Approximate Bayesian Computation Research Articles

Integrative demographic modelling reduces uncertainty in estimated rates of species' historical range shifts

AbstractAimBiogeographers have used three primary data types to examine shifts in tree ranges in response to past climate change: fossil pollen, genetic data and contemporary occurrences. Although recent efforts have explored formal integration of these types of data, we have limited understanding of how integration affects estimates of range shift rates and their uncertainty. We compared estimates of biotic velocity (i.e. rate of species' range shifts) using each data type independently to estimates obtained using integrated models.LocationEastern North America.TaxonFraxinus pennsylvanica Marshall (green ash).MethodsUsing fossil pollen, genomic data and modern occurrence data, we estimated biotic velocities directly from 24 species distribution models (SDMs) and 200 pollen surfaces created with a novel Bayesian spatio‐temporal model. We compared biotic velocity from these analyses to estimates based on coupled demographic‐coalescent simulations and Approximate Bayesian Computation that combined fossil pollen and SDMs with population genomic data collected across the F. pennsylvanica range.ResultsPatterns and magnitude of biotic velocity over time varied by the method used to estimate past range dynamics. Estimates based on fossil pollen yielded the highest rates of range movement. Overall, integrating genetic data with other data types in our simulation‐based framework reduced apparent uncertainty in biotic velocity estimates and resulted in greater similarity in estimates between SDM‐ and pollen‐integrated analyses.Main ConclusionsBy reducing uncertainty in our assessments of range shifts, integration of data types improves our understanding of the past distribution of species. Based on these results, we propose further steps to reach the integration of these three lines of biogeographical evidence into a unified analytical framework.

FitMultiCell: simulating and parameterizing computational models of multi-scale and multi-cellular processes.

Biological tissues are dynamic and highly organized. Multi-scale models are helpful tools to analyse and understand the processes determining tissue dynamics. These models usually depend on parameters that need to be inferred from experimental data to achieve a quantitative understanding, to predict the response to perturbations, and to evaluate competing hypotheses. However, even advanced inference approaches such as approximate Bayesian computation (ABC) are difficult to apply due to the computational complexity of the simulation of multi-scale models. Thus, there is a need for a scalable pipeline for modeling, simulating, and parameterizing multi-scale models of multi-cellular processes. Here, we present FitMultiCell, a computationally efficient and user-friendly open-source pipeline that can handle the full workflow of modeling, simulating, and parameterizing for multi-scale models of multi-cellular processes. The pipeline is modular and integrates the modeling and simulation tool Morpheus and the statistical inference tool pyABC. The easy integration of high-performance infrastructure allows to scale to computationally expensive problems. The introduction of a novel standard for the formulation of parameter inference problems for multi-scale models additionally ensures reproducibility and reusability. By applying the pipeline to multiple biological problems, we demonstrate its broad applicability, which will benefit in particular image-based systems biology. FitMultiCell is available open-source at https://gitlab.com/fitmulticell/fit.

Efficient multifidelity likelihood-free Bayesian inference with adaptive computational resource allocation

Likelihood-free Bayesian inference algorithms are popular methods for inferring the parameters of complex stochastic models with intractable likelihoods. These algorithms characteristically rely heavily on repeated model simulations. However, whenever the computational cost of simulation is even moderately expensive, the significant burden incurred by likelihood-free algorithms leaves them infeasible for many practical applications. The multifidelity approach has been introduced in the context of approximate Bayesian computation to reduce the simulation burden of likelihood-free inference without loss of accuracy, by using the information provided by simulating computationally cheap, approximate models in place of the model of interest. In this work we demonstrate that multifidelity techniques can be applied in the general likelihood-free Bayesian inference setting. Analytical results on the optimal allocation of computational resources to simulations at different levels of fidelity are derived, and subsequently implemented practically. We provide an adaptive multifidelity likelihood-free inference algorithm that learns the relationships between models at different fidelities and adapts resource allocation accordingly, and demonstrate that this algorithm produces posterior estimates with near-optimal efficiency.

Calibration methods to fit parameters within complex biological models.

