Estimation of spatial demographic maps from polymorphism data using a neural network.

A fundamental goal in population genetics is to understand how variation is arrayed over natural landscapes. From first principles we know that common features such as heterogeneous population densities and source sink dynamics of dispersal should shape genetic variation over space, however there are few tools currently available that can deal with these ubiquitous complexities. Geographically referenced single nucleotide polymorphism (SNP) data are increasingly accessible, presenting an opportunity to study genetic variation across geographic space in myriad species. We present a new inference method that uses geo-referenced SNPs and a deep neural network to estimate spatially heterogeneous maps of population density and dispersal rate. Our neural network trains on simulated input and output pairings, where the input consists of genotypes and sampling locations generated from a continuous space population genetic simulator, and the output is a map of the true demographic parameters. We benchmark our tool against existing methods and discuss qualitative differences between the different approaches; in particular, our program is unique because it infers the magnitude of both dispersal and density as well as their variation over the landscape, and it does so using SNP data. Similar methods are constrained to estimating relative migration rates, or require identity by descent blocks as input. We applied our tool to empirical data from North American grey wolves, for which it estimated mostly reasonable demographic parameters, but was affected by incomplete spatial sampling. Genetic based methods like ours complement other, direct methods for estimating past and present demography, and we believe will serve as valuable tools for applications in conservation, ecology, and evolutionary biology. An open source software package implementing our method is available from https://github.com/kr-colab/mapNN.

Large effects and the infinitesimal model.

The infinitesimal model of quantitative genetics relies on the Central Limit Theorem to stipulate that under additive models of quantitative traits determined by many loci having similar effect size, the difference between an offspring's genetic trait component and the average of their two parents' genetic trait components is Normally distributed and independent of the parents' values. Here, we investigate how the assumption of similar effect sizes affects the model: if, alternatively, the tail of the effect size distribution is polynomial with exponent α<2, then a different Central Limit Theorem implies that sums of effects should be well-approximated by a "stable distribution", for which single large effects are often still important. Empirically, we first find tail exponents between 1 and 2 in effect sizes estimated by genome-wide association studies of many human disease-related traits. We then show that the independence of offspring trait deviations from parental averages in many cases implies the Gaussian aspect of the infinitesimal model, suggesting that non-Gaussian models of trait evolution must explicitly track the underlying genetics, at least for loci of large effect. We also characterize possible limiting trait distributions of the infinitesimal model with infinitely divisible noise distributions, and compare our results to simulations.

Shared evolutionary processes shape landscapes of genomic variation in the great apes.

For at least the past 5 decades, population genetics, as a field, has worked to describe the precise balance of forces that shape patterns of variation in genomes. The problem is challenging because modeling the interactions between evolutionary processes is difficult, and different processes can impact genetic variation in similar ways. In this paper, we describe how diversity and divergence between closely related species change with time, using correlations between landscapes of genetic variation as a tool to understand the interplay between evolutionary processes. We find strong correlations between landscapes of diversity and divergence in a well-sampled set of great ape genomes, and explore how various processes such as incomplete lineage sorting, mutation rate variation, GC-biased gene conversion and selection contribute to these correlations. Through highly realistic, chromosome-scale, forward-in-time simulations, we show that the landscapes of diversity and divergence in the great apes are too well correlated to be explained via strictly neutral processes alone. Our best fitting simulation includes both deleterious and beneficial mutations in functional portions of the genome, in which 9% of fixations within those regions is driven by positive selection. This study provides a framework for modeling genetic variation in closely related species, an approach which can shed light on the complex balance of forces that have shaped genetic variation.

Evaluating evidence for co-geography in the Anopheles-Plasmodium host-parasite system.

