Approximate Bayesian Computation Model Research Articles

Integrating genomic data and simulations to evaluate alternative species distribution models and improve predictions of glacial refugia and future responses to climate change

Climate change poses a threat to biodiversity, and it is unclear whether species can adapt to or tolerate new conditions, or migrate to areas with suitable habitats. Reconstructions of range shifts that occurred in response to environmental changes since the last glacial maximum (LGM) from species distribution models (SDMs) can provide useful data to inform conservation efforts. However, different SDM algorithms and climate reconstructions often produce contrasting patterns, and validation methods typically focus on accuracy in recreating current distributions, limiting their relevance for assessing predictions to the past or future. We modeled historically suitable habitat for the threatened North American tree green ash Fraxinus pennsylvanica using 24 SDMs built using two climate models, three calibration regions, and four modeling algorithms. We evaluated the SDMs using contemporary data with spatial block cross‐validation and compared the relative support for alternative models using a novel integrative method based on coupled demographic‐genetic simulations. We simulated genomic datasets using habitat suitability of each of the 24 SDMs in a spatially‐explicit model. Approximate Bayesian computation (ABC) was then used to evaluate the support for alternative SDMs through comparisons to an empirical population genomic dataset. Models had very similar performance when assessed with contemporary occurrences using spatial cross‐validation, but ABC model selection analyses consistently supported SDMs based on the CCSM climate model, an intermediate calibration extent, and the generalized linear modeling algorithm. Finally, we projected the future range of green ash under four climate change scenarios. Future projections using the SDMs selected via ABC suggest only minor shifts in suitable habitat for this species, while some of those that were rejected predicted dramatic changes. Our results highlight the different inferences that may result from the application of alternative distribution modeling algorithms and provide a novel approach for selecting among a set of competing SDMs with independent data.

A random-effect Wiener process degradation model with transmuted normal distribution and ABC-Gibbs algorithm for parameter estimation

Degradation modeling is a widely used technique for evaluating the reliability of high-quality products. However, unit-to-unit variability, stemming from material fluctuations during manufacturing and environmental factors, can significantly impact the accuracy of this assessment. To tackle this issue, we propose a novel time-transformed Wiener process with a transmuted normal distribution to represent unit-to-unit variability. This distribution extends the normal distribution, offering greater flexibility by capturing a wide range of non-normal, asymmetric behaviors in unit-to-unit variability. We derive closed-form expressions for the probability density function and reliability function for the model in two scenarios: (i) assuming the degradation process observations remain unaffected by measurement errors, and (ii) assuming the degradation process observations influenced by measurement errors. Due to the complexity of the likelihood functions, we employ the Gibbs version of approximate Bayesian computation (ABC-Gibbs) for parameter estimation. The effectiveness and application of the proposed method were demonstrated through numerical examples and practical application with light-emitting diode degradation data. Moreover, we use approximate Bayesian computation model choice (ABC-MC) for model comparison studies. The results indicated that our model offers improved approximations to observed degradation results compared to existing models, showcasing its superiority in generating data under the smallest tolerance threshold.

Unravelling the mystery of endemic versus translocated populations of the endangered Australian lungfish (Neoceratodus forsteri).

The Australian lungfish is a primitive and endangered representative of the subclass Dipnoi. The distribution of this species is limited to south-east Queensland, with some populations considered endemic and others possibly descending from translocations in the late nineteenth century shortly after European discovery. Attempts to resolve the historical distribution of this species have met with conflicting results based on descriptive genetic studies. Understanding if all populations are endemic or some are the result of, or influenced by, translocation events, has implications for conservation management. In this work, we analysed the genetic variation at three types of markers (mtDNA genomes, 11 STRs and 5196 nuclear SNPs) using the approximate Bayesian computation (ABC) algorithm to compare several demographic models. We postulated different contributions of Mary River and Burnett River gene pools into the Brisbane River and North Pine River populations, related to documented translocation events. We ran the analysis for each marker type separately, and we also estimated the posterior probabilities of the models combining the markers. Nuclear SNPs have the highest power to correctly identify the true model among the simulated datasets (where the model was known), but different marker types typically provided similar answers. The most supported demographic model able to explain the real dataset implies that an endemic gene pool is still present in the Brisbane and North Pine Rivers and coexists with the gene pools derived from past documented translocation events. These results support the view that ABC modelling can be useful to reconstruct complex historical translocation events with contemporary implications, and will inform ongoing conservation efforts for the endangered and iconic Australian lungfish.

