Several detailed reviews of methods used to analyze SNP data exist.6 7 The current methods can be broadly classified into univariate and multivariate methods.

To address the research question, we used SNP data from the phase 2 HapMap (release 23) database.13 Because prior research has identified14 and verified15 that 128 AIM SNPs contain strong signal related to ancestry, we extracted genotype data for these 128 SNPs for 60 unrelated subjects from Ibadan, Nigeria (henceforth referred to as ‘Yoruba Africans’) and 60 unrelated subjects from Utah-resident Americans with ancestry from northern and western Europe (henceforth referred to as ‘Utah Americans’). Of the 128 SNPs, 78 had complete data, and the remaining 30 had missing data for <5% of the subjects; the latter 30 SNPs were excluded from the analysis. The final dataset contained genotype data for 78 SNPs and 120 subjects and had no missing genotypes.

A SNP typically has only two possible bases (eg, A or G), one of which is less common in the population (‘minor allele’), and the other is more common (‘major allele’). Because humans carry two copies of the genome, SNPs that have bases A and G can have three combinations across the two copies of the genome: AA, AG and GG. These three combinations are referred to as the ‘genotypes’ of the SNP. For each SNP, we coded the three genotypes as 0, 1, or 2 denoting whether a subject was a ‘major homozygote’ (having two copies of the major allele), a ‘heterozygote’ (having one copy of each allele), or a ‘minor homozygote’ (having two copies of the minor allele), respectively. The minor allele of a SNP was determined to be the one that had the lower frequency in the data. This encoding is referred to as the ‘additive genetic model’,2 and is typically used in many genetic analyses, including in the analysis of AIM SNPs.

Our analysis consisted of two steps: (1) ‘exploratory visual analysis’ through the use of three bipartite visual representations chosen to identify emergent bipartite relationships between subjects and SNPs; (2) ‘quantitative analysis’ through the use of methods suggested by the emergent visual patterns. This two-step method was motivated by our earlier studies16–18 that used a similar approach, and which have revealed that bipartite relationships can exhibit in different patterns (eg, nested clusters, disjoint clusters), each prompting the use of quantitative methods that make the appropriate assumptions about the underlying data.

The bipartite network visualization of 120 subjects and 78 SNPs revealed a complex but understandable clustered pattern. As shown in figure 2A, there are two major clusters of SNPs and subjects, one to the left and another to the right. The SNPs are connected to subjects via white, gray, and black edges denoting genotype values 0, 1, and 2, respectively. The left cluster (shown in blue) consists of SNPs that have predominantly the minor homozygote genotype (genotype 2) for the Yoruba African subjects (black nodes), whereas the right cluster (shown in pink) consists of SNPs that predominantly have the minor homozygote genotype for the Utah American subjects (white nodes). Henceforth, for brevity, we refer to the left SNP cluster as ‘Utah American SNPs’ and to the right SNP cluster as ‘Yoruba African SNPs’. There also appear to be additional SNPs that circle mainly the Yoruba African SNPs. These SNPs have weaker connections to both the Yoruba African subjects and the Utah American subjects, as shown by their fewer black edges.

To quantitatively verify the above visual result, we used agglomerative hierarchical clustering. As shown in figure 2B, the SNP dendrogram shows a substantial break at three as well as two clusters. Because the three clusters corresponded well to the three distinct topologies of the SNPs, we colored the SNP nodes in the bipartite network on the basis of the boundaries of the three clusters identified by the SNP dendrogram. A dendrogram of the subjects showed that the subject clusters perfectly match the two ancestries defined a priori. It is important to note that the dendrogram alone did not provide an explanation for the nature of the third less dominant SNP cluster (colored red). The nature of the third cluster was more apparent in the network based on its ring topology, and its genotype pattern with the other two dominant SNP clusters. The two methods therefore together provided an explanation for the overall topology of the bipartite network and its subparts, in addition to the quantitative verification of its boundaries.

To generate a network based on a parsimonious subset of the SNPs, and to examine the admixture based on the dominant SNP clusters (blue and pink), we removed the center SNP cluster (red nodes) from the network, and re-laid the network using the Kamada–Kawai algorithm. Figure 3A shows the result of this transformation on the network. As shown, the original Yoruba African and Utah American subjects continue to be strongly clustered around their respective SNPs. The network also revealed a subset of subjects between the two clusters that appeared to have an admixture of SNPs because the members of this subset have genotype 2 associations with some Utah American SNPs, and also with some Yoruba African SNPs.

