Joint inference of population assignment and demographic history

A new approach to assigning individuals to populations using genetic data is described. Most existing methods work by maximizing Hardy-Weinberg and linkage equilibrium within populations, neither of which will apply for many demographic histories. By including a demographic model, within a likelihood framework based on coalescent theory, we can jointly study demographic history and population assignment. Genealogies and population assignments are sampled from a posterior distribution using a general isolation-with-migration model for multiple populations. A measure of partition distance between assignments facilitates not only the summary of a posterior sample of assignments, but also the estimation of the posterior density for the demographic history. It is shown that joint estimates of assignment and demographic history are possible, including estimation of population phylogeny for samples from three populations. The new method is compared to results of a widely used assignment method, using simulated and published empirical data sets.     

Genomic data detect corresponding signatures of population size change on an ecological time scale in two salamander species

Understanding the demography of species over recent history (e.g. <100 years) is critical in studies of ecology and evolution, but records of population history are rarely available. Surveying genetic variation is a potential alternative to census‐based estimates of population size, and can yield insight into the demography of a population. However, to assess the performance of genetic methods, it is important to compare their estimates of population history to known demography. Here, we leveraged the exceptional resources from a wetland with 37 years of amphibian mark–recapture data to study the utility of genetically based demographic inference on salamander species with documented population declines (Ambystoma talpoideum) and expansions (A. opacum), patterns that have been shown to be correlated with changes in wetland hydroperiod. We generated ddRAD data from two temporally sampled populations of A. opacum (1993, 2013) and A. talpoideum (1984, 2011) and used coalescent‐based demographic inference to compare alternate evolutionary models. For both species, demographic model inference supported population size changes that corroborated mark–recapture data. Parameter estimation in A. talpoideum was robust to our variations in analytical approach, while estimates for A. opacum were highly inconsistent, tempering our confidence in detecting a demographic trend in this species. Overall, our robust results in A. talpoideum suggest that genome‐based demographic inference has utility on an ecological scale, but researchers should also be cognizant that these methods may not work in all systems and evolutionary scenarios. Demographic inference may be an important tool for population monitoring and conservation management planning.     

Beyond F<Subscript>ST</Subscript>: Analysis of population genetic data for conservation

Both the ability to generate DNA data and the variety of analytical methods for conservation genetics are expanding at an ever-increasing pace. Analytical approaches are now possible that were unthinkable even five years ago due to limitations in computational power or the availability of DNA data, and this has vastly expanded the accuracy and types of information that may be gained from population genetic data. Here we provide a guide to recently developed methods for population genetic analysis, including identification of population structure, quantification of gene flow, and inference of demographic history. We cover both allele-frequency and sequence-based approaches, with a special focus on methods relevant to conservation genetic applications. Although classical population genetic approaches such as F _st (and its derivatives) have carried the field thus far, newer, more powerful, methods can infer much more from the data, rely on fewer assumptions, and are appropriate for conservation genetic management when precise estimates are needed.     

On the importance of being structured: instantaneous coalescence rates and human evolution—lessons for ancestral population size inference?

Most species are structured and influenced by processes that either increased or reduced gene flow between populations. However, most population genetic inference methods assume panmixia and reconstruct a history characterized by population size changes. This is potentially problematic as population structure can generate spurious signals of population size change through time. Moreover, when the model assumed for demographic inference is misspecified, genomic data will likely increase the precision of misleading if not meaningless parameters. For instance, if data were generated under an n-island model (characterized by the number of islands and migrants exchanged) inference based on a model of population size change would produce precise estimates of a bottleneck that would be meaningless. In addition, archaeological or climatic events around the bottleneck''s timing might provide a reasonable but potentially misleading scenario. In a context of model uncertainty (panmixia versus structure) genomic data may thus not necessarily lead to improved statistical inference. We consider two haploid genomes and develop a theory that explains why any demographic model with structure will necessarily be interpreted as a series of changes in population size by inference methods ignoring structure. We formalize a parameter, the inverse instantaneous coalescence rate, and show that it is equivalent to a population size only in panmictic models, and is mostly misleading for structured models. We argue that this issue affects all population genetics methods ignoring population structure which may thus infer population size changes that never took place. We apply our approach to human genomic data.     