Ice age land bridges to continental islands: Repeated migration of the forest‐dwelling sable in northeastern Asia

AbstractAimThe continental island system comprising Sakhalin, Hokkaido and the southern Kuril Islands (SHSK) in northeastern Asia serves as one of the southernmost habitats for many boreal and arctic organisms, with colonization via land bridges formed during glacial periods. To understand the impacts of past land‐bridge formation under Quaternary climate changes across SHSK, we investigated the demographic history of forest‐dwelling marten species.LocationSakhalin, Hokkaido and the southern Kuril Islands in northeastern Asia.TaxonSable, Martes zibellina (Carnivora, Mustelidae).MethodsWe employed multiplexed inter‐simple sequence repeat genotyping by sequencing (MIG‐seq) to obtain genome‐wide single nucleotide polymorphisms (SNPs). We tested possible scenarios of colonization and diversification for SHSK sables using several population genetics approaches including clustering analysis, population tree estimation and approximate Bayesian computation modelling. We also examined haplotype diversity for the mitochondrial ND2 gene.ResultsThe genetic diversity of the island populations and their affinity for continental populations were found to be higher in the order Sakhalin > Hokkaido > Iturup in both nuclear SNP and mitochondrial DNA analyses. Demographic analyses indicated that the sable migrated repeatedly from the continent, particularly to the neighbouring Sakhalin Island. However, only an earlier colonized lineage has persisted on marginal Iturup Island since the Middle Pleistocene. The stronger effects of repeated migrations and/or isolation influenced by the distance to the continent have shaped the contemporary genetic diversity and differentiation of sable populations in SHSK.Main ConclusionsGenome‐wide and comprehensive sampling approaches demonstrated that the forest‐dwelling sable had long‐term persistence with partial admixture of multiple lineages in SHSK, suggesting the existence of forest corridors and refugia on the islands during the last several glacial periods. The SHSK system of continental islands is valuable for understanding the impacts of Quaternary climate changes on the genetic diversity and evolutionary histories of boreal organisms.

The influence of inter-regional delays in generating large-scale brain networks of phase synchronization

Large-scale networks of phase synchronization are considered to regulate the communication between brain regions fundamental to cognitive function, but the mapping to their structural substrates, i.e., the structure-function relationship, remains poorly understood. Biophysical Network Models (BNMs) have demonstrated the influences of local oscillatory activity and inter-regional anatomical connections in generating alpha-band (8–12 Hz) networks of phase synchronization observed with Electroencephalography (EEG) and Magnetoencephalography (MEG). Yet, the influence of inter-regional conduction delays remains unknown. In this study, we compared a BNM with standard “distance-dependent delays”, which assumes constant conduction velocity, to BNMs with delays specified by two alternative methods accounting for spatially varying conduction velocities, “isochronous delays” and “mixed delays”. We followed the Approximate Bayesian Computation (ABC) workflow, i) specifying neurophysiologically informed prior distributions of BNM parameters, ii) verifying the suitability of the prior distributions with Prior Predictive Checks, iii) fitting each of the three BNMs to alpha-band MEG resting-state data (N = 75) with Bayesian optimization for Likelihood-Free Inference (BOLFI), and iv) choosing between the fitted BNMs with ABC model comparison on a separate MEG dataset (N = 30). Prior Predictive Checks revealed the range of dynamics generated by each of the BNMs to encompass those seen in the MEG data, suggesting the suitability of the prior distributions. Fitting the models to MEG data yielded reliable posterior distributions of the parameters of each of the BNMs. Finally, model comparison revealed the BNM with “distance-dependent delays”, as the most probable to describe the generation of alpha-band networks of phase synchronization seen in MEG. These findings suggest that distance-dependent delays might contribute to the neocortical architecture of human alpha-band networks of phase synchronization. Hence, our study illuminates the role of inter-regional delays in generating the large-scale networks of phase synchronization that might subserve the communication between regions vital to cognition.