Mathematical and computational models of biological systems are increasingly complex, typically comprised of hybrid multi-scale methods such as ordinary differential equations, partial differential equations, agent-based and rule-based models, etc. These mechanistic models concurrently simulate detail at resolutions of whole host, multi-organ, organ, tissue, cellular, molecular, and genomic dynamics. Lacking analytical and numerical methods, solving complex biological models requires iterative parameter sampling-based approaches to establish appropriate ranges of model parameters that capture corresponding experimental datasets. However, these models typically comprise large numbers of parameters and therefore large degrees of freedom. Thus, fitting these models to multiple experimental datasets over time and space presents significant challenges. In this work we undertake the task of reviewing, testing, and advancing calibration practices across models and dataset types to compare methodologies for model calibration. Evaluating the process of calibrating models includes weighing strengths and applicability of each approach as well as standardizing calibration methods. Our work compares the performance of our model agnostic Calibration Protocol (CaliPro) with approximate Bayesian computing (ABC) to highlight strengths, weaknesses, synergies, and differences among these methods. We also present next-generation updates to CaliPro. We explore several model implementations and suggest a decision tree for selecting calibration approaches to match dataset types and modeling constraints.

Postglacial phylogeography, admixture, and evolution of red spruce (Picea rubens Sarg.) in Eastern North America.

Climate change is a major evolutionary force that can affect the structure of forest ecosystems worldwide. Red spruce (Picea rubens Sarg.) has recently faced a considerable decline in the Southern Appalachians due to rapid environmental change, which includes historical land use, and atmospheric pollution. In the northern part of its range, red spruce is sympatric with closely related black spruce (Picea mariana (Mill.) B.S.P.), where introgressive hybridization commonly occurs. We investigated range-wide population genetic diversity and structure and inferred postglacial migration patterns and evolution of red spruce using nuclear microsatellites. Moderate genetic diversity and differentiation were observed in red spruce. Genetic distance, maximum likelihood and Bayesian analyses identified two distinct population clusters: southern glacial populations, and the evolutionarily younger northern populations. Approximate Bayesian computation suggests that patterns of admixture are the result of divergence of red spruce and black spruce from a common ancestor and then introgressive hybridization during post-glacial migration. Genetic diversity, effective population size (Ne) and genetic differentiation were higher in the northern than in the southern populations. Our results along with previously available fossil data suggest that Picea rubens and Picea mariana occupied separate southern refugia during the last glaciation. After initial expansion in the early Holocene, these two species faced a period of recession and formed a secondary coastal refugium, where introgressive hybridization occurred, and then both species migrated northward. As a result, various levels of black spruce alleles are present in the sympatric red spruce populations. Allopatric populations of P. rubens and P. mariana have many species-specific alleles and much fewer alleles from common ancestry. The pure southern red spruce populations may become critically endangered under projected climate change conditions as their ecological niche may disappear.

The domestication and breeding history of Castanea crenata Siebold et Zucc. estimated by direction of gene flow and approximate Bayesian computation

The domestication and breeding history of Castanea crenata Siebold et Zucc. estimated by direction of gene flow and approximate Bayesian computation

Combining uncertain machine learning predictions and numerical simulation results for the extreme value analysis of cyclone-induced wave heights – Application in Guadeloupe

Assessing return level RL (with return period typically ranging from 100 to 500 years) for extreme waves in cyclone-prone regions is often made problematic by the lack of sufficient representative samples to properly fit the extreme value probability distributions. Motivated by the Guadeloupe context (French West Indies), we address this problem when the wave numerical model is too expensive to be run a large number of times. A possible option is to use a machine learning (ML) model in place of the long-running numerical mode. By construction, ML predictions are however uncertain, because they are learned from a limited number of pre-calculated wave simulation results. We propose to account for this type of error along the inference of the parameters of the extreme value probability distribution within an Approximate Bayesian Computation (ABC) scheme. Using a subset of the database of numerically computed HS for Guadeloupe (for approximately 700 synthetic cyclones representative of 1000 years of cyclonic activity), we train a random forest (RF) regression model to relate the cyclone characteristics (radius, atmospheric pressure, distance to cyclone eye) to HS. The quantile RF model is then used to model the prediction error within the ABC scheme. By comparison to the 100-year and 500-year RL reference solutions (calculated using the entire database), we show that the ML-based approach achieves low bias and high reliability of the RL estimates at locations both along Guadeloupe coasts and in deep ocean environments for low sample size (down to ∼70). Provided that the prediction error is low-to-moderate, integrating this type of uncertainty improves the performance of the ML-based approach, and decreases the computational burden of the return level estimation.

