2BAD: an application to estimate the parental contributions during two independent admixture events

Several approaches have been developed to calculate the relative contributions of parental populations in single admixture event scenarios, including Bayesian methods. In many breeds and populations, it may be more realistic to consider multiple admixture events. However, no approach has been developed to date to estimate admixture in such cases. This report describes a program application, 2BAD (for 2-event Bayesian ADmixture), which allows the consideration of up to two independent admixture events involving two or three parental populations and a single admixed population, depending on the number of populations sampled. For each of these models, it is possible to estimate several parameters (admixture, effective sizes, etc.) using an approximate Bayesian computation approach. In addition, the program allows comparing pairs of admixture models, determining which is the most likely given data. The application was tested through simulations and was found to provide good estimates for the contribution of the populations at the two admixture events. We were also able to determine whether an admixture model was more likely than a simple split model.     

Approximate Bayesian Computation Without Summary Statistics: The Case of Admixture

In recent years approximate Bayesian computation (ABC) methods have become popular in population genetics as an alternative to full-likelihood methods to make inferences under complex demographic models. Most ABC methods rely on the choice of a set of summary statistics to extract information from the data. In this article we tested the use of the full allelic distribution directly in an ABC framework. Although the ABC techniques are becoming more widely used, there is still uncertainty over how they perform in comparison with full-likelihood methods. We thus conducted a simulation study and provide a detailed examination of ABC in comparison with full likelihood in the case of a model of admixture. This model assumes that two parental populations mixed at a certain time in the past, creating a hybrid population, and that the three populations then evolve under pure drift. Several aspects of ABC methodology were investigated, such as the effect of the distance metric chosen to measure the similarity between simulated and observed data sets. Results show that in general ABC provides good approximations to the posterior distributions obtained with the full-likelihood method. This suggests that it is possible to apply ABC using allele frequencies to make inferences in cases where it is difficult to select a set of suitable summary statistics and when the complexity of the model or the size of the data set makes it computationally prohibitive to use full-likelihood methods.     

The population demography of Betula maximowicziana,a cool‐temperate tree species in Japan,in relation to the last glacial period: its admixture‐like genetic structure is the result of simple population splitting not admixing

Conservation of the local genetic variation and evolutionary integrity of economically and ecologically important trees is a key aspect of studies involving forest genetics, and a population demographic history of the target species provides valuable information for this purpose. Here, the genetic structure of 48 populations of Betula maximowicziana was assessed using 12 expressed sequence tag–simple sequence repeat (EST‐SSR) markers. Genetic diversity was lower in northern populations than southern ones and structure analysis revealed three groups: northern and southern clusters and an admixed group. Eleven more genomic‐SSR loci were added and the demographic history of these three groups was inferred by approximate Bayesian computation (ABC). The ABC revealed that a simple split scenario was much more likely than isolation with admixture, suggesting that the admixture‐like structure detected in this species was due to ancestral polymorphisms. The ABC analysis suggested that the population growth and divergence of the three groups occurred 96 800 (95% CI, 20 500–599 000) and 28 300 (95% CI, 8700–98 400) years ago, respectively. We need to be aware of several sources of uncertainty in the inference such as assumptions about the generation time, overlapping of generations, confidence intervals of the estimated parameters and the assumed model in the ABC. However, the results of the ABC together with the model‐based maps of reconstructed past species distribution and palaeoecological data suggested that the modern genetic structure of B. maximowicziana originated prior to the last glacial maximum (LGM) and that some populations survived in the northern range even during the LGM.     

Population divergence with or without admixture: selecting models using an ABC approach

Genetic data have been widely used to reconstruct the demographic history of populations, including the estimation of migration rates, divergence times and relative admixture contribution from different populations. Recently, increasing interest has been given to the ability of genetic data to distinguish alternative models. One of the issues that has plagued this kind of inference is that ancestral shared polymorphism is often difficult to separate from admixture or gene flow. Here, we applied an approximate Bayesian computation (ABC) approach to select the model that best fits microsatellite data among alternative splitting and admixture models. We performed a simulation study and showed that with reasonably large data sets (20 loci) it is possible to identify with a high level of accuracy the model that generated the data. This suggests that it is possible to distinguish genetic patterns due to past admixture events from those due to shared polymorphism (population split without admixture). We then apply this approach to microsatellite data from an endangered and endemic Iberian freshwater fish species, in which a clustering analysis suggested that one of the populations could be admixed. In contrast, our results suggest that the observed genetic patterns are better explained by a population split model without admixture.     