A wide hybrid zone mediated by precipitation contributed to confused geographical structure of Scutiger boulengeri.

Confused geographical structure of a population and mitonuclear discordance are shaped by a combination of rapid changes in population demographics and shifts in ecology. In this study, we generated a time-calibrated phylogeny of Scutiger boulengeri, an endemic Xizang alpine toad occurring in mountain streams on the Qinghai-Xizang (Tibet) Plateau (QTP). Based on three mitochondrial DNA (mtDNA) genes, eight clades were assigned to three deeply divergent lineages. Analysis of nuclear DNA (nuDNA) genes revealed three distinct clusters without geographic structure, indicating significantly high rates of gene flow. Coalescent theory framework analysis (approximate Bayesian computation model DIYABC and Migrate-N) suggested that divergence of the main intraspecific clusters was the result of hybridization after secondary contact in the Holocene around 0.59 million years ago (Ma). The ratio of mtDNA F ST (fixation index) to nuDNA F ST was 2.3, thus failing to show male-biased dispersal. Geographic cline analysis showed that a wide hybrid zone was initially established in southwestern China, without significant reproductive isolation but with strong introgression in S. boulengeri, suggesting high hybrid fitness. Furthermore, mtDNA genes exhibited isolation by distance (IBD) while nuDNA genes exhibited significant isolation by environment (IBE). Results suggested that mitonuclear discordance may have initially been caused by geographic isolation, followed by precipitation-mediated hybridization, producing a wide hybrid zone and geographic structure confusion of nuDNA genes in S. boulengeri. This study indicated that complicated historical processes may have led to specific genetic patterns, with a specific climate factor facilitating gene flow in the system.

ZipHiC: a novel Bayesian framework to identify enriched interactions and experimental biases in Hi-C data.

MotivationSeveral computational and statistical methods have been developed to analyze data generated through the 3C-based methods, especially the Hi-C. Most of the existing methods do not account for dependency in Hi-C data.ResultsHere, we present ZipHiC, a novel statistical method to explore Hi-C data focusing on the detection of enriched contacts. ZipHiC implements a Bayesian method based on a hidden Markov random field (HMRF) model and the Approximate Bayesian Computation (ABC) to detect interactions in two-dimensional space based on a Hi-C contact frequency matrix. ZipHiC uses data on the sources of biases related to the contact frequency matrix, allows borrowing information from neighbours using the Potts model and improves computation speed using the ABC model. In addition to outperforming existing tools on both simulated and real data, our model also provides insights into different sources of biases that affects Hi-C data. We show that some datasets display higher biases from DNA accessibility or Transposable Elements content. Furthermore, our analysis in Drosophila melanogaster showed that approximately half of the detected significant interactions connect promoters with other parts of the genome indicating a functional biological role. Finally, we found that the micro-C datasets display higher biases from DNA accessibility compared to a similar Hi-C experiment, but this can be corrected by ZipHiC.Availability and implementationThe R scripts are available at https://github.com/igosungithub/HMRFHiC.git.Supplementary information Supplementary data are available at Bioinformatics online.

Colonization rather than fragmentation explains the geographical distribution and diversification of treefrogs endemic to Brazilian shield sky islands