The clusteredness of the subjects in the HapMap data was statistically significant when compared with 1000 random networks based on variance of the dissimilarities (HapMap =74822.5, random mean =1023.6, p<0.001, two-tailed test), skewness of the distribution of dissimilarities (HapMap =10.56, random mean =4.3, p<0.001, two-tailed test), and kurtosis of the distribution of dissimilarities (HapMap =114.01, random mean =24.28, p<0.001, two-tailed test).

To compute modularity, we generated unweighted bipartite networks representing the dominant and recessive genetic models as described in the methods section. For the recessive network shown in figure 3A, the modularity was above 0.3 (subjects =0.47, SNPs =0.49), indicating that the clustering of the subjects, and of the SNPs, was substantial compared to random chance.23 In both cases, the highest modularity was achieved with the same clusters identified by the hierarchical clustering. For the dominant network (not shown), the modularity was lower (subjects =0.25, SNPs =0.26), suggesting that in this dataset, the recessive model discriminates between the two ancestral populations more strongly compared to the dominant model.

To analyze the admixed subjects who are located in the center of the network, we used the betweenness centrality measure. Because genotype 2 appeared to be the main determinant of the clusters, we used the recessive model to conduct this analysis. As shown by the enclosed dotted line in figure 4A, the betweenness centrality measure correctly identified 12 Utah Americans and seven Yoruba Africans who have genotype 2 relationships with SNPs in both clusters.

The betweenness centrality also identified SNPs that have strong connections to the admixed subjects, and therefore are implicated in the admixture. However, owing to the density of black edges in the network, it was difficult to determine which SNPs from each cluster were connected to subjects from the opposite cluster. Furthermore, the admixed subjects were scattered across the heat map (rows containing dark cells representing genotype 2 in the upper right and lower left areas of figure 3B) because they do not form a cluster based on their membership to the same SNPs.

To address this limitation, we used the Circos representation for a closer inspection of this subset of subjects across all the SNPs. Figure 4B shows the Circos ideogram where the edges and SNP nodes can be highlighted on the basis of one or the other cluster of subjects to which they are connected. Therefore, as shown in figure 4B, we highlighted all edges that were connected to the Utah American nodes (white nodes), to explore which Yoruba African nodes were, and were not, connected to them. As shown, the representation revealed eight SNPs (colored white on the right hand side of the diagram) that accounted for the admixture of the Utah Americans, and the remaining 10 SNPs (colored black) were not involved in that admixture. Similarly, the Circos ideogram enabled the identification of SNPs that were involved in the admixture of the Yoruba Africans, and those that were not. The Circos ideogram therefore helped to closely examine the admixture on the basis of the inter-cluster relationship, which was neither directly possible in the network, nor in the heat map representations. In addition, the outer ring of the ideogram shows the sex of the subjects (red = male, green = female), revealing how their proportion varies across the admixed subjects in the two ancestral groups. The Circos ideogram therefore enabled the exploration of the three-way association between SNPs, subjects, and their attributes.

The bipartite network of 78 SNPs in figure 2A revealed (1) SNPs that were highly discriminatory of the two ancestries, (2) SNPs that were not discriminatory of the two ancestries, and (3) the relationship of the SNP and subject clusters. Because the weakly connected SNPs formed a ring-like structure around the Yoruba African SNP cluster, it suggested a weak but nonetheless relatively strong relationship with that cluster compared with the Utah American cluster. This pattern was difficult to discover from the heat map because of a fundamental difference in the two representations: two-dimensional network layouts have two degrees of freedom in laying out the nodes, and therefore can show multiple adjacency relationships; in contrast, dendrograms have only one degree of freedom because nodes can be located along either the x or y axis, restricting the number of adjacencies that can be represented simultaneously. These adjacencies have to be inferred by inspecting the color gradations in the heat map, which is perceptually more difficult to comprehend, compared with layouts that use distance to show similarity. However, although these relationships are difficult to discover from heat maps and dendrograms, we used them to confirm those patterns after the fact. In contrast, the network layout, although suggesting distinct SNP and subject clusters (whose significance was verified through comparison with random networks, and through modularity), cannot on its own discover the boundaries of the clusters, and therefore we used the dendrograms and modularity to discover those boundaries, which we then confirmed by overlaying them as similarly colored nodes in the network. The two representations therefore together enabled the discovery and confirmation of the relationship between the clusters.