Demographic Inference Reveals African and European Admixture in the North American Drosophila melanogaster Population

Drosophila melanogaster spread from sub-Saharan Africa to the rest of the world colonizing new environments. Here, we modeled the joint demography of African (Zimbabwe), European (The Netherlands), and North American (North Carolina) populations using an approximate Bayesian computation (ABC) approach. By testing different models (including scenarios with continuous migration), we found that admixture between Africa and Europe most likely generated the North American population, with an estimated proportion of African ancestry of 15%. We also revisited the demography of the ancestral population (Africa) and found—in contrast to previous work—that a bottleneck fits the history of the population of Zimbabwe better than expansion. Finally, we compared the site-frequency spectrum of the ancestral population to analytical predictions under the estimated bottleneck model.     

The use of approximate Bayesian computation in conservation genetics and its application in a case study on yellow-eyed penguins

The inference of demographic parameters from genetic data has become an integral part of conservation studies. A group of Bayesian methods developed originally in population genetics, known as approximate Bayesian computation (ABC), has been shown to be particularly useful for the estimation of such parameters. These methods do not need to evaluate likelihood functions analytically and can therefore be used even while assuming complex models. In this paper we describe the ABC approach and identify specific parts of its algorithm that are being the subject of intensive studies in order to further expand its usability. Furthermore, we discuss applications of this Bayesian algorithm in conservation studies, providing insights on the potentialities of these tools. Finally, we present a case study in which we use a simple Isolation-Migration model to estimate a number of demographic parameters of two populations of yellow-eyed penguins (Megadyptes antipodes) in New Zealand. The resulting estimates confirm our current understanding of M. antipodes dynamic, demographic history and provide new insights into the expansion this species has undergone during the last centuries.     

A classical likelihood based approach for admixture mapping using EM algorithm

Several disease-mapping methods have been proposed recently, which use the information generated by recent admixture of populations from historically distinct geographic origins. These methods include both classic likelihood and Bayesian approaches. In this study we directly maximize the likelihood function from the hidden Markov Model for admixture mapping using the EM algorithm, allowing for uncertainty in model parameters, such as the allele frequencies in the parental populations. We determined the robustness of the proposed method by examining the ancestral allele frequency estimate and individual marker-location specific ancestry when the data were generated by different population admixture models and no learning sample was used. The proposed method outperforms a widely used Bayesian MCMC strategy for data generated from various population admixture models. The multipoint information content for ancestry was derived based on the map provided by Smith et al. (2004) and the associated statistical power was calculated. We examined the distribution of admixture LD across the genome for both real and simulated data and established a threshold for genome wide significance applicable to admixture mapping studies. The software ADMIXPROGRAM for performing admixture mapping is available from authors.     

Tournament ABC analysis of the western Palaearctic population history of an oak gall wasp,Synergus umbraculus

Approximate Bayesian computation (ABC) is a powerful and widely used approach in inference of population history. However, the computational effort required to discriminate among alternative historical scenarios often limits the set that is compared to those considered more likely a priori. While often justifiable, this approach will fail to consider unexpected but well‐supported population histories. We used a hierarchical tournament approach, in which subsets of scenarios are compared in a first round of ABC analyses and the winners are compared in a second analysis, to reconstruct the population history of an oak gall wasp, Synergus umbraculus (Hymenoptera, Cynipidae) across the Western Palaearctic. We used 4,233 bp of sequence data across seven loci to explore the relationships between four putative Pleistocene refuge populations in Iberia, Italy, the Balkans and Western Asia. We compared support for 148 alternative scenarios in eight pools, each pool comprising all possible rearrangements of four populations over a given topology of relationships, with or without founding of one population by admixture and with or without an unsampled “ghost” population. We found very little support for the directional “out of the east” scenario previously inferred for other gall wasp community members. Instead, the best‐supported models identified Iberia as the first‐regional population to diverge from the others in the late Pleistocene, followed by divergence between the Balkans and Western Asia, and founding of the Italian population through late Pleistocene admixture from Iberia and the Balkans. We compare these results with what is known for other members of the oak gall community, and consider the strengths and weaknesses of using a tournament approach to explore phylogeographic model space.     

Bayesian identification of admixture events using multilocus molecular markers

Bayesian statistical methods for the estimation of hidden genetic structure of populations have gained considerable popularity in the recent years. Utilizing molecular marker data, Bayesian mixture models attempt to identify a hidden population structure by clustering individuals into genetically divergent groups, whereas admixture models target at separating the ancestral sources of the alleles observed in different individuals. We discuss the difficulties involved in the simultaneous estimation of the number of ancestral populations and the levels of admixture in studied individuals' genomes. To resolve this issue, we introduce a computationally efficient method for the identification of admixture events in the population history. Our approach is illustrated by analyses of several challenging real and simulated data sets. The software (baps), implementing the methods introduced here, is freely available at http://www.rni.helsinki.fi/~jic/bapspage.html.     

