Quantitative & Population Genetics

Foundations of Genetic Variation and Quantitative Trait Analysis

Author
Affiliation

Peter Sørensen

Center for Quantitative Genetics and Genomics, Aarhus University, Denmark

Course Material

This course provides the theoretical foundations of population and quantitative genetics, with an 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 trait mapping.

Core Topics

Population Genetics

  • Genetic Variation & Structure: Defining the gene pool; distinguishing between loci, alleles, haplotypes, and phase; measuring heterozygosity and nucleotide diversity.
  • The Hardy–Weinberg Principle: Calculating allele and genotype frequencies; identifying assumptions of equilibrium and testing for statistical deviations.
  • Mating Systems: Effects of non-random mating on genomic architecture; quantifying inbreeding (\(F\)) and its genetic consequences.
  • Evolutionary Dynamics: How mutation, migration, and recombination drive diversity; the impact of population size on genetic drift.
  • Natural Selection: Distinguishing between directional, balancing, and purifying selection; identifying genomic signatures of selective sweeps.
  • Linkage Disequilibrium (LD): Mechanisms of LD generation and the rate of decay across the genome.
  • Applications: Utilizing population genetics in conservation biology, medical association studies, and forensic genetics.

Quantitative Genetics

  • Measuring Variation: Applying mathematical models and statistical methods (mean, variance, normal distribution) to describe and analyze continuous variation.
  • The Simple Genetic Model: Deconstructing the phenotype into genetic and environmental deviations (\(P = \mu + G + E\)); assessing the relative contributions to total phenotypic variation.
  • Genetic Architecture: Partitioning total genetic variance into additive (\(V_A\)) and dominance (\(V_D\)) components to determine the underlying landscape of complex traits.
  • Heritability Analysis: Calculating and interpreting Broad-sense (\(H^2\)) vs. Narrow-sense (\(h^2\)) heritability; understanding the biological significance of additive effects.
  • Predicting Phenotypes: Utilizing parental data and the Breeder’s Equation (\(R = h^2 S\)) to predict offspring phenotypes and response to selection.
  • Association Mapping: Explaining the principles behind Genome-Wide Association Studies (GWAS); identifying Quantitative Trait Loci (QTLs) through Linkage Disequilibrium.
  • Genomic Insights: Understanding the implications of polygenicity, effect sizes, and regulatory variants in human medicine and agricultural breeding.

Learning Objectives

Upon completion of the course, it should be possible to:

  • Explain how genetic variation is generated, maintained, and detected in populations.
  • Interpret Hardy–Weinberg equilibrium and identify the evolutionary forces causing deviations from it.
  • Quantify the effects of drift, selection, mutation, and migration on allele frequencies and genomic signatures.
  • Partition phenotypic variance into genetic (additive and dominance) and environmental components.
  • Calculate and interpret broad-sense (\(H^2\)) and narrow-sense (\(h^2\)) heritability.
  • Predict offspring phenotypes from parental values using the Breeder’s Equation.
  • Design and interpret the results of Genome-Wide Association Studies (GWAS).
  • Connect abstract mathematical models with concrete biological interpretations and real-world data.

Course Structure

This site serves as the core reference for the course. Each chapter is designed to build intuition by connecting theoretical concepts with practical data examples.

The materials include:

  • Conceptual Explanations: Definitions of key genetic principles.
  • Mathematical Basics: Step-by-step derivations of the models used in the field.
  • Worked Examples: Practical calculations of frequencies, heritability, and selection.
  • Interactive Figures: Visualizations and simulations created in R to illustrate complex dynamics.

Slides

Lecture slides are provided as interactive Reveal.js presentations. These provide a structured overview of the key concepts, mathematical models, and genomic visualizations:

Note: The slides provide lecture guidance; the online notes serve as the primary reference for study and examination preparation.

Tutorials

Hands-on tutorials are integrated into the course to explore genetic principles in practice. R is utilized as a “virtual laboratory” to simulate populations and observe genetic change over time.

Key areas covered in R:

  • Population Basics: Calculating and plotting allele frequencies, genotype distributions, and Hardy-Weinberg expectations.
  • Evolutionary Forces: Simulating how mutation, migration, selection, and genetic drift change populations across generations.
  • Genomic Patterns: Visualizing Linkage Disequilibrium (LD), haplotype sweeps, and the impact of population bottlenecks.
  • Pedigrees & History: Plotting family trees to clarify inbreeding and utilizing coalescent models to examine ancestral history.

Use of Code: The R code is provided as a starting point for experimentation. The modification of parameters—such as changing the population size or the strength of selection—allows for the observation of changes in genetic outcomes.

Interactive Tools

Interactive tools are provided to examine selected models and parameters used in population and quantitative genetics.

Population Genetics

To be added ….

Quantitative Genetics

  • Heritability Estimation Using Different Types of Relatives
    Estimate narrow-sense heritability using regression on relatives.
    🔗 Launch app

  • Breeding Value Estimation from a Single Information Source
    Investigate estimation of additive genetic effects based on limited data.
    🔗 Launch app

Downloadable R Scripts

Some tools are provided as standalone R scripts for local execution:

  • Hardy–Weinberg simulation script
    💾 Download

  • Drift simulation script
    💾 Download

To run a script locally:

source("apps/hwe_simulation.R")

Prerequisites

Engagement with the material assumes:

  • Basic Genetics: Understanding of Mendelian inheritance, meiosis, and molecular biology.
  • Introductory Statistics: Familiarity with probability, mean, variance, and the normal distribution.
  • Familiarity with R: Basic ability to load data and run scripts.