Natural selection leaves a spatial pattern along the genome, with a distortion in the haplotype distribution near the selected locus that becomes less prominent with increasing distance from the locus. Evaluating the spatial signal of a population-genetic summary statistic across the genome allows for patterns of natural selection to be distinguished from neutrality. Different summary statistics highlight diverse components of genetic variation and, therefore, considering the genomic spatial distribution of multiple summary statistics is expected to aid in uncovering subtle signatures of selection. In recent years, numerous methods have been devised that jointly consider genomic spatial distributions across summary statistics, utilizing both classical machine learning and contemporary deep learning architectures. However, better predictions may be attainable by improving the way in which features used as input to machine learning algorithms are extracted from these summary statistics. To achieve this goal, we apply three time-frequency analysis approaches (wavelet transform, multitaper spectral analysis, and S-transform) to summary statistic arrays. Each analysis method converts a one-dimensional summary statistic arrays to a two-dimensional image of spectral density or visual representation of time-frequency analysis, permitting the simultaneous assessment of temporal and spectral information. We use these images as input to convolutional neural networks and consider combining models across different time-frequency representation approaches through the ensemble stacking technique. Application of our modeling framework to data simulated from neutral and selective sweep scenarios reveals that it achieves almost perfect accuracy and power across a diverse set of evolutionary settings, including population size changes and test sets for which sweep strength, softness, and timing parameters were drawn from a wide range. Moreover, a scan of whole-genome sequencing of central European humans recapitulated previous well-established sweep candidates, as well as predicts novel cancer associated genes as sweeps with high support. Given that this modeling framework is also robust to missing data, we believe that it will represent a welcome addition to the population-genomic toolkit for learning about adaptive processes from genomic data.

Natural selection leaves a spatial pattern along the genome, with a haplotype distribution distortion near the selected locus that fades with distance. Evaluating the spatial signal of a population-genetic summary statistic across the genome allows for patterns of natural selection to be distinguished from neutrality. Considering the genomic spatial distribution of multiple summary statistics is expected to aid in uncovering subtle signatures of selection. In recent years, numerous methods have been devised that consider genomic spatial distributions across summary statistics, utilizing both classical machine learning and deep learning architectures. However, better predictions may be attainable by improving the way in which features are extracted from these summary statistics. We apply wavelet transform, multitaper spectral analysis, and S-transform to summary statistic arrays to achieve this goal. Each analysis method converts one-dimensional summary statistic arrays to two-dimensional images of spectral analysis, allowing simultaneous temporal and spectral assessment. We feed these images into convolutional neural networks and consider combining models using ensemble stacking. Our modeling framework achieves high accuracy and power across a diverse set of evolutionary settings, including population size changes and test sets of varying sweep strength, softness, and timing. A scan of central European whole-genome sequences recapitulated well-established sweep candidates and predicted novel cancer-associated genes as sweeps with high support. Given that this modeling framework is also robust to missing genomic segments, we believe that it will represent a welcome addition to the population-genomic toolkit for learning about adaptive processes from genomic data.

Inferences of adaptive events are important for learning about traits, such as human digestion of lactose after infancy, the ability of organisms to survive at extreme environments, and the rapid spread of viral variants. Early efforts toward identifying footprints of natural selection from genomic data involved development of summary statistic and likelihood methods. However, such techniques are typically grounded in simple theoretical models that may limit the complexity of settings that they can explore, running the risk of inaccurate predictions as the summary statistics are hand engineered. Due to the renaissance in artificial intelligence, machine and deep learning methods have taken center stage in recent efforts to detect natural selection, with strategies such as convolutional neural networks applied to images of haplotypes across sampled individuals to simultaneously extract important genomic features and achieve high classification accuracy and power for distinguishing selection from neutrality. Yet, limitations of such techniques include difficulty in estimating the number of model parameters and identification of features without regard to their location within an image. As a complementary approach, we consider an alternative feature extraction method, termed tensor decomposition, which falls within a class of dimensionality reduction techniques to extract features from multidimensional data while preserving the latent structure of the data. We present a novel approach titledT-REx, in which we apply tensor decomposition to images of haplotypes across sampled individuals, and then use these extracted features as input to classical linear and nonlinear machine learning methods. As a proof of concept, we explore the performance ofT-RExon simulated neutral and selective sweep scenarios, and find that it has high power and accuracy to discriminate sweeps from neutrality, robustness to missing data, and easy visualization of underlying low-dimensional features uncovered by tensor decomposition. Therefore,T-RExis a powerful addition to the toolkit for detecting adaptive processes from genomic data.