Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

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.

Population structure and migration pattern of a conifer pathogen, Grosmannia clavigera, as influenced by its symbiont, the mountain pine beetle

We investigated the population structure of Grosmannia clavigera (Gc), a fungal symbiont of the mountain pine beetle (MPB) that plays a crucial role in the establishment and reproductive success of this pathogen. This insect-fungal complex has destroyed over 16 million ha of lodgepole pine forests in Canada, the largest MPB epidemic in recorded history. During this current epidemic, MPB has expanded its range beyond historically recorded boundaries, both northward and eastward, and has now reached the jack pine of Alberta, potentially threatening the Canadian boreal forest. To better understand the dynamics between the beetle and its fungal symbiont, we sampled 19 populations in western North America and genotyped individuals from these populations with eight microsatellite markers. The fungus displayed high haplotype diversity, with over 250 unique haplotypes observed in 335 single spore isolates. Linkage equilibria in 13 of the 19 populations suggested that the fungus reproduces sexually. Bayesian clustering and distance analyses identified four genetic clusters that corresponded to four major geographical regions, which suggested that the epidemic arose from multiple geographical sources. A genetic cluster north of the Rocky Mountains, where the MPB has recently become established, experienced a population bottleneck, probably as a result of the recent range expansion. The two genetic clusters located north and west of the Rocky Mountains contained many fungal isolates admixed from all populations, possibly due to the massive movement of MPB during the epidemic. The general agreement in north-south differentiation of MPB and G. clavigera populations points to the fungal pathogen's dependence on the movement of its insect vector. In addition, the patterns of diversity and the individual assignment tests of the fungal associate suggest that migration across the Rocky Mountains occurred via a northeastern corridor, in accordance with meteorological patterns and observation of MPB movement data. Our results highlight the potential of this pathogen for both expansion and sexual reproduction, and also identify some possible barriers to gene flow. Understanding the ecological and evolutionary dynamics of this fungus-beetle association is important for the modelling and prediction of MPB epidemics.

Reconstruction of a beech population bottleneck using archival demographic information and Bayesian analysis of genetic data

Range expansion and contraction has occurred in the history of most species and can seriously impact patterns of genetic diversity. Historical data about range change are rare and generally appropriate for studies at large scales, whereas the individual pollen and seed dispersal events that form the basis of geneflow and colonization generally occur at a local scale. In this study, we investigated range change in Fagus sylvatica on Mont Ventoux, France, using historical data from 1838 to the present and approximate Bayesian computation (ABC) analyses of genetic data. From the historical data, we identified a population minimum in 1845 and located remnant populations at least 200 years old. The ABC analysis selected a demographic scenario with three populations, corresponding to two remnant populations and one area of recent expansion. It also identified expansion from a smaller ancestral population but did not find that this expansion followed a population bottleneck, as suggested by the historical data. Despite a strong support to the selected scenario for our data set, the ABC approach showed a low power to discriminate among scenarios on average and a low ability to accurately estimate effective population sizes and divergence dates, probably due to the temporal scale of the study. This study provides an unusual opportunity to test ABC analysis in a system with a well-documented demographic history and identify discrepancies between the results of historical, classical population genetic and ABC analyses. The results also provide valuable insights into genetic processes at work at a fine spatial and temporal scale in range change and colonization.

Challenges to assessing connectivity between massive populations of the Australian plague locust

Linking demographic and genetic dispersal measures is of fundamental importance for movement ecology and evolution. However, such integration can be difficult, particularly for highly fecund species that are often the target of management decisions guided by an understanding of population movement. Here, we present an example of how the influence of large population sizes can preclude genetic approaches from assessing demographic population structuring, even at a continental scale. The Australian plague locust, Chortoicetes terminifera, is a significant pest, with populations on the eastern and western sides of Australia having been monitored and managed independently to date. We used microsatellites to assess genetic variation in 12 C. terminifera population samples separated by up to 3000 km. Traditional summary statistics indicated high levels of genetic diversity and a surprising lack of population structure across the entire range. An approximate Bayesian computation treatment indicated that levels of genetic diversity in C. terminifera corresponded to effective population sizes conservatively composed of tens of thousands to several million individuals. We used these estimates and computer simulations to estimate the minimum rate of dispersal, m, that could account for the observed range-wide genetic homogeneity. The rate of dispersal between both sides of the Australian continent could be several orders of magnitude lower than that typically considered as required for the demographic connectivity of populations.