Exploring Approximate Bayesian Computation for inferring recent demographic history with genomic markers in nonmodel species

Approximate Bayesian computation (ABC) is widely used to infer demographic history of populations and species using DNA markers. Genomic markers can now be developed for nonmodel species using reduced representation library (RRL) sequencing methods that select a fraction of the genome using targeted sequence capture or restriction enzymes (genotyping‐by‐sequencing, GBS). We explored the influence of marker number and length, knowledge of gametic phase, and tradeoffs between sample size and sequencing depth on the quality of demographic inferences performed with ABC. We focused on two‐population models of recent spatial expansion with varying numbers of unknown parameters. Performing ABC on simulated data sets with known parameter values, we found that the timing of a recent spatial expansion event could be precisely estimated in a three‐parameter model. Taking into account uncertainty in parameters such as initial population size and migration rate collectively decreased the precision of inferences dramatically. Phasing haplotypes did not improve results, regardless of sequence length. Numerous short sequences were as valuable as fewer, longer sequences, and performed best when a large sample size was sequenced at low individual depth, even when sequencing errors were added. ABC results were similar to results obtained with an alternative method based on the site frequency spectrum (SFS) when performed with unphased GBS‐type markers. We conclude that unphased GBS‐type data sets can be sufficient to precisely infer simple demographic models, and discuss possible improvements for the use of ABC with genomic data.     

The demographic history of Atlantic salmon (Salmo salar) across its distribution range reconstructed from approximate Bayesian computations*

Understanding the dual roles of demographic and selective processes in the buildup of population divergence is one of the most challenging tasks in evolutionary biology. Here, we investigated the demographic history of Atlantic salmon across the entire species range using 2035 anadromous individuals from North America and Eurasia. By combining results from admixture graphs, geo‐genetic maps, and an Approximate Bayesian Computation (ABC) framework, we validated previous hypotheses pertaining to secondary contact between European and Northern American populations, but also identified secondary contacts in European populations from different glacial refugia. We further identified the major sources of admixture from the southern range of North America into more northern populations along with a strong signal of secondary gene flow between genetic regional groups. We hypothesize that these patterns reflect the spatial redistribution of ancestral variation across the entire North American range. Results also support a role for linked selection and differential introgression that likely played an underappreciated role in shaping the genomic landscape of species in the Northern hemisphere. We conclude that studies between partially isolated populations should systematically include heterogeneity in selective and introgressive effects among loci to perform more rigorous demographic inferences of the divergence process.     

Bayesian inference of a complex invasion history revealed by nuclear and chloroplast genetic diversity in the colonizing plant,Silene latifolia

Species invading new ranges are subject to a series of demographic events that can strongly shape genetic diversity. Describing this demographic history is important for understanding where invasive species come from and how they spread, and is critical to testing hypotheses of postinvasion adaptation. Here, we analyse nuclear and chloroplast genetic diversity to study the invasion history of the widespread colonizing weed, Silene latifolia (Caryophyllaceae). Bayesian clustering and PCA revealed strong population structure in the native range of Europe, and although genotypes from multiple native sources were present in the introduced range of North America, the spatial distribution of genetic variance was dramatically reorganized. Using approximate Bayesian computation (ABC), we compared support for different invasion scenarios, including the number and size of independent introduction events and the amount of admixture occurring between sources of introduced genotypes. Our results supported independent introductions into eastern and western North America, with the latter forming a bridgehead for a secondary invasion into the Great Lakes region of central North America. Despite small estimated founder population sizes, the duration of the demographic bottleneck after the initial introduction appeared extremely short‐lived. This pattern of repeated colonization and rapid expansion has effectively eroded the strong population structure and cytonuclear associations present in Europe, but has retained overall high genetic diversity since invasion. Our results highlight the flexibility of the ABC approach for constructing a narrative of the demographic history of species invasions and provide baseline for future studies of evolutionary changes in introduced S. latifolia populations.     

