6  Advanced Population Setup

6.1 Learning Objectives

• Generate realistic LD structure with founder.simulation()
• Import and use real genomic/phenotypic data
• Create populations with selection signatures
• Model population history

6.2 Creating Realistic LD Structure

Real populations have linkage disequilibrium (LD) from historical selection and drift. The founder.simulation() function creates this automatically:

# Create population with realistic LD
population <- creating.diploid(nsnp = 10000, nindi = 100)

population <- founder.simulation(
  population,
  generations = 100,        # 100 generations of random mating
  breeding.size = 200,      # Population size per generation
  mutation.rate = 0.0001    # Mutation rate per site
)

What happens: - Simulates historical random mating - Creates realistic LD decay with distance - Generates allele frequency spectrum - Produces heterozygosity patterns

6.2.1 Controlling LD Levels

# Low LD (large historical population)
pop_low_ld <- founder.simulation(
  creating.diploid(nsnp = 5000, nindi = 100),
  generations = 1000,
  breeding.size = 1000
)

# High LD (bottleneck)
pop_high_ld <- founder.simulation(
  creating.diploid(nsnp = 5000, nindi = 100),
  generations = 100,
  breeding.size = 20        # Small Ne = high LD
)

6.3 Modeling Selection Signatures

Simulate hard sweeps (selective sweeps):

# Create population
pop <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  chr.nr = 1,
  n.additive = 100
)

# Historical selection on trait 1
pop <- founder.simulation(
  pop,
  generations = 50,
  breeding.size = 200,
  selection.criteria = "bv",     # Select on breeding values
  selection.size = c(20, 20),    # Strong selection
  selection.m.gen = "all",
  selection.f.gen = "all"
)

Creates: - Reduced diversity around selected QTLs - Extended haplotype homozygosity - Realistic post-selection LD patterns

6.4 Importing Real Phenotypic Data

Use real phenotypes to estimate trait architecture:

# Example: Load data from MoBPS example population
data(ex_pop)

# Extract information
pheno <- get.pheno(ex_pop, gen = 1:5)
geno <- get.geno(ex_pop, gen = 1:5)
map <- get.map(ex_pop, use.snp.nr = TRUE)

# Estimate marker effects from data
estimated_effects <- effect.estimate.add(geno, pheno, map)

# Create new population with estimated architecture
population <- creating.diploid(
  dataset = get.haplo(ex_pop, gen = 1),
  map = map,
  real.bv.add = estimated_effects
)

Workflow: 1. Import real genotypes + phenotypes 2. Estimate marker effects (GWAS/GBLUP) 3. Use estimated effects in simulation

6.5 Creating Age-Structured Populations

Model overlapping generations:

# Create founders (year 0)
pop <- creating.diploid(
  nsnp = 5000, nindi = 100,
  n.additive = 100,
  name.cohort = "Year_0"
)

# Year 1: Some old + new animals
pop <- breeding.diploid(
  pop,
  selection.m.cohorts = "Year_0",
  selection.f.cohorts = "Year_0",
  selection.size = c(20, 40),    # Keep some old animals
  breeding.size = c(30, 60),     # Plus new calves
  name.cohort = "Year_1"
)

# Select from BOTH cohorts in Year 2
pop <- breeding.diploid(
  pop,
  selection.m.cohorts = c("Year_0", "Year_1"),
  selection.f.cohorts = c("Year_0", "Year_1"),
  selection.size = c(20, 40),
  breeding.size = c(30, 60),
  name.cohort = "Year_2"
)

Applications: - Dairy cattle (multi-parity cows) - Progeny testing schemes - Conservation programs

This mirrors classical overlapping-generation breeding program formulations described by Hill (Hill 1974).

6.6 Multi-Stage Pedigree Simulation

Create populations from pedigree structure only:

# Generate pedigree-based population
pop <- pedigree.simulation(
  population = creating.diploid(nsnp = 1000, nindi = 10),
  breeding.size = 100,
  generations = 5,
  selection.size = c(5, 10)
)

Use cases: - Quick exploration without full genomics - Very large pedigrees - When genotypes not needed

6.7 Example: Import VCF + GWAS Results

Complete workflow with real data:

# Step 1: Import VCF file
pop <- creating.diploid(
  vcf = "path/to/cattle_genotypes.vcf.gz",
  vcf.maxsnp = 50000,     # Limit to 50K SNPs
  vcf.maxindi = 1000      # Limit to 1000 animals
)

# Step 2: Load phenotypes (from external file)
pheno_data <- read.csv("phenotypes.csv")
# Assume columns: AnimalID, Trait1, Trait2, Trait3

# Step 3: Match phenotypes to individuals
# (You'll need to map VCF sample IDs to phenotype IDs)

# Step 4: Estimate effects using your favorite method
# Example with rrBLUP
library(rrBLUP)
geno_matrix <- get.geno(pop, gen = 1)
effects <- mixed.solve(pheno_data$Trait1, Z = t(geno_matrix))

# Step 5: Create trait architecture from estimated effects
qtl_effects <- cbind(
  1:length(effects$u),  # SNP number
  1,                    # Chromosome (placeholder)
  -effects$u,           # Effect for allele 0
  0,                    # Effect for allele 1
  effects$u             # Effect for allele 2
)

pop <- creating.trait(
  pop,
  real.bv.add = qtl_effects,
  trait.name = "EstimatedTrait"
)

# Now ready to simulate breeding program!

6.8 Summary

• ✅ founder.simulation() creates realistic LD structure
• ✅ Model selection signatures and population history
• ✅ Import real data (genotypes, phenotypes, GWAS results)
• ✅ Create age-structured populations
• ✅ Flexible approaches for complex scenarios

Continue to Chapter 7: Population Examples!

Hill, William G. 1974. “Prediction and Evaluation of Response to Selection with Overlapping Generations.” Animal Science 18 (2): 117–39. https://doi.org/10.1017/S0003356100017372.