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.

Choice of summary statistic weights in approximate Bayesian computation

In this paper, we develop a Genetic Algorithm that can address the fundamental problem of how one should weight the summary statistics included in an approximate Bayesian computation analysis built around an accept/reject algorithm, and how one might choose the tolerance for that analysis. We then demonstrate that using weighted statistics, and a well-chosen tolerance, in such an approximate Bayesian computation approach can result in improved performance, when compared to unweighted analyses, using one example drawn purely from statistics and two drawn from the estimation of population genetics parameters.

Molecular data reveal isolation by distance and past population expansion for the shea tree (Vitellaria paradoxa C.F. Gaertn) in West Africa

While the genetic structure of many tree species in temperate, American and Asian regions is largely explained by climatic oscillations and subsequent habitat contractions and expansions, little is known about Africa. We investigated the genetic diversity and structure of shea tree (Vitellaria paradoxa,) in Western Africa, an economically important tree species in the Sudano-Sahelian zone. Eleven nuclear microsatellites (nuc) were used to genotype 673 trees selected in 38 populations. They revealed moderate to high within-population diversity: allelic richness ranged from R(nuc) = 3.99 to 5.63. This diversity was evenly distributed across West Africa. Populations were weakly differentiated (F(STnuc) = 0.085; P < 0.0001) and a pattern of isolation by distance was noted. No phylogeographic signal could be detected across the studied sample. Additionally, two chloroplast microsatellite loci, leading to 11 chlorotypes, were used to analyse a sub-set of 370 individuals. Some variation in chloroplast allelic richness among populations could be detected (R(cp) = 0.00 to 4.36), but these differences were not significant. No trend with latitude and longitude were observed. Differentiation was marked (G(STcp) = 0.553; P < 0.0001), but without a significant phylogeographical signal. Population expansion was detected considering the total population using approximate Bayesian computation (nuclear microsatellites) and mismatch distribution (chloroplast microsatellites) methods. This expansion signal and the isolation by distance pattern could be linked to the past climatic conditions in West Africa during the Pleistocene and Holocene which should have been favourable to shea tree development. In addition, human activities through agroforestry and domestication (started 10,000 bp) have probably enhanced gene flow and population expansion.

Bayesian inference of a historical bottleneck in a heavily exploited marine mammal

Emerging Bayesian analytical approaches offer increasingly sophisticated means of reconstructing historical population dynamics from genetic data, but have been little applied to scenarios involving demographic bottlenecks. Consequently, we analysed a large mitochondrial and microsatellite dataset from the Antarctic fur seal Arctocephalus gazella, a species subjected to one of the most extreme examples of uncontrolled exploitation in history when it was reduced to the brink of extinction by the sealing industry during the late eighteenth and nineteenth centuries. Classical bottleneck tests, which exploit the fact that rare alleles are rapidly lost during demographic reduction, yielded ambiguous results. In contrast, a strong signal of recent demographic decline was detected using both Bayesian skyline plots and Approximate Bayesian Computation, the latter also allowing derivation of posterior parameter estimates that were remarkably consistent with historical observations. This was achieved using only contemporary samples, further emphasizing the potential of Bayesian approaches to address important problems in conservation and evolutionary biology.

Lack of confidence in approximate Bayesian computation model choice

Approximate Bayesian computation (ABC) have become an essential tool for the analysis of complex stochastic models. Grelaud et al. [(2009) Bayesian Anal 3:427-442] advocated the use of ABC for model choice in the specific case of Gibbs random fields, relying on an intermodel sufficiency property to show that the approximation was legitimate. We implemented ABC model choice in a wide range of phylogenetic models in the Do It Yourself-ABC (DIY-ABC) software [Cornuet et al. (2008) Bioinformatics 24:2713-2719]. We now present arguments as to why the theoretical arguments for ABC model choice are missing, because the algorithm involves an unknown loss of information induced by the use of insufficient summary statistics. The approximation error of the posterior probabilities of the models under comparison may thus be unrelated with the computational effort spent in running an ABC algorithm. We then conclude that additional empirical verifications of the performances of the ABC procedure as those available in DIY-ABC are necessary to conduct model choice.

