Comparing simulated genetic and phenotypic variance-covariance matrices across a range of sample sizes, heritabilities, and pleiotropy levels.

Workflow

1. Generate pedigree
2. Generate phenotypes along pedigree (phensim.r)
3. Estimate G matrix (WOMBAT)
4. Compare G, A, and P using utility scripts in /util/
5. Generate figures (figures.Rmd)

Scripts

Main:

• main.r — Entry point. Sets simulation parameters (number of traits, sires, heritability, error structure) and calls matrixsim() for each parameter combination.
• matrixsim.r — Core simulation function. Generates a pedigree, simulates phenotypes via phensim(), estimates G via WOMBAT, then writes A (true breeding value covariance), G (WOMBAT-estimated), and P (phenotypic covariance) matrices to a CSV file. Results are saved as *name*_matrices.csv in the project root.
• phensim.r — Simulates phenotypes along a pedigree given A and E matrices. Based on the phensim function from the Pedantics package.
• figures.Rmd — Generates all ggplot figures from the matrices CSV files and analysis outputs.

Utility scripts that take the matrices CSV as input and compute comparison statistics, returning results as dataframes:

• read_matrices.r — Reads *_matrices.csv files into R
• Angles.r — Angles between matrix subspaces
• AvgEvolvabilities.r / MaxEvolvabilities.r — Average and maximum evolvability
• Disparity.r — Matrix disparity
• KrzCorsFirst.r / KrzCorsLast.r — Krzanowski subspace correlations (first and last axes)
• MantelCors.r / MantelTests.r — Mantel correlations and tests
• RDifferences.r — Response differences
• RSkewers.r — Random skewers analysis

Data files

Simulation output matrices

• small_families_matrices.csv — Simulation results for small family structures: 20/60/200 families (10/30/100 sires × 2 dams/sire × 2 offspring/dam).
• large_families_matrices.csv — Simulation results for large family structures: 50/150/500 families (10/30/100 sires × 5 dams/sire × 3 offspring/dam).

Each row is one simulation replicate. Columns:

• A — True additive genetic covariance matrix (from phensim breeding values), stored as a space-separated vector of the lower triangle
• G — Estimated G matrix from WOMBAT, same format
• P — Phenotypic covariance matrix from phensim, same format
• n — Number of traits
• h — Heritability
• multicoll — Pleiotropy/multicollinearity level of the true G matrix (low, medium, high)
• f — Number of families
• e_type — Environmental covariance structure
• name — Simulation run identifier

Analysis results

angle_results_n4_E_small_fam.csv — Angles between pairs of matrices for 4-trait small-family simulations, varying environmental covariance structure. Each row is one parameter combination. Columns:

• Angle — Mean angle (degrees) between the compared matrices across replicates
• SE — Standard error of the mean angle
• Comparison — Matrix pair compared (e.g. P and true G, Estimated G and true G)
• X..of.Traits — Number of traits
• X..of.Families — Number of families
• Heritability — Heritability
• Multicollinearity — Pleiotropy/multicollinearity level (low, medium, high)
• E.Type — Environmental covariance structure

disparity_results_n_small_fam.csv — Matrix disparity between pairs of matrices for small-family simulations, varying number of traits. Same columns as angle results but with Disparity and SE in place of Angle and SE.

disparity_results_n_large_fam.csv — Same as above for large-family simulations.

disparity_results_n4_E_small_fam.csv — Matrix disparity for 4-trait small-family simulations, varying environmental covariance structure. Same column structure.

disparity_results_n8_E_small_fam.csv — Matrix disparity for 8-trait small-family simulations, varying environmental covariance structure. Same column structure.

fig1_regression_results_small_fam.csv — Element-wise regression of estimated G on true G and P on true G, for small-family simulations. Each row is one parameter combination. Columns:

• n — Number of traits
• h — Heritability
• E — Environmental covariance structure
• Comparison — Matrix pair compared
• slope — Regression slope
• r_squared — R² of the regression

figS1_regression_results_large_fam.csv — Same as above for large-family simulations.

mantel_tests_n4_E_small_fam.csv — Mantel test results for 4-trait small-family simulations, varying environmental covariance structure. Each row is one parameter combination. Columns:

• P — Mantel test p-value
• Comparison — Matrix pair compared
• n — Number of traits
• f — Number of families
• h — Heritability
• Multicollinearity — Pleiotropy/multicollinearity level
• E — Environmental covariance structure

mantel_tests_n4_E_large_fam.csv — Same as above for large-family simulations.

norm_small_fam.csv — Ratio of matrix norms (F_G / F_P) for small-family simulations. Each row is one parameter combination. Columns:

• Ratio — Mean ratio of Frobenius norms across replicates
• SE — Standard error of the mean ratio
• Comparison — Norm ratio computed (e.g. F_G/F_P)
• X..of.Traits — Number of traits
• X..of.Families — Number of families
• Heritability — Heritability
• Multicollinearity — Pleiotropy/multicollinearity level
• E.Type — Environmental covariance structure

norm_large_fam.csv — Same as above for large-family simulations.

Dependencies

• R with packages: tidyverse, MCMCglmm, mixtools, monomvn, here, Matrix, evolvability, evolqg, reshape2
• WOMBAT available in the system path as wombat
• UNIX-like system (Linux, macOS, WSL on Windows)

Acknowledgements

• Dr. JL Sztepanacz (principal investigator)
• Alexander MacKenzie (code to interface with WOMBAT)
• Dr. M Videlier (helpful suggestions and discussions)
• Dr. M Morrissey (phensim function)