Effects of recent population bottlenecks on reconstructing the demographic history of prairie-chickens

Current methods of DNA sequence analysis attempt to reconstruct historical patterns of population structure and growth from contemporary samples. However, these techniques may be influenced by recent population bottlenecks, which have the potential to eliminate lineages that reveal past changes in demography. One way to examine the performance of these demographic methods is to compare samples from populations before and after recent bottlenecks. We compared estimates of demographic history from populations of greater prairie-chickens (Tympanuchus cupido) before and after recent bottlenecks using four common methods (nested clade analysis [NCA], Tajima's D, mismatch distribution, and MDIV). We found that NCA did not perform well in the presence of bottleneck events, although it did recover some genetic signals associated with increased isolation and the extinction of intermediate populations. The majority of estimates for Tajima's D, including those from bottlenecked populations, were not significantly different from zero, suggesting our data conformed to neutral expectations. In contrast, mismatch distributions including the raggedness index were more likely to identify recently bottlenecked populations with this data set. Estimates of population mutation rate (theta), population divergence time (t), and time to the most recent common ancestor (TMRCA) from MDIV were similar before and after bottlenecks; however, estimates of gene flow (M) were significantly lower in a few cases following a bottleneck. These results suggest that caution should be used when assessing demographic history from contemporary data sets, as recently fragmented and bottlenecked populations may have lost lineages that affect inferences of their demographic history.     

Inference with selection,varying population size,and evolving population structure: application of ABC to a forward–backward coalescent process with interactions

Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed a priori known, the evolution of the genetic composition of a population does not affect demography nor population structure, and there is no selection nor interaction between and within genetic strains. In this paper, we present a stochastic birth-death model with competitive interactions and asexual reproduction. We develop an inferential procedure for ecological, demographic, and genetic parameters. We first show how genetic diversity and genealogies are related to birth and death rates, and to how individuals compete within and between strains. This leads us to propose an original model of phylogenies, with trait structure and interactions, that allows multiple merging. Second, we develop an Approximate Bayesian Computation framework to use our model for analyzing genetic data. We apply our procedure to simulated data from a toy model, and to real data by analyzing the genetic diversity of microsatellites on Y-chromosomes sampled from Central Asia human populations in order to test whether different social organizations show significantly different fertilities.Subject terms: Genetic variation, Phylogenetics, Ecological genetics     

Genomic inference accurately predicts the timing and severity of a recent bottleneck in a nonmodel insect population

The analysis of molecular data from natural populations has allowed researchers to answer diverse ecological questions that were previously intractable. In particular, ecologists are often interested in the demographic history of populations, information that is rarely available from historical records. Methods have been developed to infer demographic parameters from genomic data, but it is not well understood how inferred parameters compare to true population history or depend on aspects of experimental design. Here, we present and evaluate a method of SNP discovery using RNA sequencing and demographic inference using the program δaδi, which uses a diffusion approximation to the allele frequency spectrum to fit demographic models. We test these methods in a population of the checkerspot butterfly Euphydryas gillettii. This population was intentionally introduced to Gothic, Colorado in 1977 and has as experienced extreme fluctuations including bottlenecks of fewer than 25 adults, as documented by nearly annual field surveys. Using RNA sequencing of eight individuals from Colorado and eight individuals from a native population in Wyoming, we generate the first genomic resources for this system. While demographic inference is commonly used to examine ancient demography, our study demonstrates that our inexpensive, all‐in‐one approach to marker discovery and genotyping provides sufficient data to accurately infer the timing of a recent bottleneck. This demographic scenario is relevant for many species of conservation concern, few of which have sequenced genomes. Our results are remarkably insensitive to sample size or number of genomic markers, which has important implications for applying this method to other nonmodel systems.     