Estimating seroconversion rates accounting for repeated infections by approximate Bayesian computation.

This study presents a novel approach for inferring the incidence of infections by employing a quantitative model of the serum antibody response. Current methodologies often overlook the cumulative effect of an individual's infection history, making it challenging to obtain a marginal distribution for antibody concentrations. Our proposed approach leverages approximate Bayesian computation to simulate cross-sectional antibody responses and compare these to observed data, factoring in the impact of repeated infections. We then assess the empirical distribution functions of the simulated and observed antibody data utilizing Kolmogorov deviance, thereby incorporating a goodness-of-fit check. This new method not only matches the computational efficiency of preceding likelihood-based analyses but also facilitates the joint estimation of antibody noise parameters. The results affirm that the predictions generated by our within-host model closely align with the observed distributions from cross-sectional samples of a well-characterized population. Our findings mirror those of likelihood-based methodologies in scenarios of low infection pressure, such as the transmission of pertussis in Europe. However, our simulations reveal that in settings of higher infection pressure, likelihood-based approaches tend to underestimate the force of infection. Thus, our novel methodology presents significant advancements in estimating infection incidence, thereby enhancing our understanding of disease dynamics in the field of epidemiology.

Estimating two key dimensions of cultural transmission from archaeological data

Cultural-evolutionary modeling of archaeological data faces numerous challenges, perhaps the most significant being the mismatch between models of microscale activities and the macroevolutionary scale of the archaeological record. This is especially the case with identifying different kinds of social learning reflected in the record. Here we present a computational approach to social learning using a new model that compares frequencies of stylistic traits through time to an evolutionary model of social learning. Two dimensions of cultural evolution—popularity bias and information transparency—help unify a range of hitherto competing models of social learning. This model has never successfully been calibrated to real-world data, with the sparseness of archaeological data presenting an even further challenge. By calibrating the model to archaeological data, we confirm that it can be used successfully to characterize cultural transmission in the past. Our case study consists of decorative motifs on pottery from Early Neolithic Europe, ca. 5400–5000 BCE. The comparison of data to model is highly computational, involving seven different metrics and hundreds of simulations and re-samplings. Inferences are made using approximate Bayesian computation and a random-forest algorithm to estimate the best solution using a combination of all metrics. The computational modeling confirms that cultural transmission of the Neolithic pottery motifs was a process of unbiased social learning and opens the way for the exploration of a wide range of frequency data.

Population Structure and Phylogeography of Marine Gastropods Monodonta labio and M. confusa (Trochidae) along the Northwestern Pacific Coast

The genetic structure and demographic history of marine organisms are influenced by biological and ecological features, oceanic currents, and the paleo-geological effects of sea-level fluctuations. In this study, we used mitochondrial COI + 16S gene analysis to investigate the phylogeographic pattern and demography of Monodonta labio and M. confusa in Taiwan, the Ryukyu Islands, Japan, mainland China, and Korea. Our genetic analysis identified two major lineages that were not evident from the distribution patterns of different populations. The Taiwan Strait, which acted as a land bridge during Pleistocene glaciations, and the lack of strong dispersal barriers to gene flow between ocean basins after glaciations shaped the phylogeographic pattern. The genetic differentiation in the Ryukyu Islands was influenced by the specialist-generalist variation hypothesis and the Kuroshio Current. Bayesian skyline plot analyses suggested that the effective population size of M. labio and M. confusa rapidly increased approximately 0.1 and 0.075 million years ago, respectively. Our approximate Bayesian computation analysis suggested that all M. labio and M. confusa populations experienced a decline in population size following a recent population expansion and constant size, respectively. Our study provides a baseline for future investigations of the biogeographical patterns of marine gastropods in the Northwest Pacific and offers valuable insights for the management, sustainable resource utilization, and conservation of this species.

