Outputs: Recommended matings and number of offspring per parent
Widely used in dairy, beef, swine

10.7.2 Other Tools

[Content to be developed:]

Proprietary tools used by genetics companies (not publicly available)
Integration with genetic evaluation systems

10.8 Rotational Crossbreeding (Introduction)

[Content to be developed: Brief introduction, full coverage in Chapter 11.]

10.8.1 Two-Breed Rotation

[Content to be developed: Alternate breeds each generation. Maintains ~67% heterosis.]

10.8.2 Three-Breed Rotation

[Content to be developed: Rotate among three breeds. Maintains ~86% heterosis.]

10.9 R Demonstration: Inbreeding from Pedigree

[Content to be developed:]

# Calculate inbreeding coefficient from pedigree
library(pedigree)

# Example pedigree
ped <- data.frame(
  animal = c(1, 2, 3, 4, 5, 6),
  sire = c(0, 0, 1, 1, 3, 3),
  dam = c(0, 0, 2, 2, 4, 4)
)

# Calculate inbreeding
ped_obj <- pedigree(sire = ped$sire, dam = ped$dam, label = ped$animal)
F <- calcInbreeding(ped_obj)
print(data.frame(Animal = ped$animal, F = round(F, 4)))

10.10 R Demonstration: Simulating OCS

[Content to be developed:]

# Simplified demonstration of OCS concept
# (Actual OCS uses linear programming, beyond scope here)

# Example: 10 candidates, choose contributions to maximize genetic merit
# subject to inbreeding constraint

candidates <- data.frame(
  ID = 1:10,
  EBV = c(10, 8, 9, 7, 6, 5, 8, 6, 7, 5),
  relationship = runif(10, 0.05, 0.15)  # Avg relationship to population
)

# Traditional selection: Top 3 (30%)
top3 <- candidates %>% arrange(desc(EBV)) %>% slice(1:3)
cat("Traditional selection (top 3):\n")
print(top3)

# OCS would select more parents (e.g., top 5) with varying contributions
# to control inbreeding while maintaining genetic merit

10.11 Summary

[Content to be developed.]

10.11.1 Key Points

Mating decisions are distinct from selection decisions
Mating strategies affect inbreeding, genetic diversity, and offspring uniformity
Random mating is simple; minimum coancestry reduces inbreeding
Compensatory mating balances strengths and weaknesses
Optimum Contribution Selection (OCS) simultaneously optimizes selection and mating
Software like MateSel is used in commercial breeding programs

10.12 Practice Problems

[Problems to be developed]

Explain the difference between selection intensity and mating strategy. How does each affect genetic gain?
Why is managing inbreeding important in closed breeding populations?
Describe how Optimum Contribution Selection balances genetic gain and inbreeding. What is the trade-off?

10.13 Further Reading

[References to be added]

Papers on OCS and MateSel
Inbreeding depression in livestock
Effective population size and genetic diversity

