You will be presented with the abstract, introduction, and discussion section from a biomedical research article. Your task is to create a summary that a layperson can understand, capturing the essence of the research article. Keep essential scientific terms, but ensure that the language remains clear and the concepts are explained in an uncomplicated manner.

Title: Deep Learning for Population Genetic Inference}
Article:
Abstract:
Given genomic variation data from multiple individuals, computing the likelihood of complex population genetic models is often infeasible. To circumvent this problem, we introduce a novel likelihood-free inference framework by applying deep learning, a powerful modern technique in machine learning. Deep learning makes use of multilayer neural networks to learn a feature-based function from the input( e. g., hundreds of correlated summary statistics of data) to the output( e. g., population genetic parameters of interest). We demonstrate that deep learning can be effectively employed for population genetic inference and learning informative features of data. As a concrete application, we focus on the challenging problem of jointly inferring natural selection and demography( in the form of a population size change history). Our method is able to separate the global nature of demography from the local nature of selection, without sequential steps for these two factors. Studying demography and selection jointly is motivated by Drosophila, where pervasive selection confounds demographic analysis. We apply our method to 197 African Drosophila melanogaster genomes from Zambia to infer both their overall demography, and regions of their genome under selection. We find many regions of the genome that have experienced hard sweeps, and fewer under selection on standing variation( soft sweep) or balancing selection. Interestingly, we find that soft sweeps and balancing selection occur more frequently closer to the centromere of each chromosome. In addition, our demographic inference suggests that previously estimated bottlenecks for African Drosophila melanogaster are too extreme.
Introduction:
Several machine learning methods have been developed for selection only, often focusing on classifying the genome into neutral versus selected regions. Examples include methods based on support vector machines( SVMs)[7–9] or boosting[10–12]. Often these methods demonstrate robustness to different demographic scenarios, but do not explicitly infer demography. Many methods have been developed to infer ancestral population size changes, including PSMC[13], diCal[14, 15], and MSMC[16]. These methods make the underlying assumption that selection does not significantly bias the results. This is perhaps somewhat true for humans, but is not a valid assumption for many species such as Drosophila, for which selection seems ubiquitous throughout the genome. Few previous works have addressed both population size changes and selection. Galtier et al.[17] developed a likelihood-based method for distinguishing between a bottleneck and selection. They applied their method to Drosophila data to conclude that a series of selective sweeps was more likely than a bottleneck, but did not explicitly infer parameters for both selection and demography. In their method, Galtier et al. assumed that demographic events affect the entire genome, whereas selection is a local phenomenon. In contrast, Gossmann et al.[18] estimated the effective population size locally along the genome, and reported that it is correlated with the density of selected sites. To make our results as easily interpretable as evolutionary events as possible, we estimate global effective population size changes. Approximate Bayesian Computation( ABC)[19, 20] is a likelihood-free inference method based on simulating datasets and comparing their summary statistics.( A more detailed description of the framework is provided below.) This approach has been used to study various complex population genetic models( e. g.,[21–23]) for which likelihood computation is prohibitive. Partly due to several influential theoretical works[24–31], the popularity of ABC has grown rapidly over the past decade. ABC’s main advantages are that it is easy to use and is able to output a posterior distribution. There are a few challenges, however: 1) ABC suffers from the “curse of dimensionality, ” with decreasing accuracy and stability as the number of summary statistics grows[32]. 2) ABC typically uses a rejection algorithm, so the simulated datasets are not used optimally, and often a very large number are required. 3) It is difficult to interpret the output of ABC in terms of which statistics were the most informative for each parameter. 4) Although ABC can be used very effectively for continuous parameter inference, it would be difficult to use ABC for a complex scenario that involved joint inference of continuous parameters and categorical distributions. To our knowledge, ABC has thus not been previously applied to the problem of jointly inferring demography( using continuous effective population sizes) and selection( using discrete classification). The work of Bazin et al.[33] estimates demographic and selection parameters using a hierarchical ABC approach, though not in an explicit joint framework. We see our deep learning method as a complimentary approach to, rather than a direct replacement of, other likelihood-free inference methods such as ABC or SVM. Deep learning has several advantages such as making full use of datasets, elegantly handling correlations between summary statistics, and producing interpretable features of the data. It also produces an “inverse” function from the input summary statistics to the population genetic parameters of interest. However, in contrast to ABC, it does not provide a posterior distribution. Deep learning has its beginnings in neural networks, which were originally inspired by the way neurons are connected in the brain[34]. Neural networks have been studied for over 60 years and a huge body of literature exists on the topic. A neural network is typically used to learn a complex function between