BG2: Bayesian variable selection in generalized linear mixed models with nonlocal priors for non-Gaussian GWAS data

BackgroundGenome-wide association studies (GWASes) aim to identify single nucleotide polymorphisms (SNPs) associated with a given phenotype. A common approach for the analysis of GWAS is single marker analysis (SMA) based on linear mixed models (LMMs). However, LMM-based SMA usually yields a large number of false discoveries and cannot be directly applied to non-Gaussian phenotypes such as count data.ResultsWe present a novel Bayesian method to find SNPs associated with non-Gaussian phenotypes. To that end, we use generalized linear mixed models (GLMMs) and, thus, call our method Bayesian GLMMs for GWAS (BG2). To deal with the high dimensionality of GWAS analysis, we propose novel nonlocal priors specifically tailored for GLMMs. In addition, we develop related fast approximate Bayesian computations. BG2 uses a two-step procedure: first, BG2 screens for candidate SNPs; second, BG2 performs model selection that considers all screened candidate SNPs as possible regressors. A simulation study shows favorable performance of BG2 when compared to GLMM-based SMA. We illustrate the usefulness and flexibility of BG2 with three case studies on cocaine dependence (binary data), alcohol consumption (count data), and number of root-like structures in a model plant (count data).

Cophylogeny Reconstruction Allowing for Multiple Associations Through Approximate Bayesian Computation.

Phylogenetic tree reconciliation is extensively employed for the examination of coevolution between host and symbiont species. An important concern is the requirement for dependable cost values when selecting event-based parsimonious reconciliation. Although certain approaches deduce event probabilities unique to each pair of host and symbiont trees, which can subsequently be converted into cost values, a significant limitation lies in their inability to model the invasion of diverse host species by the same symbiont species (termed as a spread event), which is believed to occur in symbiotic relationships. Invasions lead to the observation of multiple associations between symbionts and their hosts (indicating that a symbiont is no longer exclusive to a single host), which are incompatible with the existing methods of coevolution. Here, we present a method called AmoCoala (an enhanced version of the tool Coala) that provides a more realistic estimation of cophylogeny event probabilities for a given pair of host and symbiont trees, even in the presence of spread events. We expand the classical 4-event coevolutionary model to include 2 additional outcomes, vertical and horizontal spreads, that lead to multiple associations. In the initial step, we estimate the probabilities of spread events using heuristic frequencies. Subsequently, in the second step, we employ an approximate Bayesian computation approach to infer the probabilities of the remaining 4 classical events (cospeciation, duplication, host switch, and loss) based on these values. By incorporating spread events, our reconciliation model enables a more accurate consideration of multiple associations. This improvement enhances the precision of estimated cost sets, paving the way to a more reliable reconciliation of host and symbiont trees. To validate our method, we conducted experiments on synthetic datasets and demonstrated its efficacy using real-world examples. Our results showcase that AmoCoala produces biologically plausible reconciliation scenarios, further emphasizing its effectiveness.

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

AbstractIn this study, a two‐parameter, upper‐bounded probability distribution called the tau distribution is introduced and its applications in reliability engineering are presented. Each of the parameters of the tau distribution has a clear semantic meaning. Namely, one of them determines the upper bound of the distribution, while the value of the other parameter influences the shape of the cumulative distribution function. A remarkable property of this new probability distribution is that its probability density function, survival function, hazard rate function (HRF), and quantile function can all be expressed in terms of its cumulative distribution function. The HRF of the proposed probability distribution can exhibit an increasing trend and various bathtub shapes with or without a low and long‐flat phase (useful time phase), which makes this new distribution suitable for modeling a wide range of real‐world problems. The constraint maximum likelihood estimation, percentile estimation, approximate Bayesian computation, and approximate quantile estimation computation are proposed to calculate the unknown parameters of the model. The suitability of the estimation methods is verified with the aid of simulation and real‐world data results. The modeling capability of the tau distribution was compared with that of some well‐known two‐ and three‐parameter probability distributions using two data sets known from the literature of reliability engineering: time between failures data of a machining center, and time to failure of data acquisition system cards. Based on empirical results, the new distribution may be viewed as a viable competitor to the Weibull, Gamma, Chen, and modified Weibull distributions.

