5 Trait Architecture

5.1 Learning Objectives

Design simple and complex trait architectures
Model additive, dominance, and epistatic effects
Create correlated traits
Add maternal/paternal effects
Implement breed-specific QTLs

5.2 Overview

Trait architecture defines the genetic basis of traits: - Which markers are QTLs - Effect sizes of each QTL - Types of genetic effects (additive, dominance, epistasis) - Correlations between traits

MoBPS provides both automated and custom approaches.

5.3 Automated Trait Generation

5.3.1 Simple Additive Trait

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  n.additive = 100,      # 100 additive QTLs
  var.target = 1,        # Genetic variance = 1
  mean.target = 100      # Mean breeding value = 100
)

What happens: - 100 random SNPs chosen as QTLs - Effects drawn from Normal(0, σ²) - Automatically scaled to target variance

5.3.2 Adding Dominance

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  n.additive = 100,
  n.dominant = 20,       # 20 loci with dominance
  var.additive = 0.8,    # 80% of variance from additive
  var.dominant = 0.2     # 20% from dominance
)

Dominance effect modeling: - Random loci chosen for dominance - Effects: genotype 0, 1, 2 each get independent effect - Can specify dominant.only.positive = TRUE for heterosis modeling

5.3.3 Epistatic Effects

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  n.additive = 80,
  n.qualitative = 10,    # Qualitative epistasis (ordered)
  n.quantitative = 5     # Quantitative epistasis (unordered)
)

Epistasis types:

Qualitative: 00 < 01 < 02 < 10 < 11 < 12 < 20 < 21 < 22 (ordered, selection always beneficial)
Quantitative: Mix of positive/negative interactions

5.3.4 Effect Size Distributions

# Gaussian effects (default)
pop_gaussian <- creating.diploid(
  nsnp = 5000, nindi = 200, n.additive = 100,
  effect.distribution = "gaussian"
)

# Gamma distribution (for skewed effects)
pop_gamma <- creating.diploid(
  nsnp = 5000, nindi = 200, n.additive = 100,
  effect.distribution = "gamma",
  gamma.shape1 = 0.4,    # Shape parameter
  gamma.shape2 = 1.66    # Rate parameter
)

# Equal effects
pop_equal <- creating.diploid(
  nsnp = 5000, nindi = 200,
  n.equal.additive = 50,           # 50 QTLs
  effect.size.equal.add = 0.5      # Each effect = 0.5
)

5.4 Multiple Traits

5.4.1 Independent Traits

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  n.additive = c(100, 80, 120),    # 3 traits
  var.target = c(1, 1.5, 0.8),     # Different variances
  trait.name = c("Yield", "Quality", "Disease_Resistance")
)

5.4.2 Correlated Traits

# Define correlation matrix
cor_matrix <- matrix(c(
  1.0,  0.5, -0.3,   # Yield
  0.5,  1.0, -0.2,   # Quality
 -0.3, -0.2,  1.0    # Disease Resistance
), nrow = 3, byrow = TRUE)

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  n.additive = c(100, 100, 100),
  trait.cor = cor_matrix,          # Correlations
  trait.name = c("Yield", "Quality", "Disease_Resistance")
)

How it works: - Same markers used as QTLs for correlated traits - Effects drawn from multivariate normal distribution - Correlations independent of LD structure

Correlation vs. Covariance

MoBPS uses correlation matrices, not covariance matrices. Standardize your traits first!

5.5 Custom Trait Architecture

5.5.1 Single-Locus Effects (real.bv.add)

Specify exactly which SNPs are QTLs and their effects:

# Create custom effects matrix
# Columns: SNP_number, chromosome, effect_0, effect_1, effect_2
custom_effects <- rbind(
  c(120,  1, -1.0,  0.0,  1.0),   # Additive effect
  c(42,   5,  0.0,  0.0,  2.0),   # Recessive
  c(17,  22,  0.1,  0.1,  0.1)    # No effect (neutral)
)

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  real.bv.add = custom_effects
)

Effect coding: - Column 1: SNP number (1 to nsnp) - Column 2: Chromosome number - Columns 3-5: Effects for genotypes 0, 1, 2