Past climate change drives current genetic structure of an endangered freshwater mussel species

Historical‐to‐recent climate change and anthropogenic disturbance affect species distributions and genetic structure. The Rio Grande watershed of the United States and Mexico encompasses ecosystems that are intensively exploited, resulting in substantial degradation of aquatic habitats. While significant anthropogenic disturbances in the Rio Grande are recent, inhospitable conditions for freshwater organisms likely existed prior to such disturbances. A combination of anthropogenic and past climate factors may contribute to current distributions of aquatic fauna in the Rio Grande basin. We used mitochondrial DNA and 18 microsatellite loci to infer evolutionary history and genetic structure of an endangered freshwater mussel, Popenaias popeii, throughout the Rio Grande drainage. We estimated spatial connectivity and gene flow across extant populations of P. popeii and used ecological niche models (ENMs) and approximate Bayesian computation (ABC) to infer its evolutionary history during the Pleistocene. structure results recovered regional and local population clusters in the Rio Grande. ENMs predicted drastic reductions in suitable habitat during the last glacial maximum. ABC analyses suggested that regional population structure likely arose in this species during the mid‐to‐late Pleistocene and was followed by a late Pleistocene population bottleneck in New Mexico populations. The local population structure arose relatively recently, perhaps due to anthropogenic factors. Popenaias popeii, one of the few freshwater mussel species native to the Rio Grande basin, is a case study for understanding how both geological and anthropogenic factors shape current population genetic structure. Conservation strategies for this species should account for the fragmented nature of contemporary populations.     

SPLATCHE2: a spatially explicit simulation framework for complex demography, genetic admixture and recombination

SUMMARY: SPLATCHE2 is a program to simulate the demography of populations and the resulting molecular diversity for a wide range of evolutionary scenarios. The spatially explicit simulation framework can account for environmental heterogeneity and fluctuations, and it can manage multiple population sources. A coalescent-based approach is used to generate genetic markers mostly used in population genetics studies (DNA sequences, SNPs, STRs or RFLPs). Various combinations of independent, fully or partially linked genetic markers can be produced under a recombination model based on the ancestral recombination graph. Competition between two populations (or species) can also be simulated with user-defined levels of admixture between the two populations. SPLATCHE2 may be used to generate the expected genetic diversity under complex demographic scenarios and can thus serve to test null hypotheses. For model parameter estimation, SPLATCHE2 can easily be integrated into an Approximate Bayesian Computation (ABC) framework. Availability and implementation: SPLATCHE2 is a C++ program compiled for Windows and Linux platforms. It is freely available at www.splatche.com, together with its related documentation and example data. CONTACT: mathias.currat@unige.ch     

Inferring the origin of populations introduced from a genetically structured native range by approximate Bayesian computation: case study of the invasive ladybird Harmonia axyridis

Correct identification of the source population of an invasive species is a prerequisite for testing hypotheses concerning the factors responsible for biological invasions. The native area of invasive species may be large, poorly known and/or genetically structured. Because the actual source population may not have been sampled, studies based on molecular markers may generate incorrect conclusions about the origin of introduced populations. In this study, we characterized the genetic structure of the invasive ladybird Harmonia axyridis in its native area using various population genetic statistics and methods. We found that native area of H. axyridis most probably consisted of two geographically distinct genetic clusters located in eastern and western Asia. We then performed approximate Bayesian computation (ABC) analyses on controlled simulated microsatellite data sets to evaluate (i) the risk of selecting incorrect introduction scenarios, including admixture between sources, when the populations of the native area are genetically structured and sampling is incomplete and (ii) the ability of ABC analysis to minimize such risks by explicitly including unsampled populations in the scenarios compared. Finally, we performed additional ABC analyses on real microsatellite data sets to retrace the origin of biocontrol and invasive populations of H. axyridis, taking into account the possibility that the structured native area may have been incompletely sampled. We found that the invasive population in eastern North America, which has served as the bridgehead for worldwide invasion by H. axyridis, was probably formed by an admixture between the eastern and western native clusters. This admixture may have facilitated adaptation of the bridgehead population.     

Historical environmental change in Africa drives divergence and admixture of Aedes aegypti mosquitoes: a precursor to successful worldwide colonization?