Genetic homogeneity across Bantu-speaking groups from Mozambique and Angola challenges early split scenarios between East and West Bantu populations

The large scale spread of Bantu-speaking populations remains one of the most debated questions in African population history. In this work we studied the genetic structure of 19 Bantu-speaking groups from Mozambique and Angola using a multilocus approach based on 14 newly developed compound haplotype systems (UEPSTRs), each consisting of a rapidly evolving short tandem repeat (STR) closely linked to a unique event polymorphism (UEP). We compared the ability of UEPs, STRs and UEPSTRs to document genetic variation at the intercontinental level and among the African Bantu populations, and found that UEPSTR systems clearly provided more resolution than UEPs or STRs alone. The observed patterns of genetic variation revealed high levels of genetic homogeneity between major populations from Angola and Mozambique, with two main outliers: the Kuvale from Angola and the Chopi from Mozambique. Within Mozambique, two Kaskazi-speaking populations from the far north (Yao and Mwani) and two Nyasa-speaking groups from the Zambezi River basin (Nyungwe and Sena) could be differentiated from the remaining groups, but no further population structure was observed across the country. The close genetic relationship between most sampled Bantu populations is consistent with high degrees of interaction between peoples living in savanna areas located to the south of the rainforest. Our results highlight the role of gene flow during the Bantu expansions and show that the genetic evidence accumulated so far is becoming increasingly difficult to reconcile with widely accepted models postulating an early split between eastern and western Bantu populations.

Reconstructing demographic events from population genetic data: the introduction of bumblebees to New Zealand

Four British bumblebee species (Bombus terrestris, Bombus hortorum, Bombus ruderatus and Bombus subterraneus) became established in New Zealand following their introduction at the turn of the last century. Of these, two remain common in the United Kingdom (B. terrestris and B. hortorum), whilst two (B. ruderatus and B. subterraneus) have undergone marked declines, the latter being declared extinct in 2000. The presence of these bumblebees in New Zealand provides an unique system in which four related species have been isolated from their source population for over 100 years, providing a rare opportunity to examine the impacts of an initial bottleneck and introduction to a novel environment on their population genetics. We used microsatellite markers to compare modern populations of B. terrestris, B. hortorum and B. ruderatus in the United Kingdom and New Zealand and to compare museum specimens of British B. subterraneus with the current New Zealand population. We used approximate Bayesian computation to estimate demographic parameters of the introduction history, notably to estimate the number of founders involved in the initial introduction. Species-specific patterns derived from genetic analysis were consistent with the predictions based on the presumed history of these populations; demographic events have left a marked genetic signature on all four species. Approximate Bayesian analyses suggest that the New Zealand population of B. subterraneus may have been founded by as few as two individuals, giving rise to low genetic diversity and marked genetic divergence from the (now extinct) UK population.

Invasive cyprinid fish in Europe originate from the single introduction of an admixed source population followed by a complex pattern of spread

The Asian cyprinid fish, the topmouth gudgeon (Pseudorasbora parva), was introduced into Europe in the 1960s. A highly invasive freshwater fish, it is currently found in at least 32 countries outside its native range. Here we analyse a 700 base pair fragment of the mitochondrial cytochrome b gene to examine different models of colonisation and spread within the invasive range, and to investigate the factors that may have contributed to their invasion success. Haplotype and nucleotide diversity of the introduced populations from continental Europe was higher than that of the native populations, although two recently introduced populations from the British Isles showed low levels of variability. Based on coalescent theory, all introduced and some native populations showed a relative excess of nucleotide diversity compared to haplotype diversity. This suggests that these populations are not in mutation-drift equilibrium, but rather that the relative inflated level of nucleotide diversity is consistent with recent admixture. This study elucidates the colonisation patterns of P. parva in Europe and provides an evolutionary framework of their invasion. It supports the hypothesis that their European colonisation was initiated by their introduction to a single location or small geographic area with subsequent complex pattern of spread including both long distance and stepping-stone dispersal. Furthermore, it was preceded by, or associated with, the admixture of genetically diverse source populations that may have augmented its invasive-potential.

