7 Population Examples

7.1 Learning Objectives

See complete worked examples of population creation
Learn patterns for common scenarios
Understand how to combine features

7.2 Example 1: Inbred Lines (DH Production)

# Heterozygous founders
pop <- creating.diploid(
  nindi = 50,
  nsnp = 5000,
  sex.quota = 0,          # All "male" (no sex distinction)
  n.additive = 100
)

# Create DH lines (instant homozygosity)
pop <- breeding.diploid(
  pop,
  breeding.size = c(200, 0),
  dh.mating = TRUE,        # Doubled haploid technology
  name.cohort = "DH_Lines"
)

# Check homozygosity
table(get.geno(pop, gen = 2))  # Should be mostly 0 and 2, few 1s

Compare with selfing:

# 5 generations of selfing
pop_selfing <- pop
for (i in 1:5) {
  pop_selfing <- breeding.diploid(
    pop_selfing,
    breeding.size = c(200, 0),
    selfing.mating = TRUE
  )
}

# Check reduction in heterozygosity
for (gen in 1:6) {
  print(table(get.geno(pop_selfing, gen = gen)))
}
# ~50% reduction per generation

7.3 Example 2: MAGIC Population (Maize)

Multi-parent Advanced Generation Inter-Cross:

# 20 fully homozygous founder lines
pop <- creating.diploid(
  nindi = 20,
  sex.quota = 0,
  template.chip = "maize",
  dataset = "homorandom",
  n.additive = 200
)

# Round 1: All pairwise crosses (190 F1s)
pop <- breeding.diploid(
  pop,
  breeding.size = c(190, 0),
  breeding.all.combination = TRUE,  # All combinations
  selection.size = c(20, 0),
  max.offspring = 19                # Each parent in 19 crosses
)

# Rounds 2-4: Random inter-mating
for (round in 1:3) {
  pop <- breeding.diploid(
    pop,
    breeding.size = c(190, 0),
    selection.size = c(190, 0),
    same.sex.activ = TRUE,
    same.sex.sex = 0,
    max.offspring = 2
  )
}

# Final: Create RILs by selfing
pop <- breeding.diploid(
  pop,
  breeding.size = c(380, 0),
  selfing.mating = TRUE
)

7.4 Example 3: Crossbreeding Setup

Two-breed cross with breed-specific QTLs:

# Breed A
pop <- creating.diploid(
  nsnp = 5000, nindi = 100,
  founder.pool = 1,
  name.cohort = "Breed_A",
  n.additive = 0  # Add traits later
)

# Breed B
pop <- creating.diploid(
  population = pop,
  nsnp = 5000, nindi = 100,
  founder.pool = 2,
  name.cohort = "Breed_B",
  freq = "diff"  # Different allele frequencies
)

# Trait only in Breed A
pop <- creating.trait(pop, n.additive = 100, trait.pool = 1)

# Trait only in Breed B
pop <- creating.trait(pop, n.additive = 100, trait.pool = 2)

# Get QTL effects
qtl_eff <- get.qtl.effects(pop)

# Combine into joint trait
combined_effects <- rbind(qtl_eff[[1]][[1]], qtl_eff[[1]][[2]])

pop <- creating.trait(
  pop,
  real.bv.add = combined_effects,
  replace.traits = TRUE,
  trait.name = "Combined"
)

# Cross the breeds
pop <- breeding.diploid(
  pop,
  selection.m.cohorts = "Breed_A",
  selection.f.cohorts = "Breed_B",
  breeding.size = c(100, 100),
  name.cohort = "F1_Cross"
)

# Visualize breed composition
pools <- get.pool(pop, gen = 3, plot = TRUE)

7.5 Example 4: Maternal Effects

Birth weight with direct and maternal components:

# Create two traits: direct and maternal
pop <- creating.diploid(
  nsnp = 5000,
  nindi = 200,
  n.additive = c(100, 100),
  var.target = c(100, 20),
  trait.cor = matrix(c(1, 0.5, 0.5, 1), nrow = 2),
  is.maternal = c(FALSE, TRUE),
  trait.name = c("Direct", "Maternal")
)

# Combine into observed trait
pop <- add.combi(
  pop,
  trait = 3,
  combi.weights = c(1, 1),
  trait.name = "BirthWeight"
)

# Generate offspring
pop <- breeding.diploid(pop, breeding.size = c(100, 100))

# Check: maternal trait depends on dam's genotype
bvs <- get.bv(pop, gen = 2)
pedi <- get.pedigree(pop, gen = 2)
head(cbind(pedi[, 3], bvs[2, ]))  # Dam ID vs maternal BV

7.6 Example 5: Import VCF + Create Trait

# Import real genotypes
pop <- creating.diploid(
  vcf = "holstein_1000genomes.vcf.gz",
  vcf.maxsnp = 50000,
  vcf.maxindi = 500
)

# Add simulated trait
pop <- creating.trait(
  pop,
  n.additive = 200,
  n.dominant = 30,
  var.target = 100,
  mean.target = 8000,
  trait.name = "MilkYield"
)