inputs( data) and outputs( response variables) in the absence of a model, so it can be thought of as a generalized regression framework. While standard regression and classification methods involve fitting linear combinations of fixed basis functions, a neural network tries to learn basis functions( usually non-linear) appropriate for the data. A neural network architecture consists of multiple layers of computational units( nodes), with connections between the layers but not between nodes within a layer. Within a layer, each node computes a transformation( usually non-linear) of the outputs from the previous layer. S1 Fig illustrates a simple feed-forward neural network with a single hidden layer. The phrase “deep learning” refers to algorithms for learning deep neural network architectures with many hidden layers. The universal approximation theorem[35, 36] states that any continuous function on compact subsets of R n can be uniformly approximated by a feed-forward neural network with a single hidden layer, provided that the number of nodes in the hidden layer is sufficiently large and the transformation( called the activation function) associated with each node satisfies some mild conditions. However, it can be challenging to learn the weights of such a network and to interpret the hidden layer. So as learning problems became more complex, it was desirable to train networks with more hidden layers. Since their introduction over 30 years ago, deep architectures have proved adept at modeling multiple levels of abstraction. However, they were notoriously difficult to train since their objective functions are non-convex and highly non-linear, and the level of non-linearity increases with the number of layers in the network. A major breakthrough was made in 2006 when Hinton and Salakhutdinov[37] showed that a deep feed-forward neural network can be trained effectively by first performing unsupervised “pretraining” one layer at a time, followed by supervised fine-tuning using a gradient-descent algorithm called back-propagation[38].( Simply put, pretraining provides a good initialization point for non-convex optimization.) They applied their learning algorithm to dimensionality reduction of images and achieved substantially better results than PCA-based methods. Following the work of Hinton and Salakhutdinov, deep learning has been applied to various challenging problems in computer science over the last several years, making groundbreaking progress. Deep learning broke long-standing records for accuracy that had been set by approaches based on hand-coded rules. Well-known examples include automatic speech recognition( transforming spoken words into typed text)[39, 40] and computer vision( automatically classifying images into different categories and tagging objects/individuals in photos)[41]. Many variations have been developed, including dropout, which attempts to learn better and more robust features of the data( see[42, 43]). Deep learning has also been applied to problems in neuroscience[44] and computational biology[45–48], but has not been used for population genetics before. We demonstrate here that deep learning can accommodate more complex models than existing techniques, and can provide a complimentary approach to existing likelihood-free inference in population genetics. For example, deep learning could be used to select optimal statistics for ABC( as demonstrated in[49]), or another method. Rejection-based methods have been used since the late 1990’s( see[19, 50]) to estimate population genetic parameters when the likelihood is difficult to compute. Early improvements to ABC quickly helped make it a popular method for a variety of scenarios( see[20] for a good introduction). ABC works by simulating many datasets under a prior for the parameters of interest. Then these datasets are reduced to a vector of summary statistics that are ideally informative for the parameters. The summary statistics that are closest to the summary statistics for the target dataset are retained, and the corresponding parameters used to estimate the desired posterior distributions. ABC has many advantages, including ease of use and the output of a posterior distribution. However, there are a few shortcomings, which various works have sought to address. In its simplest form, ABC does not naturally handle correlated or weakly informative summary statistics, which can add noise to the data. To tackle this problem, many methods for dimensionality reduction or wisely selecting summary statistics have been proposed( see[26, 29, 31, 51, 52], and[53] for a dimensionality reduction comparison). However, simple reductions cannot always learn subtle relationships between the data and the parameters. Expert pruning of statistics helps some methods, but given the lack of sufficient statistics, valuable information can be eliminated. Blum and François[28] suggested performing a dimensionality reduction step on the summary statistics via a neural network similar to S1 Fig. This reduction is similar in spirit to the work presented here, although there are many algorithmic and application differences. A second issue with ABC is the rejection step, which does not make optimal use of the datasets that are not retained. The more statistics and parameters used, the more datasets must be simulated and rejected to properly explore the space, making the interaction between these two issues problematic. To address the problem of rejecting datasets, different weighting approaches have been proposed( see[28] for a good example of how the estimation error changes as fewer datasets are rejected). The idea is to keep more datasets, but then weight each retained dataset by its distance to the target dataset. However, few approaches utilize all the datasets in this way, and the most popular implementation of ABC( ABCtoolbox,[54]) typically still rejects most of the simulated datasets by default. One final issue with ABC is the black-box nature of the output. Given the distances between the simulated datasets and the target dataset, and the posterior, there is no clear way to tell which statistics were the most informative.
