29 Continuous traits from discrete genes

29.1 Introduction

This is a fast, hands-on classroom simulation showing how many small additive genetic effects combine to produce a continuous, approximately normal trait distribution. It corresponds to the appendix chapter Continuous traits from discrete genes in the main book and connects to the Heritability from a linear regression exercise (additive genetic variance).

Each student acts as a single gene that is either ON (1) or OFF (0). With a baseline trait value and one unit added per ON gene, the class-wide distribution of trait values is bell-shaped — an intuitive route into quantitative genetics.

29.2 Learning Outcomes

By the end of this exercise, students will be able to: - Explain how additive genetic effects create continuous trait variation. - Compare a physical classroom simulation with a simple R simulation. - Relate the spread of trait values to additive genetic variance.

29.3 Activity Overview

Suggested Timings: - 5 minutes: Introduce the idea (polygenic traits, additive effects). - 10 minutes: Run the classroom “each student is a gene” simulation and record trait values for ≥30 individuals. - 10 minutes: Reproduce it in R and compare histograms. - 5 minutes: Link to additive genetic variance and heritability.

29.4 Instructions for Facilitating

  1. Set a baseline trait value (e.g. 35) and rule: add 1 for each ON gene.

  2. For each “individual”, have students randomly be ON/OFF (coin flip, 50:50) and total the trait value; repeat for at least 30 individuals.

  3. Plot a quick histogram of the observed values and describe the shape (roughly symmetric, peaked near the expected value).

  4. Reproduce in R for 100 individuals and 25 genes, then compare:

    set.seed(123)
baseline <- 35
n_genes <- 25
n_individuals <- 100
gene_on <- rbinom(n_individuals, size = n_genes, prob = 0.5)
trait_value <- baseline + gene_on
hist(trait_value, breaks = 12, col = "gray80",
     main = "Trait values", xlab = "Trait")

  5. Discuss why the distribution is continuous and bell-shaped despite the genes being discrete.

29.5 Questions & Model Answers

  1. What is the expected trait value, and why?
    • With 25 genes at 50:50, the expected number ON is \(25 \times 0.5 = 12.5\), so the expected trait value is \(35 + 12.5 = 47.5\). Individual values vary around this because each gene is ON/OFF stochastically.
  2. Why is the distribution continuous and approximately normal?
    • Summing many small independent contributions produces an approximately normal distribution (central limit theorem). Even though each gene is discrete, adding many of them yields a smooth, bell-shaped spread of totals.
  3. How does this relate to additive genetic variance?
    • The variance among individuals here arises entirely from the additive genetic contributions (all environments identical). This is the conceptual basis of additive genetic variance and links directly to the heritability exercise.

29.6 Teaching Tips

  • Physical first, then R: the coin-flip version makes the abstraction concrete before the code reproduces it at scale.
  • Vary the gene count: more genes → smoother, narrower-relative distribution; a nice illustration of how polygenic traits behave.
  • Set a seed in R so results are reproducible when comparing to the classroom histogram.

29.7 Common Pitfalls

  • Expecting a bimodal or flat distribution because the genes are binary — emphasise that it is the sum that matters.
  • Too few individuals: with fewer than ~30 the bell shape is hard to see; encourage larger samples.
  • Confusing the trait mean with a single gene’s effect — the mean comes from the expected number of ON genes, not from any one gene.