Estimating parameters of speciation models based on refined summaries of the joint site-frequency spectrum

Understanding the processes and conditions under which populations diverge to give rise to distinct species is a central question in evolutionary biology. Since recently diverged populations have high levels of shared polymorphisms, it is challenging to distinguish between recent divergence with no (or very low) inter-population gene flow and older splitting events with subsequent gene flow. Recently published methods to infer speciation parameters under the isolation-migration framework are based on summarizing polymorphism data at multiple loci in two species using the joint site-frequency spectrum (JSFS). We have developed two improvements of these methods based on a more extensive use of the JSFS classes of polymorphisms for species with high intra-locus recombination rates. First, using a likelihood based method, we demonstrate that taking into account low-frequency polymorphisms shared between species significantly improves the joint estimation of the divergence time and gene flow between species. Second, we introduce a local linear regression algorithm that considerably reduces the computational time and allows for the estimation of unequal rates of gene flow between species. We also investigate which summary statistics from the JSFS allow the greatest estimation accuracy for divergence time and migration rates for low (around 10) and high (around 100) numbers of loci. Focusing on cases with low numbers of loci and high intra-locus recombination rates we show that our methods for the estimation of divergence time and migration rates are more precise than existing approaches.

Controlling for non-independence in comparative analysis of patterns across populations within species

How do we quantify patterns (such as responses to local selection) sampled across multiple populations within a single species? Key to this question is the extent to which populations within species represent statistically independent data points in our analysis. Comparative analyses across species and higher taxa have long recognized the need to control for the non-independence of species data that arises through patterns of shared common ancestry among them (phylogenetic non-independence), as have quantitative genetic studies of individuals linked by a pedigree. Analyses across populations lacking pedigree information fall in the middle, and not only have to deal with shared common ancestry, but also the impact of exchange of migrants between populations (gene flow). As a result, phenotypes measured in one population are influenced by processes acting on others, and may not be a good guide to either the strength or direction of local selection. Although many studies examine patterns across populations within species, few consider such non-independence. Here, we discuss the sources of non-independence in comparative analysis, and show why the phylogeny-based approaches widely used in cross-species analyses are unlikely to be useful in analyses across populations within species. We outline the approaches (intraspecific contrasts, generalized least squares, generalized linear mixed models and autoregression) that have been used in this context, and explain their specific assumptions. We highlight the power of 'mixed models' in many contexts where problems of non-independence arise, and show that these allow incorporation of both shared common ancestry and gene flow. We suggest what can be done when ideal solutions are inaccessible, highlight the need for incorporation of a wider range of population models in intraspecific comparative methods and call for simulation studies of the error rates associated with alternative approaches.

Restricted gene flow at the micro- and macro-geographical scale in marble trout based on mtDNA and microsatellite polymorphism

BACKGROUND

The genetic structure of the marble trout Salmo trutta marmoratus, an endemic salmonid of northern Italy and the Balkan peninsula, was explored at the macro- and micro-scale level using a combination of mitochondrial DNA (mtDNA) and microsatellite data.

RESULTS

Sequence variation in the mitochondrial control region showed the presence of nonindigenous haplotypes indicative of introgression from brown trout into marble trout. This was confirmed using microsatellite markers, which showed a higher introgression at nuclear level. Microsatellite loci revealed a strong genetic differentiation across the geographical range of marble trout, which suggests restricted gene flow both at the micro-geographic (within rivers) and macro-geographic (among river systems) scale. A pattern of Isolation-by-Distance was found, in which genetic samples were correlated with hydrographic distances. A general West-to-East partition of the microsatellite polymorphism was observed, which was supported by the geographic distribution of mitochondrial haplotypes.

CONCLUSION

While introgression at both mitochondrial and nuclear level is unlikely to result from natural migration and might be the consequence of current restocking practices, the pattern of genetic substructuring found at microsatellites has been likely shaped by historical colonization patterns determined by the geological evolution of the hydrographic networks.

