Teaching Materials

Quantitative Genetics, Genomics, and Statistical Modeling

Author
Affiliation

Peter Sørensen

Center for Quantitative Genetics and Genomics, Aarhus University, Denmark

This site provides teaching materials, lecture notes, slides, and computational demonstrations in quantitative genetics, genomics, and statistical modeling. All materials are reproducible and developed using R and Quarto.

🎓 Modules

The modules cover complementary aspects of quantitative genetics, genomics, and statistical modeling. Some topics—such as genome-wide association studies (GWAS)—appear across multiple modules but from different perspectives, ranging from theoretical foundations to statistical methods and biological interpretation.

📘 Quantitative & Population Genetics

This module provides the theoretical foundations of population and quantitative genetics, with emphasis on the mathematical and statistical principles used to study genetic variation and complex traits. The material examines how genetic variation arises and is maintained in populations, how evolutionary forces shape allele frequencies, and how genetic and environmental factors contribute to phenotypic variation. Classical population genetics is integrated with quantitative trait analysis and modern genomic approaches to mapping complex traits.

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🧬 Genomics, Systems Biology & Bioinformatics

This module explores how genomic and multi-omics data can be used to understand complex biological systems. Topics include sequencing technologies, integration of molecular data, genome-wide association studies (GWAS), network models, and machine learning approaches for analyzing biological data.

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📊 Bayesian Linear Regression

This module introduces Bayesian linear regression as a framework for statistical modeling and inference. Topics include prior specification, posterior inference using Gibbs sampling, and interpretation of model parameters, with emphasis on practical implementation and convergence assessment.

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🧬 Genome-Wide Association Studies (GWAS)

This module introduces the statistical and genetic foundations of genome-wide association studies (GWAS), which aim to identify genetic variants associated with complex traits and diseases. Topics include statistical inference for genetic effects, population structure and relatedness, linkage disequilibrium, heritability estimation, and methods for identifying causal variants within associated genomic regions.

The material is based on lecture notes developed by Matti Pirinen and distributed under a CC-BY-SA license.

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🧰 Software

The qgg R Package

qgg provides tools for statistical modeling and analysis of large-scale genomic data, including:

  • Fine-mapping of genomic regions using Bayesian Linear Regression (BLR) models
  • Polygenic scoring using Bayesian Linear Regression (BLR) models
  • Gene set enrichment analysis using Bayesian Linear Regression (BLR) models

qgg handles large-scale genomic data through efficient algorithms and sparse matrix techniques, combined with multi-core processing using OpenMP, multithreaded matrix operations via BLAS libraries (e.g., OpenBLAS, ATLAS, or MKL), and fast, memory-efficient batch processing of genotype data stored in binary formats such as PLINK .bed files.

The gact R Package

gact provides an infrastructure for efficient processing of large-scale genomic association data, with core functions for:

  • Establishing and populating a database of genomic associations
  • Downloading and processing biological databases
  • Handling and processing GWAS summary statistics
  • Linking genetic markers to genes, proteins, metabolites, and biological pathways
  • Integration with statistical modeling tools in the qgg R package

gact is intended to serve as a practical implementation of integrative genomics, bridging statistical modeling and biological interpretation, and supporting reproducible and extensible workflows.

💻 Teaching Philosophy

The material emphasizes:

  • Mathematical foundations
  • Statistical modeling
  • Reproducible research
  • Computational implementation in R
  • Conceptual understanding of methods

Lecture materials integrate theory, simulation, and applied examples.

📚 Further Reading

For foundational principles of classical and molecular genetics:

Griffiths, A. J. F., Doebley, J. F., Peichel, C. L., & Wassarman, D. A. (2023). An Introduction to Genetic Analysis (13th ed.). W. H. Freeman.

For a unified and modern treatment of quantitative genetics theory and genomics:

Walsh, B., Visscher, P. M., & Lynch, M. (2025). Genetics and Analysis of Quantitative Traits: Foundations (2nd ed.). Cambridge University Press.

For Bayesian modeling, hierarchical inference, and statistical learning in quantitative genetics and genomics:

Sorensen, D. (2025). Statistical Learning in Genetics: An Introduction Using R. Springer.

For likelihood-based and Bayesian inference, including detailed treatment of MCMC methods:

Sorensen, D., & Gianola, D. (2002/2010). Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics. Springer.

For a comprehensive and mathematically rigorous treatment of modern statistical learning:

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.). Springer.

For an accessible and application-oriented introduction to statistical learning with R:

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An Introduction to Statistical Learning: With Applications in R (2nd ed.). Springer.

Reusing the Teaching Materials

All teaching materials are developed using Quarto and R, and are available on GitHub.

Instructors are welcome to:

  • reuse slides or tutorials
  • adapt course materials
  • contribute improvements

Repository:

https://github.com/psoerensen/qgteach

📫 Contact

Peter Sørensen
Center for Quantitative Genetics and Genomics
Aarhus University, Denmark

Email: pso@qgg.au.dk
GitHub: https://github.com/psoerensen