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Population Structure Analysis of an Inbred Population using Quantitative Shape Phenotyping from Stereo Retinal Photographs
Li Tang, Michael D Abramoff
TL;DR
Characterizing population variation matters for genetic-risk discovery. This study quantifies three-dimensional optic nerve head shape from stereo retinal photographs into hierarchical features, then examines relationships within and between groups to reflect population patterns.
Problem
Characterizing population variation is important for discovering genetic risk factors and genes associated with putative genotypes.
Source: §1 · p. 2Method
The study reconstructs three-dimensional ONH shape from retinal fundus photographs and quantifies it into hierarchical feature vectors.
Source: §4 · p. 16Results
The analysis examines within- and between-group relationships and reflects patterns of population structure.
Source: §4 · p. 16Takeaways & Limitations
The analysis may potentially lead to new genetic risk factors for glaucoma and other eye diseases.
Source: §4 · p. 16The unlabeled and labeled datasets may not be large enough to fully explore the expressive power of the deep neural network.
Source: §4 · p. 16
Abstract
from arXiv · showhide
The population structure of an inbred population of 781 people on Norfolk Island in the Pacific, 318 of which are descendants of the original Mutineers of the Bounty, is analyzed phenotypically using shape from stereo retinal fundus photographs. Three-dimensional optic nerve head (ONH) shape is reconstructed from stereo pairs by a multi-scale stereo matching algorithm. Using deep neural network, the shape of ONH, which is under genetic control, is decomposed into a set of hierarchical features through self-taught learning. Features captured at different levels are selected according to their discriminant power in identifying the two populations. The prediction accuracy is evaluated with stratified cross validation. Given the selected feature set, individuals are grouped into k hierarchical clusters and cluster membership fractions are determined for k=2,3,4,5,6,7. Population structure analysis on the basis of phenotypes through image analysis allows heritability and linkage analysis, including founder effects from English and Polynesian ancestors, potentially leading to new genetic risk factors for glaucoma and other ONH-related eye diseases.
1 Introduction
The study analyzes Norfolk Island population structure using image-derived optic nerve head (ONH) shape phenotypes from stereo retinal photographs. It uses hierarchical neural features and ancestry tracing to evaluate this approach.
1 Introduction
- Population structure can inform discovery of genetic risk factors because gene distributions are associated with population structure, and phenotypic variation can point to putative genotypes.The authors identify an inbred population as useful for testing expectations about admixture events and gene flow.Source: §1 · pp. 2, 4
- Image-based population structure analysis using complex, high-dimensional phenotypes such as retinal morphology had not been attempted, while ONH shape is heritable and difficult to quantify manually.ONH variation includes neuroretinal rim slope and retinal nerve fiber layer curvature.Source: §1 · p. 3
- Although OCT is the method of choice for ONH topography, it is not available in most clinics and may not provide easily collected longitudinal datasets over years or decades.Stereo retinal photography is described as low-cost and accessible, but its interpretation has primarily been subjective, qualitative, and imprecise.Source: §1 · p. 3
- A multi-scale stereo correspondence approach estimates ONH shape from optic disc photographs, and a deep neural network condenses the resulting maps into hierarchical features.The shape maps are disparity or topographic maps of the three-dimensional ONH structure.Source: §1 · p. 4
- The study quantified ONH morphology and population structure in Norfolk Island residents, validating the approach against whether individuals traced ancestry to the Bounty mutineers.The population was described as highly inbred, with ancestry also linked to the Tahitian wives who accompanied the mutineers.Source: §1 · p. 4
2 Subjects and Methods
This section describes the validation and methods for representing optic nerve head shape, along with the historical and sample context of the Norfolk Island study. It examines whether phenotypic shape reflects admixture in the population by using clustering to assess its structure.
