Deep Learning for Population Genetic Inference

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.

Widespread selection against deleterious mutations in theDrosophilagenome

“…Drosophila demographics is a potential compounding factor because not only derived fruit fly populations have been associated with severe bottlenecks, 47 but the ancestral range population in Sub-Saharan Africa is also predicted to have undergone a significant bottleneck. 32 These past events should reduce the magnitude of the effective population size in our framework; our predictions of θ (and using mutation rates per nucleotide from previous mutation-accumulation studies 42,43 ) yield N eff ≈ 10 6 , reasonably consistent with the population size estimates from Ref. 32 In summary, we have developed an ABC inference framework for simultaneous genome-wide prediction of selection strengths, mutation rates, and the fraction of viable alleles.…”

“…We conclude that the ABC inference procedure applied to D. melanogaster genomic data has sufficient internal consistency for at least qualitative conclusions regarding the magnitude of mutation and selection forces. This observation does not however preclude the possibility that our results are affected by the phenomena that are not explicitly included into the ABC model formulated above, such as recombination, [36][37][38][39][40][41] demographic effects, 32,47 and the assumption that any sequence in the 100-bp window can mutate into every other sequence. 21…”

“…If the steadystate assumption is correct, our inference should not be affected by past expansions and contractions in the population size, such as the significant bottleneck inferred for the Zambian D. melanogaster population that we use in this work. 32 Moreover, even if the population is still expanding after the bottleneck, our approach may still be applicable but will yield evolutionary parameters based on a reduced effective population size which is in turn affected by implicit bottleneck parameters.…”

Explosive genetic evidence for explosive human population growth

“…For example, deep learning has been utilized recently to jointly infer population size changes and selection in Drosophila [63] and can be similarly applied to data from human populations. Overall, with the combination of emerging novel methods and high-quality large-scale genetic sequencing, we expect a much more refined and accurate picture of population size history to be inferred in the near future for many more populations, and with the ability to focus on more and more recent history and to account for the X chromosome, admixture events, and joint-analysis of many populations.…”

Computational biology: deep learning

“…In genomics, they have been applied to predict the expression of all genes from a carefully selected subset of landmark genes [22], predict enhancers, [23] and to distinguish active enhancers and promoters from background sequences [24]. An early study also applied an architecture with three hidden layers and 60 neurons to estimate historical effective population size and selection for a genomic segment with reasonable results [25]. However, carefully chosen summary statistics were used as input, so there were limited gains from the traditional benefit of a network being able to figure out relevant features from raw data.…”