Genetic panmixia and demographic dependence across the North Atlantic in the deep-sea fish, blue hake (Antimora rostrata)

The efficient investment of resources and effort into conservation strategies depends on the accurate identification of management units. At the same time, understanding the processes by which population structure evolves requires an understanding of the conditions under which panmixia may exist. Here, we study a species with an unusual, apparently sex-biased pattern of distribution, and test the hypothesis that distribution processes associated with this pattern (for example, congregating at a single dominant spawning site or periodic mixing during reproduction) could lead to panmixia over a large geographic range. Using 13 microsatellite markers, we compared 393 blue hake (Antimora rostrata) from 11 sample sites across a geographic range of over 3000 km, and found no evidence of population structure. We estimated current effective population size and found it to be large (~15,000) across the sampled area. In addition, we used simulation models to test expectations about demographic correlation among populations and our ability to detect relevant levels of gene flow. All data were consistent with the interpretation of long-range panmixia.

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.

Joint inference of microsatellite mutation models, population history and genealogies using transdimensional Markov Chain Monte Carlo

We provide a framework for Bayesian coalescent inference from microsatellite data that enables inference of population history parameters averaged over microsatellite mutation models. To achieve this we first implemented a rich family of microsatellite mutation models and related components in the software package BEAST. BEAST is a powerful tool that performs Bayesian MCMC analysis on molecular data to make coalescent and evolutionary inferences. Our implementation permits the application of existing nonparametric methods to microsatellite data. The implemented microsatellite models are based on the replication slippage mechanism and focus on three properties of microsatellite mutation: length dependency of mutation rate, mutational bias toward expansion or contraction, and number of repeat units changed in a single mutation event. We develop a new model that facilitates microsatellite model averaging and Bayesian model selection by transdimensional MCMC. With Bayesian model averaging, the posterior distributions of population history parameters are integrated across a set of microsatellite models and thus account for model uncertainty. Simulated data are used to evaluate our method in terms of accuracy and precision of θ estimation and also identification of the true mutation model. Finally we apply our method to a red colobus monkey data set as an example.

MTML-msBayes: approximate Bayesian comparative phylogeographic inference from multiple taxa and multiple loci with rate heterogeneity

Background

MTML-msBayes uses hierarchical approximate Bayesian computation (HABC) under a coalescent model to infer temporal patterns of divergence and gene flow across codistributed taxon-pairs. Under a model of multiple codistributed taxa that diverge into taxon-pairs with subsequent gene flow or isolation, one can estimate hyper-parameters that quantify the mean and variability in divergence times or test models of migration and isolation. The software uses multi-locus DNA sequence data collected from multiple taxon-pairs and allows variation across taxa in demographic parameters as well as heterogeneity in DNA mutation rates across loci. The method also allows a flexible sampling scheme: different numbers of loci of varying length can be sampled from different taxon-pairs.

Results

Simulation tests reveal increasing power with increasing numbers of loci when attempting to distinguish temporal congruence from incongruence in divergence times across taxon-pairs. These results are robust to DNA mutation rate heterogeneity. Estimating mean divergence times and testing simultaneous divergence was less accurate with migration, but improved if one specified the correct migration model. Simulation validation tests demonstrated that one can detect the correct migration or isolation model with high probability, and that this HABC model testing procedure was greatly improved by incorporating a summary statistic originally developed for this task (Wakeley's Ψ_W). The method is applied to an empirical data set of three Australian avian taxon-pairs and a result of simultaneous divergence with some subsequent gene flow is inferred.

Conclusions

To retain flexibility and compatibility with existing bioinformatics tools, MTML-msBayes is a pipeline software package consisting of Perl, C and R programs that are executed via the command line. Source code and binaries are available for download at http://msbayes.sourceforge.net/ under an open source license (GNU Public License).

Stratified dispersal and increasing genetic variation during the invasion of Central Europe by the western corn rootworm, Diabrotica virgifera virgifera

Invasive species provide opportunities for investigating evolutionary aspects of colonization processes, including initial foundations of populations and geographic expansion. Using microsatellite markers and historical information, we characterized the genetic patterns of the invasion of the western corn rootworm (WCR), a pest of corn crops, in its largest area of expansion in Europe: Central and South-Eastern (CSE) Europe. We found that the invaded area probably corresponds to a single expanding population resulting from a single introduction of WCR and that gene flow is geographically limited within the population. In contrast to what is expected in classical colonization processes, an increase in genetic variation was observed from the center to the edge of the outbreak. Control measures against WCR at the center of the outbreak may have decreased effective population size in this area which could explain this observed pattern of genetic variation. We also found that small remote outbreaks in southern Germany and north-eastern Italy most likely originated from long-distance dispersal events from CSE Europe. We conclude that the large European outbreak is expanding by stratified dispersal, involving both continuous diffusion and discontinuous long-distance dispersal. This latter mode of dispersal may accelerate the expansion of WCR in Europe in the future.