2.1 Related Work
- Stereo-image ONH shape estimates reproduced SD-OCT topography, with normalized structures differing by RMS 15.9 ± 8.8% of cup depth; approximately 80% of ONH-shape-parameter variability was genetically determined.Source: §2.1 · pp. 4–5
2.2 Learning ONH Shape in Hierarchical Feature Space
- For statistical shape analysis, disparity maps are decomposed, and a stacked autoencoder forms feature vectors characterizing distinct ONH shape and overall variability, enabling quantitative analysis of shape topography.Each vector is rescaled to [0, 1], and left-eye maps are flipped to match the ONH shape of a right eye.Source: §2.2 · pp. 5, 8
- The stacked autoencoder is pretrained layer by layer, unrolled into symmetric encoder and decoder stacks, and fine-tuned to minimize reconstruction error.Its training objective includes reconstruction error, weight-decay regularization, and a sparsity penalty.Source: §2.2 · pp. 6–7
2.3 Hierarchical Clustering of the Phenotypic ONH Shape
- In 2008, 781 Norfolk Island subjects, including 343 direct descendants of the Bounty mutineers, underwent retinal imaging, DNA genotyping, and other biometric assessments.The population’s historical origins trace to the mutineers and Tahitian women who settled on Pitcairn Island before inhabitants relocated to Norfolk Island in 1856.Source: §2.3 · pp. 8–9
- The study treats the diverse-ancestry population as a natural experiment for admixture and tests whether ONH shape reflects that process.It frames the population as useful for investigating complex phenotypes.Source: §2.3 · p. 9
- ONH shape features are partitioned by k-means for k=2 to 6, assigning each shape to the nearest cluster mean while minimizing within-cluster squared distance using cosine distance.Source: §2.3 · p. 9
- Grouping the clusters across levels produces a dendrogram that displays multilevel structure and helps identify the clustering level that distinguishes structures.Source: §2.3 · p. 9
3 Results
SAE-derived ONH features captured hierarchical shape variation and modestly outperformed PCA in predicting population labels. Clustering indicated shared ONH-shape structure across the two populations, with roughly five clusters.
3.1 Data Collection
- Among 781 subjects, 722 were analyzed using 1,444 stereo retinal photograph pairs of both eyes; 318 (44%) had mutineer descent, and the remaining 404 did not.The passages also describe 4,387 pairs of stereo fundus photographs for self-taught learning of general ONH-shape variability and SAE training.Source: §3.1 · pp. 9–10
3.3 ONH Shape Features Learned by SAE
- SAE reconstructions retained major anatomical ONH-shape variations while removing high-frequency noise, and its learned features progressed from localized cupping patterns to more global structure.The first autoencoder captured localized variability, while the second captured more global, higher-level structure.Source: §3.3 · pp. 11–12
- All 15 selected SAE features came from the first two autoencoders; third-layer features represented general ONH shape but were not discriminative enough for subtle population differences.Most selected PCA features corresponded to small eigenvalues and lacked obvious visual interpretations related to underlying structure.Source: §3.3 · pp. 13–14
- With 15 selected features and ten-fold cross-validation, SAE mean AUC was 0.59 (95% CI: [0.545, 0.630]) versus PCA 0.53 (95% CI: [0.498, 0.565]); K-nearest neighbor accuracy averaged 58.4%.Source: §3.3 · p. 13, Figure 10 · p. 14
3.4 Hierarchical Clustering of Population
- The two populations shared ONH-shape structures consisting of roughly five clusters; greater-than-expected within-group variation may reflect gene flow, while lower variation may reflect genetic isolation.Cluster membership fractions were estimated for k=2–7.Source: §3.4 · p. 15, Figure 13 · p. 15
4 Discussion
The discussion presents image-derived ONH shape analysis as a way to examine population structure and morphological variation, while noting limits from admixture complexity and sample size. The approach may support larger-scale genetic and phenotype studies and population-structure analysis from other stereo images.
4 Discussion
- The analysis examines relationships within and between groups and reflects population structure and morphological variation, while admixture may produce shape changes not explained solely by gene flow.The discussion describes these admixture-related deviations as potentially arising from complicated, integrated shape changes.Source: §4 · p. 16
- A twin study found ONH shape to be largely under genetic control, offering a reference for considering how isolated-population trait composition may differ from general twin samples.The discussion links this genetic control to the relevance of the phenotype for population analysis.Source: §4 · p. 16
- The approach is limited by potentially insufficient unlabeled and labeled datasets to fully explore the deep neural network, and the authors expect better results with more data.The discussion notes that larger datasets are desirable for discovering relationships and linkable information, as in GWAS.Source: §4 · p. 16
- The approach combines automatic three-dimensional ONH shape estimation from low-cost fundus photographs with image-based phenotype identification and quantitative analysis of retinal morphology.This made a more complete study on a large dataset possible.Source: §4 · p. 17
- A next step is to analyze the full pedigree and admixture effects, but identifying family-specific groups would require a larger sample than this preliminary study.The discussion also notes that comparisons of Pitcairn and Norfolk Island population structure indicate admixture influences trait genetic architecture, which may aid ONH-related disease gene discovery.Source: §4 · p. 17
- The discussion concludes that stereo images may enable automated discovery of population structure in inbred populations and potentially in other image types, including faces.It also frames the approach as a means of discovering complex gene-expression variation from stereo images.Source: §4 · p. 17