AbstractAimGeographical patterns of montane biodiversity worldwide are related to biotic and abiotic factors, such as historical climate dynamics and species dispersal capabilities, which affect the biota from population to community levels. Understanding of processes related to population diversification in extra‐Andean Neotropical mountains remains largely unknown. Here, we tested how colonization of new areas as opposed to fragmentation of geographical ranges influenced the distribution and diversification of frogs from Brazilian mountains.LocationEspinhaço Range, the largest extra‐Andean mountain range in South America.TaxonLedge treefrog Bokermannohyla saxicola.MethodsWe used multilocus DNA and morphometric data throughout the species' distribution to delimit lineages, infer phylogenetic relationships and estimate divergence times. We used ecological niche modelling (ENM) and approximate Bayesian computation (ABC) to reconstruct changes of geographical distribution and population sizes for testing alternative hypotheses of diversification concerning fragmentation and colonization.ResultsWe found four evolutionary significant lineages that diverged from the Pliocene to the Early Pleistocene. All lineages were validated by DNA and morphometric data by independent and joint analyses. ENM showed that climatic fluctuations might have influenced the species' distribution, whereas ABC model selection further supports associated demographic changes. Taken together, a Pleistocene jump‐dispersal scenario best explains the diversification of the Bokermannohyla saxicola lineages.Main conclusionsEndemism in the Espinhaço Range is usually explained by ancient diversification, associated with long‐term isolation of climatic stable areas following climate‐driven habitat fragmentation. Our results challenge this general view, indicating recent diversification, habitat expansion and colonization of new areas as important processes explaining the current distribution and genetic diversity of B. saxicola.

Nonparametric Bayesian stochastic model updating with hybrid uncertainties

This work proposes a novel methodology to fulfil the challenging expectation in stochastic model updating to calibrate the probabilistic distributions of parameters without any assumption about the distribution formats. To achieve this task, an approximate Bayesian computation model updating framework is developed by employing staircase random variables and the Bhattacharyya distance. In this framework, parameters with aleatory and epistemic uncertainties are described by staircase random variables. The discrepancy between model predictions and observations is then quantified by the Bhattacharyya distance-based approximate likelihood. In addition, a Bayesian updating using the Euclidian distance is performed as preconditioner to avoid non-unique solutions. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated shear building model example and a challenging benchmark problem for uncertainty treatment. These examples demonstrate feasibility of the combined application of staircase random variables and the Bhattacharyya distance in stochastic model updating and uncertainty characterization.

Whole-genome re-sequencing data to infer historical demography and speciation processes in land snails: the study of two Candidula sister species.

Despite the global biodiversity of terrestrial gastropods and their ecological and economic importance, the genomic basis of ecological adaptation and speciation in land snail taxa is still largely unknown. Here, we combined whole-genome re-sequencing with population genomics to evaluate the historical demography and the speciation process of two closely related species of land snails from western Europe, Candidula unifasciata and C. rugosiuscula. Historical demographic analysis indicated fluctuations in the size of ancestral populations, probably driven by Pleistocene climatic fluctuations. Although the current population distributions of both species do not overlap, our approximate Bayesian computation model selection approach on several speciation scenarios suggested that gene flow has occurred throughout the divergence process until recently. Positively selected genes diverging early in the process were associated with intragenomic and cyto-nuclear incompatibilities, respectively, potentially fostering reproductive isolation as well as ecological divergence. Our results suggested that the speciation between species entails complex processes involving both gene flow and ecological speciation, and that further research based on whole-genome data can provide valuable understanding on species divergence.This article is part of the Theo Murphy meeting issue ‘Molluscan genomics: broad insights and future directions for a neglected phylum’.

Approximate Bayesian inference for a spatial point process model exhibiting regularity and random aggregation

AbstractIn this article, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not expressible in closed form but it is easy to simulate realizations under the model. We therefore explain how to use approximate Bayesian computation (ABC) to carry out statistical inference for this model. We suggest a method for model validation based on posterior predictions and global envelopes. We illustrate the ABC procedure and model validation approach using both simulated point patterns and a real data example.

Quantification of the weight of fingerprint evidence using a ROC-based Approximate Bayesian Computation algorithm for model selection

For more than a century, fingerprints have been used with considerable success to identify criminals or verify the identity of individuals. The categorical conclusion scheme used by fingerprint examiners, and more generally the inference process followed by forensic scientists, have been heavily criticised in the scientific and legal literature. Instead, scholars have proposed to characterise the weight of forensic evidence using the Bayes factor as the key element of the inference process. In forensic science, quantifying the magnitude of support is equally as important as determining which model is supported. Unfortunately, the complexity of fingerprint patterns render likelihood-based inference impossible. In this paper, we use an Approximate Bayesian Computation (ABC) model selection algorithm to quantify the weight of fingerprint evidence. We supplement the original ABC model selection algorithm using a Receiver Operating Characteristic curve to mitigate its known shortcomings with respect to the choice of a suitable threshold and the curse of dimensionality. In a sense, we offer an alternative to other methods that have tried to address the same issues. Our method is straightforward to implement, computationally efficient, and visually intuitive for lay individuals (i.e., jurors). We apply our method to quantify the weight of fingerprint evidence in forensic science, but we note that it can be applied to any other forensic pattern evidence.