# Generate LD structure
pop <- founder.simulation(
  pop,
  generations = 100,
  breeding.size = 300
)

7.7 Example 6: Hard Sweep (Selection Signature)

Simulate past selection:

# Create base population
pop <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  chr.nr = 5,
  n.additive = 100,
  var.target = 1
)

# Simulate 50 generations of STRONG selection
pop <- founder.simulation(
  pop,
  generations = 50,
  breeding.size = 200,
  selection.criteria = "bv",
  selection.size = c(5, 5),      # Top 2.5%!
  phenotyping = "all",
  heritability = 0.8
)

# Now selective sweep visible in allele frequencies
qtls <- get.qtl(pop)
freq_gen1 <- get.allele.freq(pop, gen = 1, snp = qtls[[1]])
freq_gen51 <- get.allele.freq(pop, gen = 51, snp = qtls[[1]])

cbind(freq_gen1, freq_gen51)  # QTL frequencies changed

7.8 Example 7: GxE (Genotype-by-Environment)

# Manual approach: Create correlated "traits" for each environment
pop <- creating.diploid(
  nsnp = 5000,
  nindi = 200,
  n.additive = c(100, 100),
  trait.cor = matrix(c(1, 0.6, 0.6, 1), nrow = 2),  # Moderate correlation
  trait.name = c("Env1", "Env2")
)

# Automated GxE model
pop <- creating.diploid(
  nsnp = 5000,
  nindi = 200,
  n.additive = 100,
  gxe.model = TRUE,
  gxe.covariance = matrix(c(1, 0.6, 0.6, 1.2), nrow = 2)
)

7.9 Example 8: Import PLINK Files

# Read PLINK .ped and .map files
ped_data <- read.pedmap(
  path_ped = "mydata.ped",
  path_map = "mydata.map"
)

# Create population
pop <- creating.diploid(
  dataset = ped_data$dataset,
  map = ped_data$map,
  n.additive = 150,
  trait.name = "ImportedTrait"
)

7.10 Summary

These examples demonstrate:

✅ Inbred line creation (DH vs selfing)
✅ MAGIC population schemes
✅ Crossbreeding with breed-specific QTLs
✅ Maternal effects modeling
✅ VCF/PLINK data import
✅ Selection signatures
✅ Genotype-by-environment interactions

7.11 What’s Next?

With populations created, let’s simulate breeding actions - selection, mating, and culling.

Continue to Chapter 8: Selection Strategies!

