Lesson 5 Population Structure and Relatedness

5.1 Why population structure matters in GWAS

GWAS assumes that genetic variants are tested in a population where individuals are comparable aside from the trait of interest.

In practice, study samples often include individuals from different ancestral backgrounds or with varying degrees of relatedness.

If population structure is not accounted for, genetic differences that reflect ancestry rather than biology can appear as false associations.

5.2 Population stratification

Population stratification refers to systematic differences in allele frequencies between subgroups of individuals.

These differences can arise from:

  • ancestral history
  • geographic separation
  • migration and admixture

When stratification aligns with trait differences, it can confound association results.

5.3 Relatedness and family structure

Relatedness describes genetic similarity between individuals due to shared ancestry.

Examples include:

  • siblings
  • parent child pairs
  • extended family members

Closely related individuals violate the assumption of independence used in many association models and can inflate test statistics.


# Plot styling and figure saving (CDI standard)
from cdi_viz.theme import cdi_notebook_init, show_and_save_mpl

# Match chapter to the lesson number used in anchors and navigation
cdi_notebook_init(chapter="05", title_x=0)

5.4 Inspecting population structure in the demo dataset

To ground these ideas, we inspect population structure signals in the CDI GWAS demo dataset.

At this stage, the goal is to:

  • understand what structure summaries look like
  • learn how they are interpreted
  • avoid premature filtering or modeling

We do not perform a full ancestry inference pipeline in this lesson.


from pathlib import Path
import pandas as pd

DATA_DIR = Path("data/gwas-demo-dataset")

phenotypes = pd.read_csv(DATA_DIR / "phenotypes.csv")
variants = pd.read_csv(DATA_DIR / "variants.csv")

phenotypes.head(), variants.head()
(  sample_id  trait_binary  trait_quant  age sex     pc1     pc2     pc3  \
 0     S0001             1      -0.0108   43   F  1.6018 -1.0624 -0.8633   
 1     S0002             1       2.0082   56   M -0.2394 -0.5294 -0.1475   
 2     S0003             1      -0.7331   55   M -1.0235 -0.8769 -0.1525   
 3     S0004             1      -0.9815   44   F  0.1793 -0.0943  0.3834   
 4     S0005             0       1.5433   66   F  0.2200 -1.7577  0.9998   
 
     batch  
 0  site-b  
 1  site-a  
 2  site-b  
 3  site-b  
 4  site-c  ,
      snp_id  chr        pos ref alt     maf
 0  rs100002    1    6891850   A   C  0.1962
 1  rs100005    1   47496996   G   A  0.0571
 2  rs100031    1  156142503   G   T  0.2254
 3  rs100018    2  106591486   G   A  0.2618
 4  rs100021    2  131748289   G   T  0.3114)

5.5 Ancestry components as summaries

In practice, population structure is often summarized using ancestry components.

These components:

  • capture major axes of genetic variation
  • reflect ancestry gradients or clusters
  • can be used as covariates in association models

In the demo dataset, ancestry components are already provided as pc1, pc2, and pc3.


# Inspect provided ancestry components
phenotypes[["pc1", "pc2", "pc3"]].describe()
pc1 pc2 pc3
count 120.000000 120.000000 120.000000
mean -0.008994 0.061467 -0.041772
std 1.011939 1.029519 0.990252
min -2.147300 -2.566700 -2.333600
25% -0.750050 -0.575950 -0.714425
50% -0.129700 0.112300 -0.007250
75% 0.562375 0.735825 0.570375
max 2.913900 2.905100 2.327700

5.6 Visualizing ancestry components

Plots of ancestry components help reveal:

  • clusters of samples
  • continuous gradients
  • potential outliers

The goal is interpretation, not classification.


import matplotlib.pyplot as plt

plt.figure()
plt.scatter(phenotypes["pc1"], phenotypes["pc2"])
plt.xlabel("PC1")
plt.ylabel("PC2")
show_and_save_mpl()

plt.figure()
plt.scatter(phenotypes["pc1"], phenotypes["pc3"])
plt.xlabel("PC1")
plt.ylabel("PC3")
show_and_save_mpl()
Saved PNG → figures/05_001.png

Saved PNG → figures/05_002.png

5.7 Structure as covariates

Rather than excluding individuals, GWAS commonly adjusts for structure.

This is done by:

  • including ancestry components as covariates
  • fitting models that account for relatedness directly

Adjustment helps control confounding while retaining sample size.

5.8 Structure versus signal

Not all population structure should be removed.

Some genetic signals may reflect true biological differences linked to ancestry.

The challenge is to distinguish:

  • confounding structure
  • meaningful genetic variation

This distinction requires careful interpretation and domain knowledge.

5.9 Key takeaways

  • Population structure can confound GWAS results
  • Relatedness violates independence assumptions
  • Ancestry components summarize genetic structure
  • Adjustment is often preferable to exclusion
  • Interpretation requires care and context
CDI – Complex Data Insights — 2026 Edition