5.5.2 Two-Locus Epistasis (real.bv.mult)

# Epistatic interaction between two loci
# 9 effects for all genotype combinations
epistatic_effects <- rbind(
  c(144, 1, 145, 1,  # SNPs 144 and 145 on chr 1
    1.0, 0.0, 0.0,   # Effects when SNP1 = 0
    0.0, 0.0, 0.0,   # Effects when SNP1 = 1
    0.0, 0.0, 0.0),  # Effects when SNP1 = 2
  c(4, 3, 188, 5,    # SNP 4 on chr 3, SNP 188 on chr 5
    0.37, 0.16, 1.35,
    1.99, 1.58, 2.51,
    0.38, 2.12, 0.98)
)

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  real.bv.mult = epistatic_effects
)

5.5.3 Multi-Locus Epistasis (real.bv.dice)

For effects involving 3+ loci:

# Complex epistatic network
dice_list <- list(
  # First network: 3 SNPs
  location = list(
    matrix(c(11, 1,
             12, 1,
             16, 2), ncol = 2, byrow = TRUE)
  ),
  # Effects for all 27 combinations (3^3)
  effects = list(
    runif(27, -1, 1)  # Random effects
  )
)

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  real.bv.dice = dice_list
)

5.6 Special Trait Types

5.6.1 Maternal/Paternal Effects

# Trait influenced by mother's genotype
population <- creating.diploid(
  nsnp = 5000,
  nindi = 100,
  n.additive = c(100, 50),
  is.maternal = c(FALSE, TRUE),  # Trait 2 is maternal
  trait.name = c("Direct", "Maternal")
)

# Combine into single trait
population <- add.combi(
  population,
  trait = 3,
  combi.weights = c(0.7, 0.3),  # 70% direct, 30% maternal
  trait.name = "Combined"
)

Use cases: - Birth weight (maternal nutrition) - Milk production (maternal effects on calves) - Egg quality (maternal contribution)

5.6.2 Breed-Specific QTLs

Model QTLs that only have effects in specific breeds:

# Create two breeds
pop <- creating.diploid(
  nsnp = 5000, nindi = 100,
  founder.pool = 1,
  name.cohort = "Breed_A"
)

pop <- creating.diploid(
  population = pop, nsnp = 5000, nindi = 100,
  founder.pool = 2,
  name.cohort = "Breed_B"
)

# Add trait only active in breed A
pop <- creating.trait(
  pop,
  n.additive = 100,
  trait.pool = 1  # Only affects pool 1 (Breed A)
)

5.6.3 Non-QTL Polygenic Traits

Simulate infinitesimal model:

population <- creating.diploid(
  nsnp = 10000,
  nindi = 200,
  n.traits = 2,              # Total traits
  n.additive = 100,          # Trait 1 has QTLs
  polygenic.variance = 1     # Trait 2 is polygenic
)

Trait 2 characteristics: - Based on parental average + inbreeding - No specific QTLs - Useful for: very highly polygenic traits

5.7 Adding Traits to Existing Populations

Use creating.trait() to add traits after population creation:

# Create population
pop <- creating.diploid(nsnp = 10000, nindi = 200)

# Later, add a new trait
pop <- creating.trait(
  pop,
  n.additive = 80,
  n.dominant = 20,
  trait.name = "NewTrait"
)

Why add traits later? - Different traits need different architectures - Want to replace/update trait definitions - Building complex multi-trait models step-by-step

5.8 Combining Traits

Create composite traits from existing traits:

# Create base traits
pop <- creating.diploid(
  nsnp = 5000, nindi = 200,
  n.additive = c(100, 80, 60),
  trait.name = c("Milk", "Fat", "Protein")
)

# Create selection index
pop <- add.combi(
  pop,
  trait = 4,  # New trait number
  combi.weights = c(1, 10, 5),  # Economic weights
  trait.name = "EconomicIndex"
)

5.9 Trait Standardization

Ensure traits have desired mean and variance:

population <- bv.standardization(
  population,
  trait = 1,              # Which trait
  mean.target = 100,      # Target mean
  var.target = 1,         # Target variance
  set.zero = TRUE         # Force 0 allele effect = 0
)

When to use: - After custom trait specification - To compare traits on same scale - Before economic index creation