The often tight association between parasites and their hosts means that under certain scenarios, the evolutionary histories of the two species can become closely coupled both through time and across space. Using spatial genetic inference, we identify a potential signal of common dispersal patterns in the Anopheles gambiae and Plasmodium falciparum host-parasite system as seen through a between-species correlation of the differences between geographic sampling location and geographic location predicted from the genome. This correlation may be due to coupled dispersal dynamics between host and parasite but may also reflect statistical artifacts due to uneven spatial distribution of sampling locations. Using continuous-space population genetics simulations, we investigate the degree to which uneven distribution of sampling locations leads to bias in prediction of spatial location from genetic data and implement methods to counter this effect. We demonstrate that while algorithmic bias presents a problem in inference from spatio-genetic data, the correlation structure between A. gambiae and P. falciparum predictions cannot be attributed to spatial bias alone and is thus likely a genetic signal of co-dispersal in a host-parasite system.

Genetic architecture, spatial heterogeneity, and the coevolutionary arms race between newts and snakes.

Coevolution between two species can lead to exaggerated phenotypes that vary in a correlated manner across space. However, the conditions under which we expect such spatially varying coevolutionary patterns in polygenic traits are not well-understood. We investigate the coevolutionary dynamics between two species undergoing reciprocal adaptation across space and time, using simulations inspired by the Taricha newt - Thamnophis garter snake system. One striking observation from this system is that newts in some areas carry much more tetrodotoxin than in other areas, and garter snakes that live near more toxic newts tend to be more resistant to this toxin, a correlation seen across several broad geographic areas. Furthermore, snakes seem to be "winning" the coevolutionary arms race, i.e., having a high level of resistance compared to local newt toxicity, despite substantial variation in both toxicity and resistance across the range. We explore how possible genetic architectures of the toxin and resistance traits would affect the coevolutionary dynamics by manipulating both mutation rate and effect size of mutations across many simulations. We find that coevolutionary dynamics alone were not sufficient in our simulations to produce the striking mosaic of levels of toxicity and resistance observed in nature, but simulations with ecological heterogeneity (in trait costliness or interaction rate) did produce such patterns. We also find that in simulations, newts tend to "win" across most combinations of genetic architectures, although the species with higher mutational genetic variance tends to have an advantage.

Evaluating evidence for co-geography in the Anopheles-Plasmodium host-parasite system.

The often tight association between parasites and their hosts means that under certain scenarios, the evolutionary histories of the two species can become closely coupled both through time and across space. Using spatial genetic inference, we identify a potential signal of common dispersal patterns in the Anopheles gambiae and Plasmodium falciparum host-parasite system as seen through a between-species correlation of the differences between geographic sampling location and geographic location predicted from the genome. This correlation may be due to coupled dispersal dynamics between host and parasite, but may also reflect statistical artifacts due to uneven spatial distribution of sampling locations. Using continuous-space population genetics simulations, we investigate the degree to which uneven distribution of sampling locations leads to bias in prediction of spatial location from genetic data and implement methods to counter this effect. We demonstrate that while algorithmic bias presents a problem in inference from spatio-genetic data, the correlation structure between A. gambiae and P. falciparum predictions cannot be attributed to spatial bias alone, and is thus likely a genetic signal of co-dispersal in a host-parasite system.

Expanding the stdpopsim species catalog, and lessons learned for realistic genome simulations.

Simulation is a key tool in population genetics for both methods development and empirical research, but producing simulations that recapitulate the main features of genomic datasets remains a major obstacle. Today, more realistic simulations are possible thanks to large increases in the quantity and quality of available genetic data, and the sophistication of inference and simulation software. However, implementing these simulations still requires substantial time and specialized knowledge. These challenges are especially pronounced for simulating genomes for species that are not well-studied, since it is not always clear what information is required to produce simulations with a level of realism sufficient to confidently answer a given question. The community-developed framework stdpopsim seeks to lower this barrier by facilitating the simulation of complex population genetic models using up-to-date information. The initial version of stdpopsim focused on establishing this framework using six well-characterized model species (Adrion et al., 2020). Here, we report on major improvements made in the new release of stdpopsim (version 0.2), which includes a significant expansion of the species catalog and substantial additions to simulation capabilities. Features added to improve the realism of the simulated genomes include non-crossover recombination and provision of species-specific genomic annotations. Through community-driven efforts, we expanded the number of species in the catalog more than threefold and broadened coverage across the tree of life. During the process of expanding the catalog, we have identified common sticking points and developed the best practices for setting up genome-scale simulations. We describe the input data required for generating a realistic simulation, suggest good practices for obtaining the relevant information from the literature, and discuss common pitfalls and major considerations. These improvements to stdpopsim aim to further promote the use of realistic whole-genome population genetic simulations, especially in non-model organisms, making them available, transparent, and accessible to everyone.