The invasion route for an insect pest species: the tobacco aphid in the New World

Biological invasions are rapid evolutionary events in which populations are usually subject to a founder event during introduction followed by rapid adaptation to the new environment. Molecular tools and Bayesian approaches have shown their utility in exploring different evolutionary scenarios regarding the invasion routes of introduced species. We examined the situation for the tobacco aphid, Myzus persicae nicotianae, a recently introduced aphid species in Chile. Using seven microsatellite loci and approximate Bayesian computation, we studied populations of the tobacco aphid sampled from several American and European countries, identifying the most likely source populations and tracking the route of introduction to Chile. Our population genetic data are consistent with available historical information, pointing to an introduction route of the tobacco aphid from Europe and/or from other putative populations (e.g. Asia) with subsequent introduction through North America to South America. Evidence of multiple introductions to North America from different genetic pools, with successive loss of genetic diversity from Europe towards North America and a strong bottleneck during the southward introduction to South America, was also found. Additionally, we examined the special case of a widespread multilocus genotype that was found in all American countries examined. This case provides further evidence for the existence of highly successful genotypes or 'superclones' in asexually reproducing organisms.

The confounding effects of population structure, genetic diversity and the sampling scheme on the detection and quantification of population size changes

The idea that molecular data should contain information on the recent evolutionary history of populations is rather old. However, much of the work carried out today owes to the work of the statisticians and theoreticians who demonstrated that it was possible to detect departures from equilibrium conditions (e.g., panmictic population/mutation-drift equilibrium) and interpret them in terms of deviations from neutrality or stationarity. During the last 20 years the detection of population size changes has usually been carried out under the assumption that samples were obtained from populations that can be approximated by a Wright-Fisher model (i.e., assuming panmixia, demographic stationarity, etc.). However, natural populations are usually part of spatial networks and are interconnected through gene flow. Here we simulated genetic data at mutation and migration-drift equilibrium under an n-island and a stepping-stone model. The simulated populations were thus stationary and not subject to any population size change. We varied the level of gene flow between populations and the scaled mutation rate. We also used several sampling schemes. We then analyzed the simulated samples using the Bayesian method implemented in MSVAR, the Markov Chain Monte Carlo simulation program, to detect and quantify putative population size changes using microsatellite data. Our results show that all three factors (genetic differentiation/gene flow, genetic diversity, and the sampling scheme) play a role in generating false bottleneck signals. We also suggest an ad hoc method to counter this effect. The confounding effect of population structure and of the sampling scheme has practical implications for many conservation studies. Indeed, if population structure is creating "spurious" bottleneck signals, the interpretation of bottleneck signals from genetic data might be less straightforward than it would seem, and several studies may have overestimated or incorrectly detected bottlenecks in endangered species.

The narrow endemic Norwegian peat moss Sphagnum troendelagicum originated before the last glacial maximum

It is commonly found that individual hybrid, polyploid species originate recurrently and that many polyploid species originated relatively recently. It has been previously hypothesized that the extremely rare allopolyploid peat moss Sphagnum troendelagicum has originated multiple times, possibly after the last glacial maximum in Scandinavia. This conclusion was based on low linkage disequilibrium in anonymous genetic markers within natural populations, in which sexual reproduction has never been observed. Here we employ microsatellite markers and chloroplast DNA (cpDNA)-encoded trnG sequence data to test hypotheses concerning the origin and evolution of this species. We find that S. tenellum is the maternal progenitor and S. balticum is the paternal progenitor of S. troendelagicum. Using various Bayesian approaches, we estimate that S. troendelagicum originated before the Holocene but not before c. 80,000 years ago (median expected time since speciation 40 000 years before present). The observed lack of complete linkage disequilibrium in the genome of this species suggests cryptic sexual reproduction and recombination. Several lines of evidence suggest multiple origins for S. troendelagicum, but a single origin is supported by approximate Bayesian computation analyses. We hypothesize that S. troendelagicum originated in a peat-dominated refugium before last glacial maximum, and subsequently immigrated to central Norway by means of spore flow during the last thousands of years.