There and back to the present: a model‐based framework to estimate phylogenetically constrained alpha diversity gradients

The imprint left by niche evolution on the variation of biological diversity across spatial and environmental gradients is still debated among ecologists. Furthermore, understanding to what extent dispersal limitation may reinforce or blur such imprint is still a gap in the ecological knowledge. In this article we introduce a simulation approach coupled to approximate Bayesian computation (ABC) that parameterizes both the adaptation rate of species' niche positions over the evolution of a monophyletic lineage and the intensity of dispersal limitation associated with the variation of species alpha diversity among assemblages distributed across spatial and environmental gradients. The analytical tool was implemented in the R package 'mcfly' (www.r‐project.org). We evaluated the statistical performance of the analytical framework using simulated datasets, which confirmed the suitability of the analysis to estimate adaptation rate parameter but showed to be less precise in relation to the dispersal limitation parameter. Also, we found that increased dispersal limitation levels improved the parameterization of the adaptation rate of species' niche positions in simulated datasets. Further, we evaluated the role played by niche evolution and dispersal limitation on species alpha diversity variation of Phyllostomidae bats across the Neotropics. The framework proposed here shed light on the links between niche evolution, dispersal limitation and gradients of biological diversity, and thereby improved our understanding of evolutionary imprints on current biological diversity patterns.

Multiple introductions and human-aided dispersal of the UK’s most widespread non-native amphibian

The alpine newt Ichthyosaura alpestris has achieved a widespread distribution as a non-native (alien) species in Britain since its initial introduction over a century ago, but the patterns of its release and subsequent dispersal have never yet been collectively analysed. We employed a multi-disciplinary combination of methods, using geographic profiling to estimate the likely number and locations of introductions, and mitochondrial DNA polymorphisms to investigate the likely geographic source of primary introductions, including the potential role of the pet trade. In parallel we used population genetic analysis and coalescence-based modelling to infer the demographics and directionality of dispersal from founding populations. Our results show that alpine newts have been released at multiple sites. We found a close resemblance between patterns of mtDNA haplotypes in the pet trade and those of established alpine newt populations, suggesting a relationship between trade, releases, and dispersal. Results from demographic modelling using Approximate Bayesian Computation are also consistent with multiple independent introductions with limited local dispersal, and additionally suggest that releases may occur from intermediate sources, such as captive populations. Our results support the hypothesis that deliberate human activity is largely responsible for both introductions of alpine newts into the UK and their wider dispersal post-introduction. The likely involvement of the international pet trade highlights the risk that ongoing releases of I. alpestris may expose native species to pathogens, whether pre-existing or novel.

Host-associated genetic differentiation and origin of a recent host shift in the generalist parasitic weed Phelipanche ramosa.

Branched broomrape, Phelipanche ramosa (L.) Pomel, is a globally distributed parasitic weed of economic importance. In Europe, where it is native, it can infest several crops, notably tomato, tobacco, and hemp. In western France, it has recently adapted to a new host crop, oilseed rape, causing substantial damage. The aim of this study was to investigate the evolutionary relationships and genetic differentiation among P. ramosa populations infesting different hosts. We collected 1611 P. ramosa samples from 109 fields cultivated with six different crops (oilseed rape, tobacco, hemp, tomato, lentil, and celery) and distributed among six European countries. All samples were genotyped for ten microsatellite loci and a subset of samples was sequenced for two nuclear genes and two chloroplast genes. Genetic differentiation among populations was high (F ST = 0.807) and mainly driven by differentiation among different host crops, with no significant geographic structure. Genetic structure analysis identified up to seven biologically meaningful clusters that matched with host crops of origin. Reconstructed networks of sequence haplotypes and multilocus SSR genotypes showed a large genetic divergence between samples collected on oilseed rape and samples collected on other crops. The phylogeny inferred from DNA sequences placed samples collected from oilseed rape as a basal lineage. Approximate Bayesian Computations were used to compare different evolutionary scenarios of divergence among the three main genetic clusters, associated, respectively, with oilseed rape, tobacco, and hemp as host crops. The best-supported scenario indicated that P. ramosa infesting oilseed rape derived recently from an ancient, unknown lineage. Our results suggest that a more complete description of the genetic diversity of P. ramosa is still needed to uncover the likely source of the recent adaptation to oilseed rape and to anticipate future new host shifts.

Sequential Bayesian Planning for Accelerated Degradation Tests Considering Sensor Degradation

Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This article addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.