Looking forwards and backwards: dynamics and genealogies of locally regulated populations.

We introduce a broad class of mechanistic spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial position and local population density, defined at a location to be the convolution of the point measure with a suitable non-negative integrable kernel centred on that location. We pass to three different scaling limits: an interacting superprocess, a nonlocal partial differential equation (PDE), and a classical PDE. The classical PDE is obtained both by a two-step convergence argument, in which we first scale time and population size and pass to the nonlocal PDE, and then scale the kernel that determines local population density; and in the important special case in which the limit is a reaction-diffusion equation, directly by simultaneously scaling the kernel width, timescale and population size in our individual based model. A novelty of our model is that we explicitly model a juvenile phase. The number of juveniles produced by an individual depends on local population density at the location of the parent; these juvenile offspring are thrown off in a (possibly heterogeneous, anisotropic) Gaussian distribution around the location of the parent; they then reach (instant) maturity with a probability that can depend on the local population density at the location at which they land. Although we only record mature individuals, a trace of this two-step description remains in our population models, resulting in novel limits in which the spatial dynamics are governed by a nonlinear diffusion. Using a lookdown representation, we are able to retain information about genealogies relating individuals in our population and, in the case of deterministic limiting models, we use this to deduce the backwards in time motion of the ancestral lineage of an individual sampled from the population. We observe that knowing the history of the population density is not enough to determine the motion of ancestral lineages in our model. We also investigate (and contrast) the behaviour of lineages for three different deterministic models of a population expanding its range as a travelling wave: the Fisher-KPP equation, the Allen-Cahn equation, and a porous medium equation with logistic growth.

Dispersal inference from population genetic variation using a convolutional neural network.

The geographic nature of biological dispersal shapes patterns of genetic variation over landscapes, making it possible to infer properties of dispersal from genetic variation data. Here, we present an inference tool that uses geographically distributed genotype data in combination with a convolutional neural network to estimate a critical population parameter: the mean per-generation dispersal distance. Using extensive simulation, we show that our deep learning approach is competitive with or outperforms state-of-the-art methods, particularly at small sample sizes. In addition, we evaluate varying nuisance parameters during training-including population density, demographic history, habitat size, and sampling area-and show that this strategy is effective for estimating dispersal distance when other model parameters are unknown. Whereas competing methods depend on information about local population density or accurate inference of identity-by-descent tracts, our method uses only single-nucleotide-polymorphism data and the spatial scale of sampling as input. Strikingly, and unlike other methods, our method does not use the geographic coordinates of the genotyped individuals. These features make our method, which we call "disperseNN," a potentially valuable new tool for estimating dispersal distance in nonmodel systems with whole genome data or reduced representation data. We apply disperseNN to 12 different species with publicly available data, yielding reasonable estimates for most species. Importantly, our method estimated consistently larger dispersal distances than mark-recapture calculations in the same species, which may be due to the limited geographic sampling area covered by some mark-recapture studies. Thus genetic tools like ours complement direct methods for improving our understanding of dispersal.

Shared evolutionary processes shape landscapes of genomic variation in the great apes.