5.10 Practical Examples

5.10.1 Example 1: Dairy Cattle (Multiple Traits)

# Correlated production traits
cor_matrix <- matrix(c(
  1.0,  0.6,  0.5,   # Milk
  0.6,  1.0,  0.7,   # Fat
  0.5,  0.7,  1.0    # Protein
), nrow = 3, byrow = TRUE)

dairy <- creating.diploid(
  nsnp = 50000,
  nindi = 500,
  template.chip = "cattle",
  n.additive = c(200, 150, 150),
  n.dominant = c(20, 10, 10),
  trait.cor = cor_matrix,
  var.target = c(2000, 50, 30),
  mean.target = c(8000, 350, 320),
  trait.name = c("Milk_kg", "Fat_kg", "Protein_kg")
)

5.10.2 Example 2: Maize Hybrid Performance

# Model heterosis with dominance
maize <- creating.diploid(
  nsnp = 10000,
  nindi = 20,
  template.chip = "maize",
  dataset = "homorandom",      # Inbred lines
  n.additive = 200,
  n.dominant = 50,
  dominant.only.positive = TRUE,  # Heterosis = positive dominance
  var.additive = 0.7,
  var.dominant = 0.3,
  trait.name = "GrainYield"
)

5.10.3 Example 3: Disease Resistance (Binary Trait)

# Create underlying continuous trait
pop <- creating.diploid(
  nsnp = 5000, nindi = 500,
  n.additive = 50,
  mean.target = 0,
  var.target = 1,
  trait.name = "Liability"
)

# Apply threshold transformation
pop <- creating.phenotypic.transform(
  pop,
  trait = 1,
  trafo.function = function(x) { return(x > 0) }  # 50% prevalence
)

5.11 Summary

✅ Automated trait generation for common architectures
✅ Custom effects for precise control
✅ Multiple correlated traits supported
✅ Dominance and epistasis modeling
✅ Special traits: maternal, breed-specific, polygenic
✅ Flexible trait combination and standardization

5.12 What’s Next?

With realistic populations and traits, let’s build more complex scenarios with LD structure and data import.

Continue to Chapter 6: Advanced Population Setup!

