Minimal-assumption inference from population-genomic data

Isolation by distance in populations with power-law dispersal

Limited dispersal of individuals between generations results in isolation by distance, in which individuals further apart in space tend to be less related. Classic models of isolation by distance assume that dispersal distances are drawn from a thin-tailed distribution and predict that the proportion of the genome that is identical by descent between a pair of individuals should decrease exponentially with the spatial separation between them. However, in many natural populations, individuals occasionally disperse over very long distances. In this work, we use mathematical analysis and coalescent simulations to study the effect of long-range (power-law) dispersal on patterns of isolation by distance. We find that it leads to power-law decay of identity-by-descent at large distances with the same exponent as dispersal. We also find that broad power-law dispersal produces another, shallow power-law decay of identity-by-descent at short distances. These results suggest that the distribution of long-range dispersal events could be estimated from sequencing large population samples taken from a wide range of spatial scales.

Sweeps in time: leveraging the joint distribution of branch lengths

Current methods of identifying positively selected regions in the genome are limited in two key ways: the underlying models cannot account for the timing of adaptive events and the comparison between models of selective sweeps and sequence data is generally made via simple summaries of genetic diversity. Here, we develop a tractable method of describing the effect of positive selection on the genealogical histories in the surrounding genome, explicitly modeling both the timing and context of an adaptive event. In addition, our framework allows us to go beyond analyzing polymorphism data via the site frequency spectrum or summaries thereof and instead leverage information contained in patterns of linked variants. Tests on both simulations and a human data example, as well as a comparison to SweepFinder2, show that even with very small sample sizes, our analytic framework has higher power to identify old selective sweeps and to correctly infer both the time and strength of selection. Finally, we derived the marginal distribution of genealogical branch lengths at a locus affected by selection acting at a linked site. This provides a much-needed link between our analytic understanding of the effects of sweeps on sequence variation and recent advances in simulation and heuristic inference procedures that allow researchers to examine the sequence of genealogical histories along the genome.

fastsimcoal2: demographic inference under complex evolutionary scenarios

Motivation

fastsimcoal2 extends fastsimcoal, a continuous time coalescent-based genetic simulation program, by enabling the estimation of demographic parameters under very complex scenarios from the site frequency spectrum under a maximum-likelihood framework.

Results

Other improvements include multi-threading, handling of population inbreeding, extended input file syntax facilitating the description of complex demographic scenarios, and more efficient simulations of sparsely structured populations and of large chromosomes.

Availability and implementation

fastsimcoal2 is freely available on http://cmpg.unibe.ch/software/fastsimcoal2/. It includes console versions for Linux, Windows and MacOS, additional scripts for the analysis and visualization of simulated and estimated scenarios, as well as a detailed documentation and ready-to-use examples.

Inference of Historical Population-Size Changes with Allele-Frequency Data

With up to millions of nearly neutral polymorphisms now being routinely sampled in population-genomic surveys, it is possible to estimate the site-frequency spectrum of such sites with high precision. Each frequency class reflects a mixture of potentially unique demographic histories, which can be revealed using theory for the probability distributions of the starting and ending points of branch segments over all possible coalescence trees. Such distributions are completely independent of past population history, which only influences the segment lengths, providing the basis for estimating average population sizes separating tree-wide coalescence events. The history of population-size change experienced by a sample of polymorphisms can then be dissected in a model-flexible fashion, and extension of this theory allows estimation of the mean and full distribution of long-term effective population sizes and ages of alleles of specific frequencies. Here, we outline the basic theory underlying the conceptual approach, develop and test an efficient statistical procedure for parameter estimation, and apply this to multiple population-genomic datasets for the microcrustacean Daphnia pulex.

A practical introduction to sequentially Markovian coalescent methods for estimating demographic history from genomic data

A common goal of population genomics and molecular ecology is to reconstruct the demographic history of a species of interest. A pair of powerful tools based on the sequentially Markovian coalescent have been developed to infer past population sizes using genome sequences. These methods are most useful when sequences are available for only a limited number of genomes and when the aim is to study ancient demographic events. The results of these analyses can be difficult to interpret accurately, because doing so requires some understanding of their theoretical basis and of their sensitivity to confounding factors. In this practical review, we explain some of the key concepts underpinning the pairwise and multiple sequentially Markovian coalescent methods (PSMC and MSMC, respectively). We relate these concepts to the use and interpretation of these methods, and we explain how the choice of different parameter values by the user can affect the accuracy and precision of the inferences. Based on our survey of 100 PSMC studies and 30 MSMC studies, we describe how the two methods are used in practice. Readers of this article will become familiar with the principles, practice, and interpretation of the sequentially Markovian coalescent for inferring demographic history.

Genetic variation across trophic levels: A test of the correlation between population size and genetic diversity in sympatric desert lizards

Understanding the causes of genetic variation in real populations has been elusive. Competing theories claim that neutral vs. selective processes have a greater influence on the genetic variation within a population. A key difference among theories is the relationship between population size and genetic diversity. Our study tests this empirically by sampling two species of herbivorous lizards (Dipsosaurus dorsalis and Sauromalus ater) and two species of carnivorous lizards (Crotaphytus bicinctores and Gambelia wislizenii) that vary in population size at the same locality, and comparing metrics of genetic diversity. Contrary to neutral expectations, results from four independent loci showed levels of diversity were usually higher for species with smaller population sizes. This suggests that selective processes may be having an important impact on intraspecific diversity in this reptile community, although tests showed little evidence for selection on the loci sequenced for this study. It is also possible that idiosyncratic histories of the focal species may be overriding predictions from simple neutral models. If future studies show that lack of correlation between population size and genetic diversity is common, methods using genetic diversity to estimate population parameters like population size or time to common ancestor should be used with caution, as these estimates are based on neutral theory predictions.

