Simulate Multi-Cycle Selection Using Different Indices

Performs a stochastic simulation comparing the long-term performance of four selection indices (LPSI, ESIM, RLPSI, RESIM) over multiple breeding cycles. Models linkage between loci using Haldane's mapping function.

Usage

simulate_selection_cycles(
  n_cycles = 50,
  n_individuals = 1000,
  n_loci = 100,
  n_traits = 3,
  heritability = 0.5,
  selection_proportion = 0.1,
  economic_weights = NULL,
  restricted_traits = NULL,
  genetic_distances = NULL,
  qtl_effects = NULL,
  seed = NULL
)

Arguments

n_cycles

Number of selection cycles to simulate (default: 50)

n_individuals

Initial population size (default: 1000)

n_loci

Number of QTL per trait (default: 100)

n_traits

Number of quantitative traits (default: 3)

heritability

Heritability for all traits (scalar or vector, default: 0.5)

selection_proportion

Proportion of individuals selected (default: 0.1)

economic_weights

Economic weights for LPSI (default: equal weights)

restricted_traits

Trait indices to restrict to zero gain for RLPSI/RESIM (default: NULL)

genetic_distances

Vector of genetic distances between loci in Morgans (default: 0.1)

qtl_effects

Optional matrix of QTL effects (n_loci x n_traits)

seed

Random seed for reproducibility (default: NULL)

Value

List with components:

• lpsi_gain - Matrix of genetic gains per cycle for LPSI (n_cycles x n_traits)

• esim_gain - Matrix of genetic gains per cycle for ESIM

• rlpsi_gain - Matrix of genetic gains per cycle for RLPSI

• resim_gain - Matrix of genetic gains per cycle for RESIM

• lpsi_mean - Mean genetic value per cycle for LPSI (n_cycles x n_traits)

• esim_mean - Mean genetic value per cycle for ESIM

• rlpsi_mean - Mean genetic value per cycle for RLPSI

• resim_mean - Mean genetic value per cycle for RESIM

• parameters - List of simulation parameters used

Details

Simulation Procedure (Chapter 10):

1. Initialize population with random QTL alleles at linked loci 2. For each cycle: - Compute genetic values from diploid genotypes - Add environmental noise to create phenotypes - Calculate variance-covariance matrices - Apply each selection index (LPSI, ESIM, RLPSI, RESIM) - Select top individuals based on index scores - Generate offspring through recombination (using Haldane's function) 3. Track genetic gain and population mean across cycles

The Four Indices (Chapter 10, Section 10.2):

• LPSI: Unrestricted index maximizing genetic gain: b = P^(-1)Gw

• ESIM: Unrestricted eigen index maximizing accuracy: (P^(-1)C - lambda^2 I)b = 0

• RLPSI: Restricted LPSI with constraints: U'Gb = 0

• RESIM: Restricted ESIM with constraints: U'Cb = 0

Important Simulation Assumptions:

Note: Environmental variance is calculated once at generation 0 and held constant across all cycles. Heritability will naturally decline over cycles as genetic variance is depleted (Bulmer effect). This models the biological reality that selection exhausts additive genetic variance while environmental variation remains stable.

Examples

if (FALSE) { # \dontrun{
# Basic simulation with 3 traits over 20 cycles
results <- simulate_selection_cycles(
  n_cycles = 20,
  n_individuals = 500,
  n_loci = 50,
  n_traits = 3,
  heritability = 0.5,
  selection_proportion = 0.1,
  economic_weights = c(10, 5, 3),
  seed = 123
)

# Plot genetic gains
plot(1:20, results$lpsi_mean[, 1],
  type = "l", col = "blue",
  ylab = "Mean Genetic Value", xlab = "Cycle",
  main = "Genetic Gain - Trait 1"
)
lines(1:20, results$esim_mean[, 1], col = "red")
lines(1:20, results$rlpsi_mean[, 1], col = "green")
lines(1:20, results$resim_mean[, 1], col = "orange")
legend("topleft", c("LPSI", "ESIM", "RLPSI", "RESIM"),
  col = c("blue", "red", "green", "orange"), lty = 1
)

# Restrict trait 2 to zero gain
results_restricted <- simulate_selection_cycles(
  n_cycles = 20,
  n_traits = 3,
  restricted_traits = 2,
  seed = 456
)
} # }