Genome-scale analysis of demographic history and adaptive selection

One of the main topics in population genetics is identification of adaptive selection among populations. For this purpose, population history should be correctly inferred to evaluate the effect of random drift and exclude it in selection identification. With the rapid progress in genomics in the past decade, vast genomescale variations are available for population genetic analysis, which however requires more sophisticated models to infer species’ demographic history and robust methods to detect local adaptation. Here we aim to review what have been achieved in the fields of demographic modeling and selection detection. We summarize their rationales, implementations, and some classical applications. We also propose that some widely-used methods can be improved in both theoretical and practical aspects in near future.     

Inferring population decline and expansion from microsatellite data: a simulation-based evaluation of the Msvar method

Reconstructing the demographic history of populations is a central issue in evolutionary biology. Using likelihood-based methods coupled with Monte Carlo simulations, it is now possible to reconstruct past changes in population size from genetic data. Using simulated data sets under various demographic scenarios, we evaluate the statistical performance of Msvar, a full-likelihood Bayesian method that infers past demographic change from microsatellite data. Our simulation tests show that Msvar is very efficient at detecting population declines and expansions, provided the event is neither too weak nor too recent. We further show that Msvar outperforms two moment-based methods (the M-ratio test and Bottleneck) for detecting population size changes, whatever the time and the severity of the event. The same trend emerges from a compilation of empirical studies. The latest version of Msvar provides estimates of the current and the ancestral population size and the time since the population started changing in size. We show that, in the absence of prior knowledge, Msvar provides little information on the mutation rate, which results in biased estimates and/or wide credibility intervals for each of the demographic parameters. However, scaling the population size parameters with the mutation rate and scaling the time with current population size, as coalescent theory requires, significantly improves the quality of the estimates for contraction but not for expansion scenarios. Finally, our results suggest that Msvar is robust to moderate departures from a strict stepwise mutation model.     

On the Use of Published Demographic Data for Population-Level Risk Assessment in Birds

As the practice of using population models for wildlife risk assessment has become more common, so has the practice of using surrogate data, typically taken from the published scientific literature, as inputs for demographic models. This practice clearly exposes the user to inferential errors. However, it is likely to continue because demographic data are expensive to gather. We review potential errors associated with the use of previously published demographic data and how those errors propagate into the endpoints of demographic projection models. We suggest methods for inferring bias in model endpoints when multiple and opposing biases are present in the demographic input data. We provide an example using Eastern Meadowlarks (Sturnella magna), a common songbird in Midwestern grasslands and agro-ecosystems. We conclude with a brief review of methods that could improve inference made using published demographic data, including methods from life-history theory, meta-analysis, and Bayesian statistics.     

Bayesian coalescent inference of past population dynamics from molecular sequences

We introduce the Bayesian skyline plot, a new method for estimating past population dynamics through time from a sample of molecular sequences without dependence on a prespecified parametric model of demographic history. We describe a Markov chain Monte Carlo sampling procedure that efficiently samples a variant of the generalized skyline plot, given sequence data, and combines these plots to generate a posterior distribution of effective population size through time. We apply the Bayesian skyline plot to simulated data sets and show that it correctly reconstructs demographic history under canonical scenarios. Finally, we compare the Bayesian skyline plot model to previous coalescent approaches by analyzing two real data sets (hepatitis C virus in Egypt and mitochondrial DNA of Beringian bison) that have been previously investigated using alternative coalescent methods. In the bison analysis, we detect a severe but previously unrecognized bottleneck, estimated to have occurred 10,000 radiocarbon years ago, which coincides with both the earliest undisputed record of large numbers of humans in Alaska and the megafaunal extinctions in North America at the beginning of the Holocene.     