Reconstructing routes of invasion using genetic data: why, how and so what?

Detailed knowledge about the geographical pathways followed by propagules from their source to the invading populations--referred to here as routes of invasion-provides information about the history of the invasion process and the origin and genetic composition of the invading populations. The reconstruction of invasion routes is required for defining and testing different hypotheses concerning the environmental and evolutionary factors responsible for biological invasions. In practical terms, it facilitates the design of strategies for controlling or preventing invasions. Most of our knowledge about the introduction routes of invasive species is derived from historical and observational data, which are often sparse, incomplete and, sometimes, misleading. In this context, population genetics has proved a useful approach for reconstructing routes of introduction, highlighting the complexity and the often counterintuitive nature of the true story. This approach has proved particularly useful since the recent development of new model-based methods, such as approximate Bayesian computation, making it possible to make quantitative inferences in the complex evolutionary scenarios typically encountered in invasive species. In this review, we summarize some of the fundamental aspects of routes of invasion, explain why the reconstruction of these routes is useful for addressing both practical and theoretical questions, and comment on the various reconstruction methods available. Finally, we consider the main insights obtained to date from studies of invasion routes.

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.

RESULTS

We used controlled simulated data sets generated under evolutionary scenarios involving various divergence and admixture events to evaluate the effect of mixing autosomal microsatellite, mtDNA and/or nuclear autosomal DNA sequence data on inferences. This evaluation included the comparison of competing scenarios and the quantification of their relative support, and the estimation of parameter posterior distributions under a given scenario. We also considered a set of scenarios often compared when making ABC inferences on the routes of introduction of invasive species to illustrate the interest of the new model checking option of DIYABC to assess model misfit.

CONCLUSIONS

Our new developments of the integrated software DIYABC should be particularly useful to make inference on complex evolutionary scenarios involving both recent and ancient historical events and using various types of molecular markers in diploid or haploid organisms. They offer a handy way for non-expert users to achieve model checking computation within an ABC framework, hence filling up a gap of ABC analysis. The software DIYABC V1.0 is freely available at http://www1.montpellier.inra.fr/CBGP/diyabc.

ABC-SysBio--approximate Bayesian computation in Python with GPU support

MOTIVATION

The growing field of systems biology has driven demand for flexible tools to model and simulate biological systems. Two established problems in the modeling of biological processes are model selection and the estimation of associated parameters. A number of statistical approaches, both frequentist and Bayesian, have been proposed to answer these questions.

RESULTS

Here we present a Python package, ABC-SysBio, that implements parameter inference and model selection for dynamical systems in an approximate Bayesian computation (ABC) framework. ABC-SysBio combines three algorithms: ABC rejection sampler, ABC SMC for parameter inference and ABC SMC for model selection. It is designed to work with models written in Systems Biology Markup Language (SBML). Deterministic and stochastic models can be analyzed in ABC-SysBio.

AVAILABILITY

http://abc-sysbio.sourceforge.net

ABC as a flexible framework to estimate demography over space and time: some cons, many pros

The analysis of genetic variation to estimate demographic and historical parameters and to quantitatively compare alternative scenarios recently gained a powerful and flexible approach: the Approximate Bayesian Computation (ABC). The likelihood functions does not need to be theoretically specified, but posterior distributions can be approximated by simulation even assuming very complex population models including both natural and human-induced processes. Prior information can be easily incorporated and the quality of the results can be analysed with rather limited additional effort. ABC is not a statistical analysis per se, but rather a statistical framework and any specific application is a sort of hybrid between a simulation and a data-analysis study. Complete software packages performing the necessary steps under a set of models and for specific genetic markers are already available, but the flexibility of the method is better exploited combining different programs. Many questions relevant in ecology can be addressed using ABC, but adequate amount of time should be dedicated to decide among alternative options and to evaluate the results. In this paper we will describe and critically comment on the different steps of an ABC analysis, analyse some of the published applications of ABC and provide user guidelines.

