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. 2016 Apr;202(4):1299-312.
doi: 10.1534/genetics.115.182626. Epub 2016 Feb 17.

Inference and Analysis of Population Structure Using Genetic Data and Network Theory

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Free PMC article

Inference and Analysis of Population Structure Using Genetic Data and Network Theory

Gili Greenbaum et al. Genetics. .
Free PMC article

Abstract

Clustering individuals to subpopulations based on genetic data has become commonplace in many genetic studies. Inference about population structure is most often done by applying model-based approaches, aided by visualization using distance-based approaches such as multidimensional scaling. While existing distance-based approaches suffer from a lack of statistical rigor, model-based approaches entail assumptions of prior conditions such as that the subpopulations are at Hardy-Weinberg equilibria. Here we present a distance-based approach for inference about population structure using genetic data by defining population structure using network theory terminology and methods. A network is constructed from a pairwise genetic-similarity matrix of all sampled individuals. The community partition, a partition of a network to dense subgraphs, is equated with population structure, a partition of the population to genetically related groups. Community-detection algorithms are used to partition the network into communities, interpreted as a partition of the population to subpopulations. The statistical significance of the structure can be estimated by using permutation tests to evaluate the significance of the partition's modularity, a network theory measure indicating the quality of community partitions. To further characterize population structure, a new measure of the strength of association (SA) for an individual to its assigned community is presented. The strength of association distribution (SAD) of the communities is analyzed to provide additional population structure characteristics, such as the relative amount of gene flow experienced by the different subpopulations and identification of hybrid individuals. Human genetic data and simulations are used to demonstrate the applicability of the analyses. The approach presented here provides a novel, computationally efficient model-free method for inference about population structure that does not entail assumption of prior conditions. The method is implemented in the software NetStruct (available at https://giligreenbaum.wordpress.com/software/).

Keywords: community detection; hierarchical population structure; modularity; subpopulations.

Figures

Figure 1
Figure 1
Community detection on three networks with different thresholds. Each node represents an individual, with colors representing the community assigned by the community-detection algorithm. (A) High threshold (0.207 for East Asian component, 0.198 for the rest of the network). (B) Medium threshold (0.194). (C) Low threshold (0.188). For visualization purposes, individuals are placed on the world map roughly corresponding to their ancestry.
Figure 2
Figure 2
Strength of association distribution (SAD) analysis for the network in Figure 1B. Shown are the distributions of the SA values for each of the three communities detected. Mean SA for each community is indicated by a dashed line.
Figure 3
Figure 3
Model-based analysis of human SNP data assuming three subpopulations (K = 3) using the program STRUCTURE. The sampled population labels are the same as in Figure 1. The colors of the subpopulations correspond to the colors in Figure 1B and Figure 2.
Figure 4
Figure 4
Strength of association distribution (SAD) analysis for the Indo-European (blue) community. (A) Distribution of the Indo-European community as shown in Figure 2. (B) SA distribution of the individuals in the community for different sampled subpopulations. It can be seen that the individuals with European ancestry are responsible for the higher SA values in the distribution in A, while the individuals with Mexican or Indian ancestry have lower association with this community.
Figure 5
Figure 5
Strength of association distribution (SAD) analysis for the African (orange) community. (A) Distribution of the African community as shown in Figure 2. (B) Distribution of the individuals in the community for different sampled populations. The left mode in A is due to Masai individuals, who were detected as a distinct population by some algorithms (File S1). The African-ancestry American individuals have a slightly lower association with the community than individuals from Nigeria and Kenya, as well as a distinct left tail, perhaps due to recent admixture with people of European or Native American origin.
Figure 6
Figure 6
An example of hybrid identification using strength of association distribution (SAD) analysis. Distribution charts show the SAD for the three detected communities, with the SA of the hybrid shown as a red dot (distribution of P3 in S3 is out of scale). The analysis was performed on simulated scenarios S1, S2, and S3, where H1 is a hybrid between populations P1 and P2, and H2 is a second-generation hybrid between H1 and P1. Hybrids are identified as low SAD outliers in all cases except for H2 in S3.

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