Increasing globalization has promoted the spread of exotic species, including disease vectors. Understanding the evolutionary processes involved in such colonizations is both of intrinsic biological interest and important to predict and mitigate future disease risks. The Aedes aegypti mosquito is a major vector of dengue, chikungunya and Zika, the worldwide spread of which has been facilitated by Ae. aegypti's adaption to human‐modified environments. Understanding the evolutionary processes involved in this invasion requires characterization of the genetic make‐up of the source population(s). The application of approximate Bayesian computation (ABC) to sequence data from four nuclear and one mitochondrial marker revealed that African populations of Ae. aegypti best fit a demographic model of lineage diversification, historical admixture and recent population structuring. As ancestral Ae. aegypti were dependent on forests, this population history is consistent with the effects of forest fragmentation and expansion driven by Pleistocene climatic change. Alternatively, or additionally, historical human movement across the continent may have facilitated their recent spread and mixing. ABC analysis and haplotype networks support earlier inferences of a single out‐of‐Africa colonization event, while a cline of decreasing genetic diversity indicates that Ae. aegypti moved first from Africa to the Americas and then to Asia. ABC analysis was unable to verify this colonization route, possibly because the genetic signal of admixture obscures the true colonization pathway. By increasing genetic diversity and forming novel allelic combinations, divergence and historical admixture within Africa could have provided the adaptive potential needed for the successful worldwide spread of Ae. aegypti.     

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well‐studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θ_S), the rate of gene flow among patches (4Nm), the founding population size (N₀) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat‐specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750 000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150 000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography.     

Comparison of Bayesian and maximum-likelihood inference of population genetic parameters

Comparison of the performance and accuracy of different inference methods, such as maximum likelihood (ML) and Bayesian inference, is difficult because the inference methods are implemented in different programs, often written by different authors. Both methods were implemented in the program MIGRATE, that estimates population genetic parameters, such as population sizes and migration rates, using coalescence theory. Both inference methods use the same Markov chain Monte Carlo algorithm and differ from each other in only two aspects: parameter proposal distribution and maximization of the likelihood function. Using simulated datasets, the Bayesian method generally fares better than the ML approach in accuracy and coverage, although for some values the two approaches are equal in performance. MOTIVATION: The Markov chain Monte Carlo-based ML framework can fail on sparse data and can deliver non-conservative support intervals. A Bayesian framework with appropriate prior distribution is able to remedy some of these problems. RESULTS: The program MIGRATE was extended to allow not only for ML(-) maximum likelihood estimation of population genetics parameters but also for using a Bayesian framework. Comparisons between the Bayesian approach and the ML approach are facilitated because both modes estimate the same parameters under the same population model and assumptions.     

Identification of winter moth (Operophtera brumata) refugia in North Africa and the Italian Peninsula during the last glacial maximum

Numerous studies have shown that the genetic diversity of species inhabiting temperate regions has been shaped by changes in their distributions during the Quaternary climatic oscillations. For some species, the genetic distinctness of isolated populations is maintained during secondary contact, while for others, admixture is frequently observed. For the winter moth (Operophtera brumata), an important defoliator of oak forests across Europe and northern Africa, we previously determined that contemporary populations correspond to genetic diversity obtained during the last glacial maximum (LGM) through the use of refugia in the Iberian and Aegean peninsulas, and to a lesser extent the Caucasus region. Missing from this sampling were populations from the Italian peninsula and from North Africa, both regions known to have played important roles as glacial refugia for other species. Therefore, we genotyped field‐collected winter moth individuals from southern Italy and northwestern Tunisia—the latter a region where severe oak forest defoliation by winter moth has recently been reported—using polymorphic microsatellite. We reconstructed the genetic relationships of these populations in comparison to moths previously sampled from the Iberian and Aegean peninsulas, the Caucasus region, and western Europe using genetic distance, Bayesian clustering, and approximate Bayesian computation (ABC) methods. Our results indicate that both the southern Italian and the Tunisian populations are genetically distinct from other sampled populations, and likely originated in their respective refugium during the LGM after diverging from a population that eventually settled in the Iberian refugium. These suggest that winter moth populations persisted in at least five Mediterranean LGM refugia. Finally, we comment that outbreaks by winter moth in northwestern Tunisia are not the result of a recent introduction of a nonnative species, but rather are most likely due to land use or environmental changes.     

Inference on population history and model checking using DNA sequence and microsatellite data with the software DIYABC (v1.0)

Background  

Approximate Bayesian computation (ABC) is a recent flexible class of Monte-Carlo algorithms increasingly used to make model-based inference on complex evolutionary scenarios that have acted on natural populations. The software DIYABC offers a user-friendly interface allowing non-expert users to consider population histories involving any combination of population divergences, admixtures and population size changes. We here describe and illustrate new developments of this software that mainly include (i) inference from DNA sequence data in addition or separately to microsatellite data, (ii) the possibility to analyze five categories of loci considering balanced or non balanced sex ratios: autosomal diploid, autosomal haploid, X-linked, Y-linked and mitochondrial, and (iii) the possibility to perform model checking computation to assess the "goodness-of-fit" of a model, a feature of ABC analysis that has been so far neglected.