Mid‐Holocene decline in African buffalos inferred from Bayesian coalescent‐based analyses of microsatellites and mitochondrial DNA

Genetic studies concerned with the demographic history of wildlife species can help elucidate the role of climate change and other forces such as human activity in shaping patterns of divergence and distribution. The African buffalo (Syncerus caffer) declined dramatically during the rinderpest pandemic in the late 1800s, but little is known about the earlier demographic history of the species. We analysed genetic variation at 17 microsatellite loci and a 302‐bp fragment of the mitochondrial DNA control region to infer past demographic changes in buffalo populations from East Africa. Two Bayesian coalescent‐based methods as well as traditional bottleneck tests were applied to infer detailed dynamics in buffalo demographic history. No clear genetic signature of population declines related to the rinderpest pandemic could be detected. However, Bayesian coalescent modelling detected a strong signal of African buffalo population declines in the order of 75–98%, starting in the mid‐Holocene (approximately 3–7000 years ago). The signature of decline was remarkably consistent using two different coalescent‐based methods and two types of molecular markers. Exploratory analyses involving various prior assumptions did not seriously affect the magnitude or timing of the inferred population decline. Climate data show that tropical Africa experienced a pronounced transition to a drier climate approximately 4500 years ago, concurrent with the buffalo decline. We therefore propose that the mid‐Holocene aridification of East Africa caused a major decline in the effective population size of the buffalo, a species reliant on moist savannah habitat for its existence.     

Inferring number of populations and changes in connectivity under the n-island model

Inferring the demographic history of species is one of the greatest challenges in populations genetics. This history is often represented as a history of size changes, ignoring population structure. Alternatively, when structure is assumed, it is defined a priori as a population tree and not inferred. Here we propose a framework based on the IICR (Inverse Instantaneous Coalescence Rate). The IICR can be estimated for a single diploid individual using the PSMC method of Li and Durbin (2011). For an isolated panmictic population, the IICR matches the population size history, and this is how the PSMC outputs are generally interpreted. However, it is increasingly acknowledged that the IICR is a function of the demographic model and sampling scheme with limited connection to population size changes. Our method fits observed IICR curves of diploid individuals with IICR curves obtained under piecewise stationary symmetrical island models. In our models we assume a fixed number of time periods during which gene flow is constant, but gene flow is allowed to change between time periods. We infer the number of islands, their sizes, the periods at which connectivity changes and the corresponding rates of connectivity. Validation with simulated data showed that the method can accurately recover most of the scenario parameters. Our application to a set of five human PSMCs yielded demographic histories that are in agreement with previous studies using similar methods and with recent research suggesting ancient human structure. They are in contrast with the view of human evolution consisting of one ancestral population branching into three large continental and panmictic populations with varying degrees of connectivity and no population structure within each continent.Subject terms: Population genetics, Biological models, Population genetics     

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.     

Life span correlates with population dynamics in perennial herbaceous plants

Survival and fecundity are basic components of demography and therefore have a strong influence on population dynamics. These two key parameters and their relationship are crucial to understand the evolution of life histories. It remains, however, to be empirically established how life span, fecundity, and population dynamics are linked in different organism groups. We conducted a comparative study based on demographic data sets of 55 populations of 23 perennial herbs for which structured demographic models and among-year natural variation in demographic attributes were available. Life span (from 4 to 128 yr old), estimated by using an algorithm, was inversely correlated with the deviance of the population growth rate from equilibrium as well as with among-year population fluctuations. Temporal variability was greater for short-lived species than for the long-lived ones because fecundity was more variable than survival and relatively more important for population dynamics for the short-lived species. The relationship between life span and population stability suggests that selection for longevity may have played an important role in the life history evolution of plants because of its ability to buffer temporal fluctuations in population size.     

