Laplacian eigenfunctions learn population structure.

Area of Science:

• Population genetics
• Genomics
• Bioinformatics

Background:

• Principal components analysis (PCA) is a standard tool for summarizing genetic variation and inferring population migration history.
• PCA is widely used in genome-wide association studies (GWAS) to detect and correct for population structure.
• Concerns exist regarding PCA's sensitivity to outliers and its interpretation.

Purpose of the Study:

• To introduce a novel method for inferring population structure using spectral graph theory.
• To compare the effectiveness of Laplacian eigenfunctions against principal components for population structure analysis.

Main Methods:

• Constructing a weighted graph where study subjects are nodes and edges represent relationships between neighbors.
• Utilizing the spectrum of the graph Laplacian operator, specifically Laplacian eigenfunctions, to infer population structure.

Main Results:

• Laplacian eigenfunctions revealed more meaningful and less noisy population structure compared to principal components.
• The proposed method demonstrated superior performance in both simulations and real-world data analysis (ring species of birds).

Conclusions:

• Spectral graph theory provides a robust alternative to PCA for population structure inference.
• The proposed Laplacian eigenfunction approach is simple, computationally fast, and promising for population genetics and disease association studies.