Robust Design for Coalescent Model Inference

The coalescent process describes how changes in the size or structure of a population influence the genealogical patterns of sequences sampled from that population. The estimation of (effective) population size changes from genealogies that are reconstructed from these sampled sequences is an important problem in many biological fields. Often, population size is characterized by a piecewise-constant function, with each piece serving as a population size parameter to be estimated. Estimation quality depends on both the statistical coalescent inference method employed, and on the experimental protocol, which controls variables such as the sampling of sequences through time and space, or the transformation of model parameters. While there is an extensive literature on coalescent inference methodology, there is comparatively little work on experimental design. The research that does exist is largely simulation-based, precluding the development of provable or general design theorems. We examine three key design problems: temporal sampling of sequences under the skyline demographic coalescent model, spatio-temporal sampling under the structured coalescent model, and time discretization for sequentially Markovian coalescent models. In all cases, we prove that 1) working in the logarithm of the parameters to be inferred (e.g., population size) and 2) distributing informative coalescent events uniformly among these log-parameters, is uniquely robust. "Robust" means that the total and maximum uncertainty of our parameter estimates are minimized, and made insensitive to their unknown (true) values. This robust design theorem provides rigorous justification for several existing coalescent experimental design decisions and leads to usable guidelines for future empirical or simulation-based investigations. Given its persistence among models, this theorem may form the basis of an experimental design paradigm for coalescent inference.

Using Genomic Data to Infer Historic Population Dynamics of Nonmodel Organisms

Genome sequence data are now being routinely obtained from many nonmodel organisms. These data contain a wealth of information about the demographic history of the populations from which they originate. Many sophisticated statistical inference procedures have been developed to infer the demographic history of populations from this type of genomic data. In this review, we discuss the different statistical methods available for inference of demography, providing an overview of the underlying theory and logic behind each approach. We also discuss the types of data required and the pros and cons of each method. We then discuss how these methods have been applied to a variety of nonmodel organisms. We conclude by presenting some recommendations for researchers looking to use genomic data to infer demographic history.

Selection-Like Biases Emerge in Population Models with Recurrent Jackpot Events

Evolutionary dynamics driven out of equilibrium by growth, expansion, or adaptation often generate a characteristically skewed distribution of descendant numbers: the earliest, the most advanced, or the fittest ancestors have exceptionally large number of descendants, which Luria and Delbrück called "jackpot" events. Here, I show that recurrent jackpot events generate a deterministic median bias favoring majority alleles, which is akin to positive frequency-dependent selection (proportional to the log ratio of the frequencies of mutant and wild-type alleles). This fictitious selection force results from the fact that majority alleles tend to sample deeper into the tail of the descendant distribution. The flip side of this sampling effect is the rare occurrence of large frequency hikes in favor of minority alleles, which ensures that the allele frequency dynamics remains neutral in expectation, unless genuine selection is present. The resulting picture of a selection-like bias compensated by rare big jumps allows for an intuitive understanding of allele frequency trajectories and enables the exact calculation of transition densities for a range of important scenarios, including population-size variations and different forms of natural selection. As a general signature of evolution by rare events, fictitious selection hampers the establishment of new beneficial mutations, counteracts balancing selection, and confounds methods to infer selection from data over limited timescales.

ABLE: blockwise site frequency spectra for inferring complex population histories and recombination

We introduce ABLE (Approximate Blockwise Likelihood Estimation), a novel simulation-based composite likelihood method that uses the blockwise site frequency spectrum to jointly infer past demography and recombination. ABLE is explicitly designed for a wide variety of data from unphased diploid genomes to genome-wide multi-locus data (for example, RADSeq) and can also accommodate arbitrarily large samples. We use simulations to demonstrate the accuracy of this method to infer complex histories of divergence and gene flow and reanalyze whole genome data from two species of orangutan. ABLE is available for download at https://github.com/champost/ABLE.

Digest: Demographic inferences accounting for selection at linked sites†

Complex demography and selection at linked sites can generate spurious signatures of divergent selection. Unfortunately, many attempts at demographic inference consider overly simple models and neglect the effect of selection at linked sites. In this issue, Rougemont and Bernatchez (2018) applied an approximate Bayesian computation (ABC) framework that accounts for indirect selection to reveal a complex history of secondary contacts in Atlantic salmon (Salmo salar) that might explain a high rate of latitudinal clines in this species.

Comparison of Single Genome and Allele Frequency Data Reveals Discordant Demographic Histories

Inference of demographic history from genetic data is a primary goal of population genetics of model and nonmodel organisms. Whole genome-based approaches such as the pairwise/multiple sequentially Markovian coalescent methods use genomic data from one to four individuals to infer the demographic history of an entire population, while site frequency spectrum (SFS)-based methods use the distribution of allele frequencies in a sample to reconstruct the same historical events. Although both methods are extensively used in empirical studies and perform well on data simulated under simple models, there have been only limited comparisons of them in more complex and realistic settings. Here we use published demographic models based on data from three human populations (Yoruba, descendants of northwest-Europeans, and Han Chinese) as an empirical test case to study the behavior of both inference procedures. We find that several of the demographic histories inferred by the whole genome-based methods do not predict the genome-wide distribution of heterozygosity, nor do they predict the empirical SFS. However, using simulated data, we also find that the whole genome methods can reconstruct the complex demographic models inferred by SFS-based methods, suggesting that the discordant patterns of genetic variation are not attributable to a lack of statistical power, but may reflect unmodeled complexities in the underlying demography. More generally, our findings indicate that demographic inference from a small number of genomes, routine in genomic studies of nonmodel organisms, should be interpreted cautiously, as these models cannot recapitulate other summaries of the data.