For at least the past five decades population genetics, as a field, has worked to describe the precise balance of forces that shape patterns of variation in genomes. The problem is challenging because modelling the interactions between evolutionary processes is difficult, and different processes can impact genetic variation in similar ways. In this paper, we describe how diversity and divergence between closely related species change with time, using correlations between landscapes of genetic variation as a tool to understand the interplay between evolutionary processes. We find strong correlations between landscapes of diversity and divergence in a well sampled set of great ape genomes, and explore how various processes such as incomplete lineage sorting, mutation rate variation, GC-biased gene conversion and selection contribute to these correlations. Through highly realistic, chromosome-scale, forward-in-time simulations we show that the landscapes of diversity and divergence in the great apes are too well correlated to be explained via strictly neutral processes alone. Our best fitting simulation includes both deleterious and beneficial mutations in functional portions of the genome, in which 9% of fixations within those regions is driven by positive selection. This study provides a framework for modelling genetic variation in closely related species, an approach which can shed light on the complex balance of forces that have shaped genetic variation.

Enabling Inference for Context-Dependent Models of Mutation by Bounding the Propagation of Dependency.

Although the rates at which positions in the genome mutate are known to depend not only on the nucleotide to be mutated, but also on neighboring nucleotides, it remains challenging to do phylogenetic inference using models of context-dependent mutation. In these models, the effects of one mutation may in principle propagate to faraway locations, making it difficult to compute exact likelihoods. This article shows how to use bounds on the propagation of dependency to compute likelihoods of mutation of a given segment of genome by marginalizing over sufficiently long flanking sequence. This can be used for maximum likelihood or Bayesian inference. Protocols examining residuals and iterative model refinement are also discussed. Tools for efficiently working with these models are provided in an R package, which could be used in other applications. The method is used to examine context dependence of mutations since the common ancestor of humans and chimpanzee.

System drift and speciation.

Even if a species' phenotype does not change over evolutionary time, the underlying mechanism may change, as distinct molecular pathways can realize identical phenotypes. Here we use linear system theory to explore the consequences of this idea, describing how a gene network underlying a conserved phenotype evolves, as the genetic drift of small changes to these molecular pathways causes a population to explore the set of mechanisms with identical phenotypes. To do this, we model an organism's internal state as a linear system of differential equations for which the environment provides input and the phenotype is the output, in which context there exists an exact characterization of the set of all mechanisms that give the same input-output relationship. This characterization implies that selectively neutral directions in genotype space should be common and that the evolutionary exploration of these distinct but equivalent mechanisms can lead to the reproductive incompatibility of independently evolving populations. This evolutionary exploration, or system drift, is expected to proceed at a rate proportional to the amount of intrapopulation genetic variation divided by the effective population size ( Ne$N_e$ ). At biologically reasonable parameter values this could lead to substantial interpopulation incompatibility, and thus speciation, on a time scale of Ne$N_e$ generations. This model also naturally predicts Haldane's rule, thus providing a concrete explanation of why heterogametic hybrids tend to be disrupted more often than homogametes during the early stages of speciation.

Efficient ancestry and mutation simulation with msprime 1.0.

Stochastic simulation is a key tool in population genetics, since the models involved are often analytically intractable and simulation is usually the only way of obtaining ground-truth data to evaluate inferences. Because of this, a large number of specialized simulation programs have been developed, each filling a particular niche, but with largely overlapping functionality and a substantial duplication of effort. Here, we introduce msprime version 1.0, which efficiently implements ancestry and mutation simulations based on the succinct tree sequence data structure and the tskit library. We summarize msprime's many features, and show that its performance is excellent, often many times faster and more memory efficient than specialized alternatives. These high-performance features have been thoroughly tested and validated, and built using a collaborative, open source development model, which reduces duplication of effort and promotes software quality via community engagement.

Evaluating human autosomal loci for sexually antagonistic viability selection in two large biobanks.