Population Genetic Structure and Demographic History of Primula fasciculata in Southwest China.

Understanding the factors that drive the genetic structure of a species and its responses to past climatic changes is an important first step in modern population management. The response to the last glacial maximum (LGM) has been well studied, however, the effect of previous glaciation periods on plant demographic history is still not well studied. Here we investigated the population structure and demographic history of Primula fasciculata that widely occurs in the Hengduan Mountains and Qinghai-Tibetan Plateau. We obtained genomic data for 234 samples of the species using restriction site-associated DNA (RAD) sequencing and combined approximate Bayesian computation (ABC) and species distribution modeling (SDM) to evaluate the effects of multiple glaciation periods by testing several population divergence models and demographic scenarios. The analyses of population structure showed that P. fasciculata displays a striking population structure with six groups that could be identified genetically. Our ABC modeling suggested that the current groups diverged from ancestral populations located in the eastern Hengduan Mountains after the largest glaciation occurred in the region (~ 0.8–0.5 million years ago), which is consistent with the result of SDMs. Each current group has survived in different glacial refugia during the LGM and experienced expansions and/or bottlenecks since their divergence during or across the following Quaternary glacial cycles. Our study demonstrates the usefulness of population genomics for evaluating the effects of past climatic changes in alpine plant species with shallow population structure.

Inference of coevolutionary dynamics and parameters from host and parasite polymorphism data of repeated experiments.

There is a long-standing interest in understanding host-parasite coevolutionary dynamics and associated fitness effects. Increasing amounts of genomic data for both interacting species offer a promising source to identify candidate loci and to infer the main parameters of the past coevolutionary history. However, so far no method exists to perform the latter. By coupling a gene-for-gene model with coalescent simulations, we first show that three types of biological costs, namely, resistance, infectivity and infection, define the allele frequencies at the internal equilibrium point of the coevolution model. These in return determine the strength of selective signatures at the coevolving host and parasite loci. We apply an Approximate Bayesian Computation (ABC) approach on simulated datasets to infer these costs by jointly integrating host and parasite polymorphism data at the coevolving loci. To control for the effect of genetic drift on coevolutionary dynamics, we assume that 10 or 30 repetitions are available from controlled experiments or several natural populations. We study two scenarios: 1) the cost of infection and population sizes (host and parasite) are unknown while costs of infectivity and resistance are known, and 2) all three costs are unknown while populations sizes are known. Using the ABC model choice procedure, we show that for both scenarios, we can distinguish with high accuracy pairs of coevolving host and parasite loci from pairs of neutrally evolving loci, though the statistical power decreases with higher cost of infection. The accuracy of parameter inference is high under both scenarios especially when using both host and parasite data because parasite polymorphism data do inform on costs applying to the host and vice-versa. As the false positive rate to detect pairs of genes under coevolution is small, we suggest that our method complements recently developed methods to identify host and parasite candidate loci for functional studies.

Signature of the Paleo-Course Changes in the São Francisco River as Source of Genetic Structure in Neotropical Pithecopus nordestinus (Phyllomedusinae, Anura) Treefrog.