# Trait Architecture {#sec-trait-architecture} ## Learning Objectives - Design simple and complex trait architectures - Model additive, dominance, and epistatic effects - Create correlated traits - Add maternal/paternal effects - Implement breed-specific QTLs ## Overview **Trait architecture** defines the genetic basis of traits: - Which markers are QTLs - Effect sizes of each QTL - Types of genetic effects (additive, dominance, epistasis) - Correlations between traits MoBPS provides both **automated** and **custom** approaches. ## Automated Trait Generation {#sec-auto-traits} ### Simple Additive Trait ```{r} #| eval: false population <- creating.diploid( nsnp = 10000, nindi = 200, n.additive = 100, # 100 additive QTLs var.target = 1, # Genetic variance = 1 mean.target = 100 # Mean breeding value = 100 ) ``` **What happens:** - 100 random SNPs chosen as QTLs - Effects drawn from Normal(0, σ²) - Automatically scaled to target variance ### Adding Dominance ```{r} #| eval: false population <- creating.diploid( nsnp = 10000, nindi = 200, n.additive = 100, n.dominant = 20, # 20 loci with dominance var.additive = 0.8, # 80% of variance from additive var.dominant = 0.2 # 20% from dominance ) ``` **Dominance effect modeling:** - Random loci chosen for dominance - Effects: genotype 0, 1, 2 each get independent effect - Can specify `dominant.only.positive = TRUE` for heterosis modeling ### Epistatic Effects ```{r} #| eval: false population <- creating.diploid( nsnp = 10000, nindi = 200, n.additive = 80, n.qualitative = 10, # Qualitative epistasis (ordered) n.quantitative = 5 # Quantitative epistasis (unordered) ) ``` **Epistasis types:** 1. **Qualitative:** 00 < 01 < 02 < 10 < 11 < 12 < 20 < 21 < 22 (ordered, selection always beneficial) 2. **Quantitative:** Mix of positive/negative interactions ### Effect Size Distributions ```{r} #| eval: false # Gaussian effects (default) pop_gaussian <- creating.diploid( nsnp = 5000, nindi = 200, n.additive = 100, effect.distribution = "gaussian" ) # Gamma distribution (for skewed effects) pop_gamma <- creating.diploid( nsnp = 5000, nindi = 200, n.additive = 100, effect.distribution = "gamma", gamma.shape1 = 0.4, # Shape parameter gamma.shape2 = 1.66 # Rate parameter ) # Equal effects pop_equal <- creating.diploid( nsnp = 5000, nindi = 200, n.equal.additive = 50, # 50 QTLs effect.size.equal.add = 0.5 # Each effect = 0.5 ) ``` ## Multiple Traits {#sec-multiple-traits} ### Independent Traits ```{r} #| eval: false population <- creating.diploid( nsnp = 10000, nindi = 200, n.additive = c(100, 80, 120), # 3 traits var.target = c(1, 1.5, 0.8), # Different variances trait.name = c("Yield", "Quality", "Disease_Resistance") ) ``` ### Correlated Traits ```{r} #| eval: false # Define correlation matrix cor_matrix <- matrix(c( 1.0, 0.5, -0.3, # Yield 0.5, 1.0, -0.2, # Quality -0.3, -0.2, 1.0 # Disease Resistance ), nrow = 3, byrow = TRUE) population <- creating.diploid( nsnp = 10000, nindi = 200, n.additive = c(100, 100, 100), trait.cor = cor_matrix, # Correlations trait.name = c("Yield", "Quality", "Disease_Resistance") ) ``` **How it works:** - Same markers used as QTLs for correlated traits - Effects drawn from multivariate normal distribution - Correlations independent of LD structure :::{.callout-warning} ## Correlation vs. Covariance MoBPS uses **correlation** matrices, not covariance matrices. Standardize your traits first! ::: ## Custom Trait Architecture {#sec-custom-traits} ### Single-Locus Effects (real.bv.add) Specify exactly which SNPs are QTLs and their effects: ```{r} #| eval: false # Create custom effects matrix # Columns: SNP_number, chromosome, effect_0, effect_1, effect_2 custom_effects <- rbind( c(120, 1, -1.0, 0.0, 1.0), # Additive effect c(42, 5, 0.0, 0.0, 2.0), # Recessive c(17, 22, 0.1, 0.1, 0.1) # No effect (neutral) ) population <- creating.diploid( nsnp = 10000, nindi = 200, real.bv.add = custom_effects ) ``` **Effect coding:** - Column 1: SNP number (1 to nsnp) - Column 2: Chromosome number - Columns 3-5: Effects for genotypes 0, 1, 2 ### Two-Locus Epistasis (real.bv.mult) ```{r} #| eval: false # Epistatic interaction between two loci # 9 effects for all genotype combinations epistatic_effects <- rbind( c(144, 1, 145, 1, # SNPs 144 and 145 on chr 1 1.0, 0.0, 0.0, # Effects when SNP1 = 0 0.0, 0.0, 0.0, # Effects when SNP1 = 1 0.0, 0.0, 0.0), # Effects when SNP1 = 2 c(4, 3, 188, 5, # SNP 4 on chr 3, SNP 188 on chr 5 0.37, 0.16, 1.35, 1.99, 1.58, 2.51, 0.38, 2.12, 0.98) ) population <- creating.diploid( nsnp = 10000, nindi = 200, real.bv.mult = epistatic_effects ) ``` ### Multi-Locus Epistasis (real.bv.dice) For effects involving 3+ loci: ```{r} #| eval: false # Complex epistatic network dice_list <- list( # First network: 3 SNPs location = list( matrix(c(11, 1, 12, 1, 16, 2), ncol = 2, byrow = TRUE) ), # Effects for all 27 combinations (3^3) effects = list( runif(27, -1, 1) # Random effects ) ) population <- creating.diploid( nsnp = 10000, nindi = 200, real.bv.dice = dice_list ) ``` ## Special Trait Types {#sec-special-traits} ### Maternal/Paternal Effects ```{r} #| eval: false # Trait influenced by mother's genotype population <- creating.diploid( nsnp = 5000, nindi = 100, n.additive = c(100, 50), is.maternal = c(FALSE, TRUE), # Trait 2 is maternal trait.name = c("Direct", "Maternal") ) # Combine into single trait population <- add.combi( population, trait = 3, combi.weights = c(0.7, 0.3), # 70% direct, 30% maternal trait.name = "Combined" ) ``` **Use cases:** - Birth weight (maternal nutrition) - Milk production (maternal effects on calves) - Egg quality (maternal contribution) ### Breed-Specific QTLs Model QTLs that only have effects in specific breeds: ```{r} #| eval: false # Create two breeds pop <- creating.diploid( nsnp = 5000, nindi = 100, founder.pool = 1, name.cohort = "Breed_A" ) pop <- creating.diploid( population = pop, nsnp = 5000, nindi = 100, founder.pool = 2, name.cohort = "Breed_B" ) # Add trait only active in breed A pop <- creating.trait( pop, n.additive = 100, trait.pool = 1 # Only affects pool 1 (Breed A) ) ``` ### Non-QTL Polygenic Traits Simulate infinitesimal model: ```{r} #| eval: false population <- creating.diploid( nsnp = 10000, nindi = 200, n.traits = 2, # Total traits n.additive = 100, # Trait 1 has QTLs polygenic.variance = 1 # Trait 2 is polygenic ) ``` **Trait 2 characteristics:** - Based on parental average + inbreeding - No specific QTLs - Useful for: very highly polygenic traits ## Adding Traits to Existing Populations {#sec-add-traits} Use `creating.trait()` to add traits after population creation: ```{r} #| eval: false # Create population pop <- creating.diploid(nsnp = 10000, nindi = 200) # Later, add a new trait pop <- creating.trait( pop, n.additive = 80, n.dominant = 20, trait.name = "NewTrait" ) ``` **Why add traits later?** - Different traits need different architectures - Want to replace/update trait definitions - Building complex multi-trait models step-by-step ## Combining Traits {#sec-combine-traits} Create composite traits from existing traits: ```{r} #| eval: false # Create base traits pop <- creating.diploid( nsnp = 5000, nindi = 200, n.additive = c(100, 80, 60), trait.name = c("Milk", "Fat", "Protein") ) # Create selection index pop <- add.combi( pop, trait = 4, # New trait number combi.weights = c(1, 10, 5), # Economic weights trait.name = "EconomicIndex" ) ``` ## Trait Standardization {#sec-standardization} Ensure traits have desired mean and variance: ```{r} #| eval: false population <- bv.standardization( population, trait = 1, # Which trait mean.target = 100, # Target mean var.target = 1, # Target variance set.zero = TRUE # Force 0 allele effect = 0 ) ``` **When to use:** - After custom trait specification - To compare traits on same scale - Before economic index creation ## Practical Examples {#sec-examples-traits} ### Example 1: Dairy Cattle (Multiple Traits) ```{r} #| eval: false # Correlated production traits cor_matrix <- matrix(c( 1.0, 0.6, 0.5, # Milk 0.6, 1.0, 0.7, # Fat 0.5, 0.7, 1.0 # Protein ), nrow = 3, byrow = TRUE) dairy <- creating.diploid( nsnp = 50000, nindi = 500, template.chip = "cattle", n.additive = c(200, 150, 150), n.dominant = c(20, 10, 10), trait.cor = cor_matrix, var.target = c(2000, 50, 30), mean.target = c(8000, 350, 320), trait.name = c("Milk_kg", "Fat_kg", "Protein_kg") ) ``` ### Example 2: Maize Hybrid Performance ```{r} #| eval: false # Model heterosis with dominance maize <- creating.diploid( nsnp = 10000, nindi = 20, template.chip = "maize", dataset = "homorandom", # Inbred lines n.additive = 200, n.dominant = 50, dominant.only.positive = TRUE, # Heterosis = positive dominance var.additive = 0.7, var.dominant = 0.3, trait.name = "GrainYield" ) ``` ### Example 3: Disease Resistance (Binary Trait) ```{r} #| eval: false # Create underlying continuous trait pop <- creating.diploid( nsnp = 5000, nindi = 500, n.additive = 50, mean.target = 0, var.target = 1, trait.name = "Liability" ) # Apply threshold transformation pop <- creating.phenotypic.transform( pop, trait = 1, trafo.function = function(x) { return(x > 0) } # 50% prevalence ) ``` ## Summary - ✅ Automated trait generation for common architectures - ✅ Custom effects for precise control - ✅ Multiple correlated traits supported - ✅ Dominance and epistasis modeling - ✅ Special traits: maternal, breed-specific, polygenic - ✅ Flexible trait combination and standardization ## What's Next? With realistic populations and traits, let's build more complex scenarios with LD structure and data import. Continue to [Chapter 6: Advanced Population Setup](06-advanced-population-setup.qmd)!