Sex and sexual differentiation are pervasive across the tree of life. Because females and males often have substantially different functional requirements, we expect selection to differ between the sexes. Recent studies in diverse species, including humans, suggest that sexually antagonistic viability selection creates allele frequency differences between the sexes at many different loci. However, theory and population-level simulations indicate that sex-specific differences in viability would need to be very large to produce and maintain reported levels of between-sex allelic differentiation. We address this contradiction between theoretical predictions and empirical observations by evaluating evidence for sexually antagonistic viability selection on autosomal loci in humans using the largest cohort to date (UK Biobank, n = 487,999) along with a second large, independent cohort (BioVU, n = 93,864). We performed association tests between genetically ascertained sex and autosomal loci. Although we found dozens of genome-wide significant associations, none replicated across cohorts. Moreover, closer inspection revealed that all associations are likely due to cross-hybridization with sex chromosome regions during genotyping. We report loci with potential for mis-hybridization found on commonly used genotyping platforms that should be carefully considered in future genetic studies of sex-specific differences. Despite being well powered to detect allele frequency differences of up to 0.8% between the sexes, we do not detect clear evidence for this signature of sexually antagonistic viability selection on autosomal variation. These findings suggest a lack of strong ongoing sexually antagonistic viability selection acting on single locus autosomal variation in humans.

Predicting geographic location from genetic variation with deep neural networks.

Most organisms are more closely related to nearby than distant members of their species, creating spatial autocorrelations in genetic data. This allows us to predict the location of origin of a genetic sample by comparing it to a set of samples of known geographic origin. Here, we describe a deep learning method, which we call Locator, to accomplish this task faster and more accurately than existing approaches. In simulations, Locator infers sample location to within 4.1 generations of dispersal and runs at least an order of magnitude faster than a recent model-based approach. We leverage Locator's computational efficiency to predict locations separately in windows across the genome, which allows us to both quantify uncertainty and describe the mosaic ancestry and patterns of geographic mixing that characterize many populations. Applied to whole-genome sequence data from Plasmodium parasites, Anopheles mosquitoes, and global human populations, this approach yields median test errors of 16.9km, 5.7km, and 85km, respectively.

A community-maintained standard library of population genetic models.

The explosion in population genomic data demands ever more complex modes of analysis, and increasingly, these analyses depend on sophisticated simulations. Recent advances in population genetic simulation have made it possible to simulate large and complex models, but specifying such models for a particular simulation engine remains a difficult and error-prone task. Computational genetics researchers currently re-implement simulation models independently, leading to inconsistency and duplication of effort. This situation presents a major barrier to empirical researchers seeking to use simulations for power analyses of upcoming studies or sanity checks on existing genomic data. Population genetics, as a field, also lacks standard benchmarks by which new tools for inference might be measured. Here, we describe a new resource, stdpopsim, that attempts to rectify this situation. Stdpopsim is a community-driven open source project, which provides easy access to a growing catalog of published simulation models from a range of organisms and supports multiple simulation engine backends. This resource is available as a well-documented python library with a simple command-line interface. We share some examples demonstrating how stdpopsim can be used to systematically compare demographic inference methods, and we encourage a broader community of developers to contribute to this growing resource.

Space is the Place: Effects of Continuous Spatial Structure on Analysis of Population Genetic Data.

Real geography is continuous, but standard models in population genetics are based on discrete, well-mixed populations. As a result, many methods of analyzing genetic data assume that samples are a random draw from a well-mixed population, but are applied to clustered samples from populations that are structured clinally over space. Here, we use simulations of populations living in continuous geography to study the impacts of dispersal and sampling strategy on population genetic summary statistics, demographic inference, and genome-wide association studies (GWAS). We find that most common summary statistics have distributions that differ substantially from those seen in well-mixed populations, especially when Wright's neighborhood size is < 100 and sampling is spatially clustered. "Stepping-stone" models reproduce some of these effects, but discretizing the landscape introduces artifacts that in some cases are exacerbated at higher resolutions. The combination of low dispersal and clustered sampling causes demographic inference from the site frequency spectrum to infer more turbulent demographic histories, but averaged results across multiple simulations revealed surprisingly little systematic bias. We also show that the combination of spatially autocorrelated environments and limited dispersal causes GWAS to identify spurious signals of genetic association with purely environmentally determined phenotypes, and that this bias is only partially corrected by regressing out principal components of ancestry. Last, we discuss the relevance of our simulation results for inference from genetic variation in real organisms.