Historical processes that have interrupted gene flow between distinct evolutionary lineages have played a fundamental role in the evolution of the enormous diversity of species found in the Neotropical region. Numerous studies have discussed the role of geographic barriers and Pleistocene forest refugia in the diversification of the region’s biodiversity. In the present study, we investigated the relative contribution of these different factors to the evolutionary history of Pithecopus nordestinus, a Neotropical tree frog, which is amply distributed in the Brazilian Atlantic Forest and adjacent areas of the Caatinga biome. We used an extensive sample and multilocus DNA sequences to provide an overview of the intraspecific genetic diversity of P. nordestinus, characterize historical diversification patterns, and identify possible phylogenetic splits. We tested different scenarios of diversification based on Pleistocene Refugia and river barrier models using approximate Bayesian computation (ABC) and ecological niche modeling (ENM). The phylogenetic approach indicate the occurrence of processes of phylogeographic divergence in both time and space, related to historical shifts in the course of the São Francisco River during Plio-Pleistocene period, resulting in two principal, highly divergent clades. The ABC model provided strong statistical support for this scenario, confirming the hypothesis that the São Francisco River acted as an effective geographical barrier during vicariant events in the evolutionary history of P. nordestinus. We believe that the climatic changes that occurred during the Pleistocene also played a secondary role in the genetic signatures identified, reinforcing the divergence of populations isolated by physical barriers. These findings reinforce the conclusion that the two models of diversification (geographic barriers and refugia) are not mutually exclusive in the Neotropical domain but may interact extensively during the diversification of species on a regional scale.

Genetic Diversity and Population Structure of Wild Sunflower (Helianthus annuus L.) in Argentina: Reconstructing Its Invasion History.

Studying the levels and patterns of genetic diversity of invasive populations is important to understand the evolutionary and ecological factors promoting invasions and for better designing preventive and control strategies. Wild sunflower (Helianthus annuus L.) is native to North America and was introduced, and has become invasive, in several countries, including Argentina (ARG). Here, using classical population genetic analyses and approximate Bayesian computation (ABC) modeling, we studied the invasion history of wild sunflower in ARG. We analyzed 115 individuals belonging to 15 populations from ARG (invasive range) and United States (US, native range) at 14 nuclear and 3 chloroplast simple sequence repeat markers along with 23 phenotypic variables. Populations from ARG showed similar levels of nuclear genetic diversity to US populations and higher genetic diversity in the chloroplast genome, indicating no severe genetic bottlenecks during the invasion process. Bayesian clustering analysis, based on nuclear markers, suggests the presence of 3 genetic clusters, all present in both US and ARG. Discriminant analysis of principal components (DAPC) detected an overall low population structure between central US and ARG populations but separated 2 invasive populations from the rest. ABC modeling supports multiple introductions but also a southward dispersal within ARG. Genetic and phenotypic data support the central US as a source of introduction while the source of secondary introductions could not be resolved. Finally, using genetic markers from the chloroplast genome, we found lower population structure in ARG when compared with US populations, suggesting a role for seed-mediated gene flow in Argentina.

Phylogenomics Reveals an Ancient Hybrid Origin of the Persian Walnut.

Persian walnut (Juglans regia) is cultivated worldwide for its high-quality wood and nuts, but its origin has remained mysterious because in phylogenies it occupies an unresolved position between American black walnuts and Asian butternuts. Equally unclear is the origin of the only American butternut, J. cinerea. We resequenced the whole genome of 80 individuals from 19 of the 22 species of Juglans and assembled the genome of its relatives Pterocarya stenoptera and Platycarya strobilacea. Using phylogenetic-network analysis of single-copy nuclear genes, genome-wide site pattern probabilities, and Approximate Bayesian Computation, we discovered that J. regia (and its landrace J. sigillata) arose as a hybrid between the American and the Asian lineages and that J. cinerea resulted from massive introgression from an immigrating Asian butternut into the genome of an American black walnut. Approximate Bayesian Computation modeling placed the hybrid origin in the late Pliocene, ∼3.45 My, with both parental lineages since having gone extinct in Europe.