Discussion:
In this paper, we have sought to demonstrate the potential of deep learning as a new inference framework for population genomic analysis. This investigation is still in its infancy, and there are many directions of future work. One important advantage of deep learning is that it provides a way to distinguish informative summary statistics from uninformative ones. Here we have presented two methods for extracting informative statistics given a trained deep network. Other methods are possible, and it is an open question which one would produce the most accurate results. It would be interesting to down-sample statistics using a variety of methods, then compare the results. Overall, learning more about how various summary statistics relate to parameters would be useful for population genetics going forward. The prospect of using deep learning to classify regions as neutral or selected is very appealing for subsequent demographic inference. There are other machine learning methods that perform such classification, but they are generally limited to two classes( selected or neutral). One exception is a study in humans[66], which classifies genomic regions as neutral or under positive, negative, or balancing selection. Although their approach does not jointly infer selection and demography, it would be interesting to see their method used on Drosophila. We infer many hard sweeps in African Drosophila, which is perhaps expected given their large effective population size. However, when restricting our analysis to selected regions with high confidence, the numbers of hard sweeps and soft sweeps are comparable. It would be interesting to analyze our results in the context of a simulation study by Schrider et al.[67], which found that regions classified as soft sweeps are often truly the “shoulders” of hard sweeps. This possibility is worth investigating, as the signatures of soft sweeps and soft shoulders are extremely similar. In our simulations, both hard and soft sweeps are relatively recent, which makes them easier to detect. It would be useful to incorporate datasets with a wider range of selection onset times, which could capture regions of the real data that are currently being classified as neutral. Right now we have 4 different selection classes which are all forms of positive selection. To incorporate background or purifying selection, a 5th class of( weakly) deleterious mutations could be added. One aspect of the simulations that warrants future study is the effect of the ratio of recombination to mutation rate, ρ/θ. From running PSMC on 20 haplotypes from Zambia, we inferred ρ/θ = 1, whereas other studies have found ρ/θ = 6. 8[59] and ρ/θ = 10[58] for a population from Zimbabwe. Both these works also show significant variation in this ratio across different Drosophila populations. Andolfatto and Przeworski[60] also find significant variation in this ratio across the genome. As noted by Haddrill et al.[59], recent bottlenecks can make this ratio appear lower than it actually is, which is possibly the case for our dataset. As shown in the Supporting Information, misspecification of this ratio can lead to poor selection classification results. In general, assuming a lower recombination rate than reality leads to conservative results, since sites are assumed to be less independent[58–60]. Our takeaway from this analysis is that ρ/θ should be accurately estimated using a more robust method than PSMC or incorporated as a model parameter, with datasets simulated under a variety of ratios. It would also be interesting to investigate variation in the recombination rate across the genome, which could be incorporated into future simulations. Deep learning can make efficient use of even a limited number of simulated datasets. In this vein, it would be interesting to use an approach such as ABC MCMC[24] to simulate data, and then use deep learning on these simulated datasets. Alternatively, deep learning could be used to select informative statistics for a subsequent method such as ABC[49]. Blum and François[28] used a single-layer neural network to perform( non-linear) regression to obtain a posterior mean, which they used to adjust the parameters of the posterior sample for a more accurate posterior distribution. It is unclear whether deep networks( where the theory is much more complicated) could be used in the same way, although there is the concept of a residual which could be used for parameter adjustment in an rejection-based framework. Such hybrid approaches could be a fruitful area of further exploration, potentially extending the generality and usefulness of ABC. We would also like to apply deep learning to a wider variety of scenarios in populations genetics. Population structure and splits would be examples, although these scenarios would most likely require very different sets of summary statistics. On the computer science side, deep learning has almost exclusively been used for classification, not continuous parameter inference. It would be interesting to see the type of continuous parameter inference presented here used in other fields and applications. Finally, machine learning methods have been criticized for their “black-box” nature. In some sense they throw away a lot of the coalescent modeling that we know to be realistic, although this is included somewhat in the expert summary statistics of the data. It would be advantageous to somehow combine the strengths of coalescent theory and the strengths of machine learning to create a robust method for population genetic inference.
Deep learning is an active area of research in machine learning which has been applied to various challenging problems in computer science over the past several years , breaking long-standing records of classification accuracy . Here , we apply deep learning to develop a novel likelihood-free inference framework to estimate population genetic parameters and learn informative features of DNA sequence data . As a concrete example , we focus on the challenging problem of jointly inferring natural selection and demographic history .