# Population Examples {#sec-population-examples} ## Learning Objectives - See complete worked examples of population creation - Learn patterns for common scenarios - Understand how to combine features ## Example 1: Inbred Lines (DH Production) {#sec-example-inbred} ```{r} #| eval: false # Heterozygous founders pop <- creating.diploid( nindi = 50, nsnp = 5000, sex.quota = 0, # All "male" (no sex distinction) n.additive = 100 ) # Create DH lines (instant homozygosity) pop <- breeding.diploid( pop, breeding.size = c(200, 0), dh.mating = TRUE, # Doubled haploid technology name.cohort = "DH_Lines" ) # Check homozygosity table(get.geno(pop, gen = 2)) # Should be mostly 0 and 2, few 1s ``` **Compare with selfing:** ```{r} #| eval: false # 5 generations of selfing pop_selfing <- pop for (i in 1:5) { pop_selfing <- breeding.diploid( pop_selfing, breeding.size = c(200, 0), selfing.mating = TRUE ) } # Check reduction in heterozygosity for (gen in 1:6) { print(table(get.geno(pop_selfing, gen = gen))) } # ~50% reduction per generation ``` ## Example 2: MAGIC Population (Maize) {#sec-example-magic} Multi-parent Advanced Generation Inter-Cross: ```{r} #| eval: false # 20 fully homozygous founder lines pop <- creating.diploid( nindi = 20, sex.quota = 0, template.chip = "maize", dataset = "homorandom", n.additive = 200 ) # Round 1: All pairwise crosses (190 F1s) pop <- breeding.diploid( pop, breeding.size = c(190, 0), breeding.all.combination = TRUE, # All combinations selection.size = c(20, 0), max.offspring = 19 # Each parent in 19 crosses ) # Rounds 2-4: Random inter-mating for (round in 1:3) { pop <- breeding.diploid( pop, breeding.size = c(190, 0), selection.size = c(190, 0), same.sex.activ = TRUE, same.sex.sex = 0, max.offspring = 2 ) } # Final: Create RILs by selfing pop <- breeding.diploid( pop, breeding.size = c(380, 0), selfing.mating = TRUE ) ``` ## Example 3: Crossbreeding Setup {#sec-example-crossbreeding} Two-breed cross with breed-specific QTLs: ```{r} #| eval: false # Breed A pop <- creating.diploid( nsnp = 5000, nindi = 100, founder.pool = 1, name.cohort = "Breed_A", n.additive = 0 # Add traits later ) # Breed B pop <- creating.diploid( population = pop, nsnp = 5000, nindi = 100, founder.pool = 2, name.cohort = "Breed_B", freq = "diff" # Different allele frequencies ) # Trait only in Breed A pop <- creating.trait(pop, n.additive = 100, trait.pool = 1) # Trait only in Breed B pop <- creating.trait(pop, n.additive = 100, trait.pool = 2) # Get QTL effects qtl_eff <- get.qtl.effects(pop) # Combine into joint trait combined_effects <- rbind(qtl_eff[[1]][[1]], qtl_eff[[1]][[2]]) pop <- creating.trait( pop, real.bv.add = combined_effects, replace.traits = TRUE, trait.name = "Combined" ) # Cross the breeds pop <- breeding.diploid( pop, selection.m.cohorts = "Breed_A", selection.f.cohorts = "Breed_B", breeding.size = c(100, 100), name.cohort = "F1_Cross" ) # Visualize breed composition pools <- get.pool(pop, gen = 3, plot = TRUE) ``` ## Example 4: Maternal Effects {#sec-example-maternal} Birth weight with direct and maternal components: ```{r} #| eval: false # Create two traits: direct and maternal pop <- creating.diploid( nsnp = 5000, nindi = 200, n.additive = c(100, 100), var.target = c(100, 20), trait.cor = matrix(c(1, 0.5, 0.5, 1), nrow = 2), is.maternal = c(FALSE, TRUE), trait.name = c("Direct", "Maternal") ) # Combine into observed trait pop <- add.combi( pop, trait = 3, combi.weights = c(1, 1), trait.name = "BirthWeight" ) # Generate offspring pop <- breeding.diploid(pop, breeding.size = c(100, 100)) # Check: maternal trait depends on dam's genotype bvs <- get.bv(pop, gen = 2) pedi <- get.pedigree(pop, gen = 2) head(cbind(pedi[, 3], bvs[2, ])) # Dam ID vs maternal BV ``` ## Example 5: Import VCF + Create Trait {#sec-example-vcf-import} ```{r} #| eval: false # Import real genotypes pop <- creating.diploid( vcf = "holstein_1000genomes.vcf.gz", vcf.maxsnp = 50000, vcf.maxindi = 500 ) # Add simulated trait pop <- creating.trait( pop, n.additive = 200, n.dominant = 30, var.target = 100, mean.target = 8000, trait.name = "MilkYield" ) # Generate LD structure pop <- founder.simulation( pop, generations = 100, breeding.size = 300 ) ``` ## Example 6: Hard Sweep (Selection Signature) {#sec-example-hard-sweep} Simulate past selection: ```{r} #| eval: false # Create base population pop <- creating.diploid( nsnp = 10000, nindi = 200, chr.nr = 5, n.additive = 100, var.target = 1 ) # Simulate 50 generations of STRONG selection pop <- founder.simulation( pop, generations = 50, breeding.size = 200, selection.criteria = "bv", selection.size = c(5, 5), # Top 2.5%! phenotyping = "all", heritability = 0.8 ) # Now selective sweep visible in allele frequencies qtls <- get.qtl(pop) freq_gen1 <- get.allele.freq(pop, gen = 1, snp = qtls[[1]]) freq_gen51 <- get.allele.freq(pop, gen = 51, snp = qtls[[1]]) cbind(freq_gen1, freq_gen51) # QTL frequencies changed ``` ## Example 7: GxE (Genotype-by-Environment) {#sec-example-gxe} ```{r} #| eval: false # Manual approach: Create correlated "traits" for each environment pop <- creating.diploid( nsnp = 5000, nindi = 200, n.additive = c(100, 100), trait.cor = matrix(c(1, 0.6, 0.6, 1), nrow = 2), # Moderate correlation trait.name = c("Env1", "Env2") ) # Automated GxE model pop <- creating.diploid( nsnp = 5000, nindi = 200, n.additive = 100, gxe.model = TRUE, gxe.covariance = matrix(c(1, 0.6, 0.6, 1.2), nrow = 2) ) ``` ## Example 8: Import PLINK Files {#sec-example-plink} ```{r} #| eval: false # Read PLINK .ped and .map files ped_data <- read.pedmap( path_ped = "mydata.ped", path_map = "mydata.map" ) # Create population pop <- creating.diploid( dataset = ped_data$dataset, map = ped_data$map, n.additive = 150, trait.name = "ImportedTrait" ) ``` ## Summary These examples demonstrate: - ✅ Inbred line creation (DH vs selfing) - ✅ MAGIC population schemes - ✅ Crossbreeding with breed-specific QTLs - ✅ Maternal effects modeling - ✅ VCF/PLINK data import - ✅ Selection signatures - ✅ Genotype-by-environment interactions ## What's Next? With populations created, let's simulate **breeding actions** - selection, mating, and culling. Continue to [Chapter 8: Selection Strategies](08-selection-strategies.qmd)!