In addition to the identification of the cluster boundaries, and the relationship between the clusters, the bipartite representations also revealed the nature of the cluster memberships. Unlike unipartite representations used by methods such as PCA, k-means, and unipartite networks, bipartite networks through weighted edges explicitly show the nature of the relationship between a subject and a SNP. This feature, along with the overall topology of the network, revealed insights such as what kind of relationship is responsible for the formation of the clusters. For example, the two dominant clusters in our dataset were mainly held together because of the genotype 2 relationships from their respective subject populations. This might not necessarily be the case in other datasets. For example, clusters could be held together with very few genotype 2 relationships, and be dominated instead with many genotype 1 relationships. One might argue that such information can be extracted directly from the raw data, but the power of the bipartite visual analytical representations is that they can suggest patterns that the researcher might not otherwise think about analyzing.

Similar to the inadequacy of any single representation to enable the comprehension of the clusters and their relationship to each other, networks and heat maps were also unable to provide a more complete view of the admixed population. While the network helped to identify the existence of the admixed population, the density of the edges did not allow a direct inspection of the nature of their admixture, and which SNPs in both clusters were responsible for that admixture. Furthermore, these admixed subjects were spread out in the heat map, as their discovery is based on a network-based relationship which is not the basis of the clustering algorithm. In contrast, the Circos representation enabled the selection of edges on the basis of the subject cluster to which they were connected, which helped to quickly identify which nodes were, or were not, implicated in the admixture. Therefore, although the Circos representation is not designed to identify clusters, it enabled the inspection of the admixture in a much more effective way compared with networks and heat maps.

The results have methodological and theoretical implications. From a methodological perspective, the bipartite representations intuitively show a researcher studying the data from a case–control study, not only which subjects have high admixture, but also the reason for that admixture based on the type and nature of SNP cluster membership. For example, if SNPs are the focus of the study, then the bipartite representation can reveal important information for making critical decisions to prevent confounding experimental results. Furthermore, when studying SNP data beyond AIMs, researchers can use the identity of the SNP membership to rapidly derive data-driven hypotheses for disease causation. For example, we used the Genetic Association Database31 to analyze the known association of the 18 Yoruba African SNPs and the 22 Utah American SNPs with diseases. We found that the Yoruba African SNPs were associated with hypertension, schizophrenia, prostate cancer, Parkinson's disease, and autoimmune inflammatory diseases. In contrast, the Utah American SNPs were associated with osteoporosis, schizophrenia, bipolar disorder, and multiple sclerosis. These associations demonstrate a differential prevalence of diseases in the two populations based on the SNPs with which they were associated. In case–control SNP data, such differential prevalence of SNP–disease associations provides a starting point for elucidating the associations between the disease under study, and with other diseases.

From a theoretical perspective, we have demonstrated that the network representation enabled us to rapidly explore the effect of different genetic models (eg, recessive, dominant) on the SNP and subject clustering, and how the emergent patterns were detected and quantitatively verified through network measures such as modularity and betweenness. We have also elucidated the limitations of networks, and how to overcome them through the use of multiple bipartite visual representations. The results show that each representation provides different affordances, and therefore plays the role of enabling discovery, confirmation, explanation, and inspection for different tasks. This understanding has inspired us to explore the development of a complementary visual analytical framework, which could explain and guide the use of multiple visual analytical representations for rapidly enabling discoveries in complex SNP data.

Although we have focused on separately identifying SNP and subject clusters to understand how they are related, biclustering methods are designed to identify clusters that allow membership of both types of node (eg, SNPs and subjects). Indeed, our use of biclustering32 put into separate clusters the Utah American and their SNPs, and the Yoruba subjects and their SNPs. However, this method does not appear to help identify subjects with high admixture, which motivated the use of betweenness centrality, as we have demonstrated.

There are three main limitations to our study. (1) Because it was designed as a proof-of-concept for the application of multiple visual analytical representations to comprehend the relationship between subjects and SNPs, we focused on the use of existing visual analytical methods that are well known in the bioinformatics community. However, there exist several other visual analytical representations, such as TreeMap33 and CateRank,34 which should be analyzed for their affordances, and for their complementary potential to bipartite networks. Furthermore, several researchers have proposed the use of advanced interactive methods for exploring bipartite networks,35 and for linking multiple representations,36 which should enable the rapid comprehension of such complex data. (2) SNP datasets typically are high dimensional, with a large number of SNPs—potentially in the millions—which require visualization methods that scale up computationally and perceptually. In our future research, we therefore plan to develop methods that exploit advanced computing resources, such as large memory resources and parallel computing capabilities, which should enable the analysis of such ‘big data’, in addition to interactive methods that help to rapidly filter out biomarkers that are not discriminatory for the phenotype of interest. (3) We have demonstrated the use of three bipartite visual analytical representations on only one SNP dataset, and the generality of our approach needs to be tested in additional datasets, particularly in ones where little is already known about the significant SNPs.