Species divergence and maintenance of species cohesion of three closely related Primula species in the Qinghai–Tibet Plateau

AbstractAimUnderstanding the relative roles of geography and ecology in driving speciation, population divergence and maintenance of species cohesion is of great interest to molecular ecology. Closely related species that are parapatrically distributed in mountainous areas provide an ideal model to evaluate these key issues, especially when genomic data are analyzed within a spatially and ecologically explicit context. Here, we used three closely related species of Primula that occur in the Himalayas, the Hengduan Mountains and north‐east Qinghai–Tibet Plateau (QTP) to examine spatial and ecological effects on interspecific divergence and maintenance of species cohesion.LocationHimalayas, the Hengduan Mountains and north‐east QTP.MethodsWe used genomic data for 770 samples of the three species using double‐digest restriction site‐associated DNA (ddRAD) sequencing and combined approximate Bayesian computation (ABC) modeling, generalized linear mixed modeling (GLMM) and niche‐based species distribution modeling (SDM).ResultsThe three species are clearly delimited by the RADseq data. Further ABC modeling indicates that Primula tibetica diverged first followed by a later divergence between Primula nutans and Primula fasciculata. The time frames of the divergences among the three species coincide with the uplifts of the Hengduan Mountains and the northern QTP during the late Miocene and Pliocene followed by a long period of founder events. SDMs indicate that the three species might have survived in different refugia during glaciations and came into secondary contact during the postglacial expansions but with no significant introgression. Finally, GLMM suggests that both the geographical and ecological factors play roles in population differentiation in P. fasciculata and P. tibetica, while for P. nutans, geography is the major driver of genomic variation. The different roles played by geographical and ecological factors in the three species may have affected the maintenance of species cohesion.Main conclusionOur results provide insights of unprecedented details into the start and maintenance of interspecific divergence in the context of changing environments in mountains. Our findings highlight the significance of combining population genomics with environmental data when evaluating the effects of geography and ecology on interspecific divergence and maintenance of closely related species.

Phylogeography of an endangered disjunct herb: long-distance dispersal, refugia and colonization routes.

Quaternary glacial cycles appear to have had a consistent role in shaping the genetic diversity and structure of plant species. Despite the unusual combination of the characteristics of the western Mediterranean–Macaronesian area, there are no studies that have specifically examined the effects of palaeoclimatic and palaeogeographic factors on the genetic composition and structure of annual herbs. Astragalus edulis is a disjunct endemic found in the easternmost Canary Islands and the semi-arid areas of north-eastern Africa and south-eastern Iberian Peninsula. This endangered species shows no evident adaptations to long-distance dispersal. Amplified fragment length polymorphism (AFLP) data and plastid DNA sequences were analysed from a total of 360 individuals distributed throughout the range of this species. The modelled potential distribution of A. edulis under current conditions was projected over the climatic conditions of the Last Interglacial (130 ka BP) and Last Glacial Maximum (21 ka BP) to analyse changes in habitat suitability and to look for associations between the modelling and genetic results. Amplified fragment length polymorphism analysis showed clear phylogeographic structure with four distinct genetic clusters. Approximate Bayesian computation (ABC) models based on plastid DNA sequences indicated a Middle Pleistocene long-distance dispersal event as the origin of the populations of the Canary Islands. The models also suggested south-western Morocco as the ancestral area for the species, as well as subsequent colonization of north-eastern Morocco and the Iberian Peninsula. The data compiled indicated the possibility of the presence of refuge areas at favourable locations around the High Atlas and Anti-Atlas mountain ranges. Moreover, palaeodistribution models strongly support the events inferred by ABC modelling and show the potential distribution of the species in the past, suggesting a putative colonization route.

The role of the Bhattacharyya distance in stochastic model updating

Abstract The Bhattacharyya distance is a stochastic measurement between two samples and taking into account their probability distributions. The objective of this work is to further generalize the application of the Bhattacharyya distance as a novel uncertainty quantification metric by developing an approximate Bayesian computation model updating framework, in which the Bhattacharyya distance is fully embedded. The Bhattacharyya distance between sample sets is evaluated via a binning algorithm. And then the approximate likelihood function built upon the concept of the distance is developed in a two-step Bayesian updating framework, where the Euclidian and Bhattacharyya distances are utilized in the first and second steps, respectively. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated mass-spring example and a quite challenging benchmark problem for uncertainty treatment. These examples demonstrate a gain in quality of the stochastic updating by utilizing the superior features of the Bhattacharyya distance, representing a convenient, efficient, and capable metric for stochastic model updating and uncertainty characterization.