Guided wave-based characterisation of cracks in pipes utilising approximate Bayesian computation

This paper proposed a probabilistic framework of damage characterisation to detect and identify early-state cracks in pipe-like structures using ultrasonic guided waves. The crack location, crack sizes (e.g., depth and width of the crack), and Young's modulus are considered as unknown parameters in the model updating using a Bayesian approach, by which their values and the associated uncertainties are quantified. The proposed framework is developed based on approximate Bayesian computation (ABC) by subset simulation, which is a likelihood-free Bayesian approach. This algorithm estimates the posterior distributions of unknown parameters by directly accessing the similarity between the measured signals from experiments and the simulated guided wave (GW) signals from the numerical model. In this case, the evaluation of likelihood functions can be smartly circumvented during Bayesian inference. A time-domain spectral finite element (SFE) method with a cracked finite element model is employed to model the pipes to enhance the computational efficiency of the simulation and model updating. Numerical and experimental case studies are carried out to evaluate the performance of the proposed likelihood-free approach. Numerical results show the accuracy and robustness of the proposed approach in identifying unknown parameters under different scenarios. The associated uncertainties of each parameter are also quantified by analysing the statistical properties of the sample set, such as mean and coefficient of variation (COV) values. Experimental results show that the proposed method can accurately identify the unknown parameters, which further verifies the accuracy and practicability of the probabilistic damage characterisation framework.

Limited population genetic structure in the littoral gastropod Nerita tessellata (Neritimorpha, Neritidae) suggests high dispersal across the Caribbean Sea

The Caribbean Sea is characterized by an incredible biodiversity, including several endemic mollusk species, most of which have larval dispersal as their main mechanism of gene flow. It is known that the present-day population structure of a species reflects the combination of oceanographic currents, life-history traits, and historical events. Nerita tessellata is a common gastropod species in coastal, rocky, and exposed shores across the Caribbean Sea; however, little is known about the mechanisms that have shaped its distribution. Here, we tested potential barriers to gene flow and the associated genetic structure of N. tessellata in 12 populations across the Caribbean using digest restriction-site associated DNA sequencing (ddRAD-seq). Likewise, we evaluated demographic history and migration patterns through two coalescence approaches using Approximate Bayesian Computation (ABC) combined with supervised machine learning. The global analysis, based on 26,421 single nucleotide polymorphism (SNP) markers derived from ddRAD-seq, revealed low nucleotide diversity with high levels of gene flow and a lack of significant population differentiation within the survey area, indicating that N. tessellata is panmictic across the Caribbean Sea. Our results reveal that a pattern of north to south movement along Caribbean currents could potentially explain the limited genetic structure and high gene flow among N. tessellata populations. The scenarios simulated with ABC showed a constant effective population size for the ancestral population. Additionally, the four populations tested experienced demographic expansions that date to the Pleistocene. An extended pelagic larval stage could explain the large-scale genetic uniformity of this species across its distribution. Our findings contribute to understanding genetic diversity and population structure in a common gastropod within the Caribbean Sea.

Geographic Variation in Genomic Signals of Admixture Between Two Closely Related European Sepsid Fly Species

The extent of interspecific gene flow and its consequences for the initiation, maintenance, and breakdown of species barriers in natural systems remain poorly understood. Interspecific gene flow by hybridization may weaken adaptive divergence, but can be overcome by selection against hybrids, which may ultimately promote reinforcement. An informative step towards understanding the role of gene flow during speciation is to describe patterns of past gene flow among extant species. We investigate signals of admixture between allopatric and sympatric populations of the two closely related European dung fly species Sepsis cynipsea and S. neocynipsea (Diptera: Sepsidae). Based on microsatellite genotypes, we first inferred a baseline demographic history using Approximate Bayesian Computation. We then used genomic data from pooled DNA of natural and laboratory populations to test for past interspecific gene flow based on allelic configurations discordant with the inferred population tree (ABBA–BABA test with D-statistic). Comparing the detected signals of gene flow with the contemporary geographic relationship among interspecific pairs of populations (sympatric vs. allopatric), we made two contrasting observations. At one site in the French Cevennes, we detected an excess of past interspecific gene flow, while at two sites in Switzerland we observed lower signals of past microsatellite genotypes gene flow among populations in sympatry compared to allopatric populations. These results suggest that the species boundaries between these two species depend on the past and/or present eco-geographic context in Europe, which indicates that there is no uniform link between contemporary geographic proximity and past interspecific gene flow in natural populations.