Limits to Genomic Divergence Under Sexually Antagonistic Selection.

Since the autosomal genome is shared between the sexes, sex-specific fitness optima present an evolutionary challenge. While sexually antagonistic selection might favor different alleles within females and males, segregation randomly reassorts alleles at autosomal loci between sexes each generation. This process of homogenization during transmission thus prevents between-sex allelic divergence generated by sexually antagonistic selection from accumulating across multiple generations. However, recent empirical studies have reported high male-female FST statistics. Here, we use a population genetic model to evaluate whether these observations could plausibly be produced by sexually antagonistic selection. To do this, we use both a single-locus model with nonrandom mate choice, and individual-based simulations to study the relationship between strength of selection, degree of between-sex divergence, and the associated genetic load. We show that selection must be exceptionally strong to create measurable divergence between the sexes and that the decrease in population fitness due to this process is correspondingly high. Individual-based simulations with selection genome-wide recapitulate these patterns and indicate that small sample sizes and sampling variance can easily generate substantial male-female divergence. We therefore conclude that caution should be taken when interpreting autosomal allelic differentiation between the sexes.

Widespread selection and gene flow shape the genomic landscape during a radiation of monkeyflowers.

Speciation genomic studies aim to interpret patterns of genome-wide variation in light of the processes that give rise to new species. However, interpreting the genomic "landscape" of speciation is difficult, because many evolutionary processes can impact levels of variation. Facilitated by the first chromosome-level assembly for the group, we use whole-genome sequencing and simulations to shed light on the processes that have shaped the genomic landscape during a radiation of monkeyflowers. After inferring the phylogenetic relationships among the 9 taxa in this radiation, we show that highly similar diversity (π) and differentiation (FST) landscapes have emerged across the group. Variation in these landscapes was strongly predicted by the local density of functional elements and the recombination rate, suggesting that the landscapes have been shaped by widespread natural selection. Using the varying divergence times between pairs of taxa, we show that the correlations between FST and genome features arose almost immediately after a population split and have become stronger over time. Simulations of genomic landscape evolution suggest that background selection (BGS; i.e., selection against deleterious mutations) alone is too subtle to generate the observed patterns, but scenarios that involve positive selection and genetic incompatibilities are plausible alternative explanations. Finally, tests for introgression among these taxa reveal widespread evidence of heterogeneous selection against gene flow during this radiation. Combined with previous evidence for adaptation in this system, we conclude that the correlation in FST among these taxa informs us about the processes contributing to adaptation and speciation during a rapid radiation.

Are populations like a circuit? Comparing isolation by resistance to a new coalescent-based method.

A number of methods commonly used in landscape genetics use an analogy to electrical resistance on a network to describe and fit barriers to movement across the landscape using genetic distance data. These are motivated by a mathematical equivalence between electrical resistance between two nodes of a network and the 'commute time', which is the mean time for a random walk on that network to leave one node, visit the other, and return. However, genetic data are more accurately modelled by a different quantity, the coalescence time. Here, we describe the differences between resistance distance and coalescence time, and explore the consequences for inference. We implemented a Bayesian method to infer effective movement rates and population sizes under both these models, and found that inference using commute times could produce misleading results in the presence of biased gene flow. We then used forwards-time simulation with continuous geography to demonstrate that coalescence-based inference remains more accurate than resistance-based methods on realistic data, but difficulties highlight the need for methods that explicitly model continuous, heterogeneous geography.