[Paper Review] LinkedNN: a neural model of linkage disequilibrium decay for recent effective population size inference

Smith, Chris C R|arXiv (Cornell University)|Feb 13, 2026

Bioinformatics and Genomic Networks0 citations

TL;DR

LinkedNN introduces a neural LD-decay layer that automatically learns LD-related features across genomic distances to infer recent effective population size, outperforming CNN and traditional summary-statistic methods on simulated data and showing applicability to sparse, unphased data.

ABSTRACT

Summary: A bioinformatics tool is presented for estimating recent effective population size by using a neural network to automatically compute linkage disequilibrium-related features as a function of genomic distance between polymorphisms. The new method outperforms existing deep learning and summary statistic-based approaches using relatively few sequenced individuals and variant sites, making it particularly valuable for molecular ecology applications with sparse, unphased data. Availability and implementation: The program is available as an easily installable Python package with documentation here: https://pypi.org/project/linkedNN/. The open source code is available from: https://github.com/the-smith-lab/LinkedNN.

Motivation & Objective

• Develop a neural architecture that directly learns LD decay features as a function of genomic distance.
• Improve accuracy of recent effective population size estimation from sparse, unphased SNP data.
• Compare LD-layer performance against CNN-based and summary-statistic regression approaches.
• Provide an implementable tool (LinkedNN) for population genetics inference across species.

Proposed method

• Introduce an LD layer that samples SNP pairs with log-uniform genomic distances to capture LD decay.
• Encode unphased genotypes as minor allele counts with shared, position-wise weights.
• Apply radial basis functions to distances to create a distance-aware feature vector.
• Compute distance-conditioned genotype features via learned per-pair distance coefficients that scale genotype features multiplicatively.
• Average transformed features across SNP pairs and pass through a regression head to estimate N_e.
• Evaluate against CNN-based models and summary-statistic regressors using simulated two-epoch demographic histories.

Figure 1 : (Left) Neural network diagram. The inputs are genotypes for all SNP pairs $x_{1},\dots,x_{P}$ and corresponding genomic distances $d_{1},\dots,d_{P}$ . The number of filters is $f=64$ and rectified linear unit (ReLU) activation is used on all trainable layers except the final layer. Radia

Experimental results

Research questions

• RQ1 Can a distance-aware LD layer outperform CNNs and traditional LD-based regression for estimating recent N_e from sparse, unphased SNP data?
• RQ2 How does automatically learned LD decay information compare to manually tuned LD-bin statistics in accuracy and robustness?
• RQ3 Is LinkedNN effective with small sample sizes (e.g., n=10) and moderate SNP sets (e.g., M~5,000) across demographic scenarios?
• RQ4 Does the LD layer provide interpretable distance cues that align with LD decay patterns observed in simulations and empirical data?

Key findings

• The LD layer achieved the best recent N_e estimation with mean relative absolute error (MRAE) of 0.380 on hold-out simulations, outperforming CNN and statistics-based methods.
• Among competitors, the pairwise-CNN had MRAE 0.422 and summary-statistic regression 0.429/0.456 (neural network/random forest).
• LD layer reduced MRAE by 25.6% relative to the basic CNN baseline for N_e estimation.
• The learned distance coefficients show structure and identify distance ranges (e.g., 5e5–5e6 bp) important for LD features, indicating the model captures meaningful LD decay signals.
• Empirical application to harbour porpoises yielded an estimated recent N_e of 1,411 (range 1,119–1,659) with a population-change time ~42 generations ago, demonstrating practical applicability with sparse data.
• The LD layer’s estimates differ from some SMC-based approaches, highlighting strengths in very recent demographic history inference.

Figure S1 : Blue lines are $f=64$ different coefficients output by the distance-mapping network at initialization—without training—for a range of distance inputs.