Approximate Bayesian Computation (ABC) in practice

Understanding the forces that influence natural variation within and among populations has been a major objective of evolutionary biologists for decades. Motivated by the growth in computational power and data complexity, modern approaches to this question make intensive use of simulation methods. Approximate Bayesian Computation (ABC) is one of these methods. Here we review the foundations of ABC, its recent algorithmic developments, and its applications in evolutionary biology and ecology. We argue that the use of ABC should incorporate all aspects of Bayesian data analysis: formulation, fitting, and improvement of a model. ABC can be a powerful tool to make inferences with complex models if these principles are carefully applied.

An examination of genetic diversity and effective population size in Atlantic salmon populations

Effective population size (Ne) is an important parameter in the conservation of genetic diversity. Comparative studies of empirical data that gauge the relative accuracy of Ne methods are limited, and a better understanding of the limitations and potential of Ne estimators is needed. This paper investigates genetic diversity and Ne in four populations of wild anadromous Atlantic salmon (Salmo salar L.) in Europe, from the Rivers Oir and Scorff (France) and Spey and Shin (Scotland). We aimed to understand present diversity and historical processes influencing current population structure. Our results showed high genetic diversity for all populations studied, despite their wide range of current effective sizes. To improve understanding of high genetic diversity observed in the populations with low effective size, we developed a model predicting present diversity as a function of past demographic history. This suggested that high genetic diversity could be explained by a bottleneck occurring within recent centuries rather than by gene flow. Previous studies have demonstrated the efficiency of coalescence models to estimate Ne. Using nine subsets from 37 microsatellite DNA markers from the four salmon populations, we compared three coalescence estimators based on single and dual samples. Comparing Ne estimates confirmed the efficiency of increasing the number and variability of microsatellite markers. This efficiency was more accentuated for the smaller populations. Analysis with low numbers of neutral markers revealed uneven distributions of allelic frequencies and overestimated short-term Ne. In addition, we found evidence of artificial stock enhancement using native and non-native origin. We propose estimates of Ne for the four populations, and their applications for salmon conservation and management are discussed.

Genetic structure in African populations: implications for human demographic history

The continent of Africa is the source of all anatomically modern humans that dispersed across the planet during the past 100,000 years. As such, African populations are characterized by high genetic diversity and low levels of linkage disequilibrium (LD) among loci, as compared to populations from other continents. African populations also possess a number of genetic adaptations that have evolved in response to the diverse climates, diets, geographic environments, and infectious agents that characterize the African continent. Recently, Tishkoff et al. (2009) performed a genome-wide analysis of substructure based on DNA from 2432 Africans from 121 geographically diverse populations. The authors analyzed patterns of variation at 1327 nuclear microsatellite and insertion/deletion markers and identified 14 ancestral population clusters that correlate well with self-described ethnicity and shared cultural or linguistic properties. The results suggest that African populations may have maintained a large and subdivided population structure throughout much of their evolutionary history. In this chapter, we synthesize recent work documenting evidence of African population structure and discuss the implications for inferences about evolutionary history in both African populations and anatomically modern humans as a whole.

Bridgehead effect in the worldwide invasion of the biocontrol harlequin ladybird

Recent studies of the routes of worldwide introductions of alien organisms suggest that many widespread invasions could have stemmed not from the native range, but from a particularly successful invasive population, which serves as the source of colonists for remote new territories. We call here this phenomenon the invasive bridgehead effect. Evaluating the likelihood of such a scenario is heuristically challenging. We solved this problem by using approximate Bayesian computation methods to quantitatively compare complex invasion scenarios based on the analysis of population genetics (microsatellite variation) and historical (first observation dates) data. We applied this approach to the Harlequin ladybird Harmonia axyridis (HA), a coccinellid native to Asia that was repeatedly introduced as a biocontrol agent without becoming established for decades. We show that the recent burst of worldwide invasions of HA followed a bridgehead scenario, in which an invasive population in eastern North America acted as the source of the colonists that invaded the European, South American and African continents, with some admixture with a biocontrol strain in Europe. This demonstration of a mechanism of invasion via a bridgehead has important implications both for invasion theory (i.e., a single evolutionary shift in the bridgehead population versus multiple changes in case of introduced populations becoming invasive independently) and for ongoing efforts to manage invasions by alien organisms (i.e., heightened vigilance against invasive bridgeheads).

ABCtoolbox: a versatile toolkit for approximate Bayesian computations

BACKGROUND

The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations.

RESULTS

Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females.

CONCLUSION

ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.