Recent progress in polymorphism-based population genetic inference

The recent availability of whole-genome sequencing data affords tremendous power for statistical inference. With this, there has been great interest in the development of polymorphism-based approaches for the estimation of population genetic parameters. These approaches seek to estimate, for example, recently fixed or sweeping beneficial mutations, the rate of recurrent positive selection, the distribution of selection coefficients, and the demographic history of the population. Yet despite estimating similar parameters using similar data sets, results between methodologies are far from consistent. We here summarize the current state of the field, compare existing approaches, and attempt to reconcile emerging discrepancies. We also discuss the biases in selection estimators introduced by ignoring the demographic history of the population, discuss the biases in demographic estimators introduced by assuming neutrality, and highlight the important challenge to the field of achieving a true joint estimation procedure to circumvent these confounding effects.     

Maximum-likelihood estimation of demographic parameters using the frequency spectrum of unlinked single-nucleotide polymorphisms

A maximum-likelihood method for demographic inference is applied to data sets consisting of the frequency spectrum of unlinked single-nucleotide polymorphisms (SNPs). We use simulation analyses to explore the effect of sample size and number of polymorphic sites on both the power to reject the null hypothesis of constant population size and the properties of two- and three-dimensional maximum-likelihood estimators (MLEs). Large amounts of data are required to produce accurate demographic inferences, particularly for scenarios of recent growth. Properties of the MLEs are highly dependent upon the demographic scenario, as estimates improve with a more ancient time of growth onset and smaller degree of growth. Severe episodes of growth lead to an upward bias in the estimates of the current population size, and that bias increases with the magnitude of growth. One data set of African origin supports a model of mild, ancient growth, and another is compatible with both constant population size and a variety of growth scenarios, rejecting greater than fivefold growth beginning >36,000 years ago. Analysis of a data set of European origin indicates a bottlenecked population history, with an 85% population reduction occurring approximately 30,000 years ago.     

An integrated framework for the inference of viral population history from reconstructed genealogies

We describe a unified set of methods for the inference of demographic history using genealogies reconstructed from gene sequence data. We introduce the skyline plot, a graphical, nonparametric estimate of demographic history. We discuss both maximum-likelihood parameter estimation and demographic hypothesis testing. Simulations are carried out to investigate the statistical properties of maximum-likelihood estimates of demographic parameters. The simulations reveal that (i) the performance of exponential growth model estimates is determined by a simple function of the true parameter values and (ii) under some conditions, estimates from reconstructed trees perform as well as estimates from perfect trees. We apply our methods to HIV-1 sequence data and find strong evidence that subtypes A and B have different demographic histories. We also provide the first (albeit tentative) genetic evidence for a recent decrease in the growth rate of subtype B.     

Genetics of recent habitat contraction and reduction in population size: does isolation by distance matter?

Fragmentation and loss of natural habitats are recognized as major threats to contemporary flora and fauna. Detecting past or current reductions in population size is therefore a major aim in conservation genetics. Statistical methods developed to this purpose have tended to ignore the effects of spatial population structure. However in many species, individual dispersal is restricted in space and fine-scale spatial structure such as isolation by distance (IBD) is commonly observed in continuous populations. Using a simulation-based approach, we investigated how comparative and single-point methods, traditionally used in a Wright-Fisher (WF) population context for detecting population size reduction, behave for IBD populations. We found that a complex 'quartet' of factors was acting that includes restricted dispersal, population size (i.e. habitat size), demographic history, and sampling scale. After habitat reduction, IBD populations were characterized by a stronger inertia in the loss of genetic diversity than WF populations. This inertia increases with the strength of IBD, and decreases when the sampling scale increases. Depending on the method used to detect a population size reduction, a local sampling can be more informative than a sample scaled to habitat size or vice versa. However, IBD structure led in numerous cases to incorrect inferences on population demographic history. The reanalysis of a real microsatellite data set of skink populations from fragmented and intact rainforest habitats confirmed most of our simulation results.