# Mating Strategies and Optimum Contribution Selection {#sec-mating-strategies} <div class="learning-objectives"> ### Learning Objectives {.unnumbered} By the end of this chapter, you will be able to: 1. Distinguish selection decisions from mating decisions 2. Explain why mating strategies matter for managing inbreeding and genetic diversity 3. Describe different types of mating systems (random, assortative, compensatory) 4. Understand the concept and purpose of Optimum Contribution Selection (OCS) 5. Identify software tools used for mating optimization in commercial breeding </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: After selecting which animals become parents (Chapter 7-9), we must decide which parents to mate with each other. Mating decisions affect genetic diversity, inbreeding, and offspring quality.] ## Selection vs. Mating [Content to be developed: Two distinct decisions.] ### Selection: Who Becomes a Parent? [Content to be developed: Choose animals with highest EBVs or index values.] ### Mating: Who Mates with Whom? [Content to be developed: Allocate matings among selected parents. Affects:] - Inbreeding and genetic diversity - Offspring uniformity vs. variability - Rate of genetic gain (indirectly) ## Types of Mating Systems [Content to be developed: Different strategies for allocating matings.] ### Random Mating [Content to be developed:] - Mates chosen at random from selected parents - Simple but doesn't optimize inbreeding or offspring quality - Baseline for comparison ### Assortative Mating [Content to be developed:] **Positive assortative**: Mate like to like (high EBV males with high EBV females) - Increases variance in offspring - Can accelerate genetic gain in top tier - Risk of increasing inbreeding **Negative assortative**: Mate unlike to unlike (high EBV with low EBV) - Reduces variance in offspring - More uniform offspring quality - Rarely used in practice ### Inbreeding Avoidance [Content to be developed:] - Avoid mating close relatives - Reduces risk of inbreeding depression - Common in all breeding programs ## Mating to Manage Inbreeding [Content to be developed: Inbreeding is a major concern in closed populations.] ### Inbreeding Depression [Content to be developed: Reduction in performance due to increased homozygosity, especially for fitness traits (reproduction, health, survival).] ### Inbreeding Coefficient (F) [Content to be developed:] $$ F = \text{Probability that two alleles at a locus are identical by descent} $$ Range: 0 to 1. ### Rate of Inbreeding (ΔF) [Content to be developed:] $$ \Delta F = \frac{1}{2 N_e} $$ Where N_e is the effective population size. ### Minimum Coancestry Mating [Content to be developed: Pair animals to minimize the average relationship (coancestry) of offspring.] - Helps control inbreeding - Can be computed from pedigree or genomic relationships ## Compensatory Mating [Content to be developed: Mating to balance strengths and weaknesses.] ### Purpose [Content to be developed: Reduce variation in offspring quality by mating animals with complementary strengths.] ### Example: Terminal Sire Systems [Content to be developed: Mate terminal sires strong in growth and carcass with maternal lines strong in reproduction.] ### Limitations [Content to be developed: Doesn't change the average breeding value of offspring, just reduces variance.] ## Optimum Contribution Selection (OCS) [Content to be developed: Modern approach to simultaneously optimize selection and mating.] ### Concept [Content to be developed:] - Traditional approach: Select parents first, then decide matings - OCS approach: Simultaneously decide: 1. How many offspring each animal should produce 2. Which animals to mate together ### Objective [Content to be developed:] $$ \max \ \text{Genetic merit subject to } \Delta F \leq \text{constraint} $$ Maximize genetic gain while constraining the rate of inbreeding. ### How OCS Works [Content to be developed:] 1. Calculate EBVs or index values for all candidates 2. Calculate relationship matrix (pedigree or genomic) 3. Optimize number of offspring per animal 4. Allocate specific matings ### Benefits of OCS [Content to be developed:] - Balances short-term genetic gain with long-term genetic diversity - Can use more parents (lower intensity) while maintaining gain - Explicitly controls inbreeding rate - Used by commercial breeding companies ### Software for OCS [Content to be developed:] - **MateSel**: Developed by AGBU (Australia), widely used in industry - **AlphaMate**: Research tool - **EVA**: Used in some breeding programs ## Software Tools for Mating Decisions [Content to be developed: Industry tools.] ### MateSel [Content to be developed:] - Optimizes mate allocations to maximize index value while constraining inbreeding - Inputs: EBVs, relationships, mating constraints - Outputs: Recommended matings and number of offspring per parent - Widely used in dairy, beef, swine ### Other Tools [Content to be developed:] - Proprietary tools used by genetics companies (not publicly available) - Integration with genetic evaluation systems ## Rotational Crossbreeding (Introduction) [Content to be developed: Brief introduction, full coverage in Chapter 11.] ### Two-Breed Rotation [Content to be developed: Alternate breeds each generation. Maintains ~67% heterosis.] ### Three-Breed Rotation [Content to be developed: Rotate among three breeds. Maintains ~86% heterosis.] ## R Demonstration: Inbreeding from Pedigree [Content to be developed:] ```{r} #| echo: true #| eval: false # Calculate inbreeding coefficient from pedigree library(pedigree) # Example pedigree ped <- data.frame( animal = c(1, 2, 3, 4, 5, 6), sire = c(0, 0, 1, 1, 3, 3), dam = c(0, 0, 2, 2, 4, 4) ) # Calculate inbreeding ped_obj <- pedigree(sire = ped$sire, dam = ped$dam, label = ped$animal) F <- calcInbreeding(ped_obj) print(data.frame(Animal = ped$animal, F = round(F, 4))) ``` ## R Demonstration: Simulating OCS [Content to be developed:] ```{r} #| echo: true #| eval: false # Simplified demonstration of OCS concept # (Actual OCS uses linear programming, beyond scope here) # Example: 10 candidates, choose contributions to maximize genetic merit # subject to inbreeding constraint candidates <- data.frame( ID = 1:10, EBV = c(10, 8, 9, 7, 6, 5, 8, 6, 7, 5), relationship = runif(10, 0.05, 0.15) # Avg relationship to population ) # Traditional selection: Top 3 (30%) top3 <- candidates %>% arrange(desc(EBV)) %>% slice(1:3) cat("Traditional selection (top 3):\n") print(top3) # OCS would select more parents (e.g., top 5) with varying contributions # to control inbreeding while maintaining genetic merit ``` ## Summary [Content to be developed.] ### Key Points - Mating decisions are distinct from selection decisions - Mating strategies affect inbreeding, genetic diversity, and offspring uniformity - Random mating is simple; minimum coancestry reduces inbreeding - Compensatory mating balances strengths and weaknesses - Optimum Contribution Selection (OCS) simultaneously optimizes selection and mating - Software like MateSel is used in commercial breeding programs ## Practice Problems [Problems to be developed] 1. Explain the difference between selection intensity and mating strategy. How does each affect genetic gain? 2. Why is managing inbreeding important in closed breeding populations? 3. Describe how Optimum Contribution Selection balances genetic gain and inbreeding. What is the trade-off? ## Further Reading [References to be added] - Papers on OCS and MateSel - Inbreeding depression in livestock - Effective population size and genetic diversity