Approximate Bayesian Computation Methods Research Articles

Mathematical Modelling of Parasite Dynamics: A Stochastic Simulation-Based Approach and Parameter Estimation via Modified Sequential-Type Approximate Bayesian Computation

The development of mathematical models for studying newly emerging and re-emerging infectious diseases has gained momentum due to global events. The gyrodactylid-fish system, like many host-parasite systems, serves as a valuable resource for ecological, evolutionary, and epidemiological investigations owing to its ease of experimental manipulation and long-term monitoring. Although this system has an existing individual-based model, it falls short in capturing information about species-specific microhabitat preferences and other biological details for different Gyrodactylus strains across diverse fish populations. This current study introduces a new individual-based stochastic simulation model that uses a hybrid τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}-leaping algorithm to incorporate this essential data, enhancing our understanding of the complexity of the gyrodactylid-fish system. We compare the infection dynamics of three gyrodactylid strains across three host populations. A modified sequential-type approximate Bayesian computation (ABC) method, based on sequential Monte Carlo and sequential importance sampling, is developed. Additionally, we establish two penalised local-linear regression methods (based on L1 and L2 regularisations) for ABC post-processing analysis to fit our model using existing empirical data. With the support of experimental data and the fitted mathematical model, we address open biological questions for the first time and propose directions for future studies on the gyrodactylid-fish system. The adaptability of the mathematical model extends beyond the gyrodactylid-fish system to other host-parasite systems. Furthermore, the modified ABC methodologies provide efficient calibration for other multi-parameter models characterised by a large set of correlated or independent summary statistics.

Impact of time resolution on estimation of energy savings using a copula-based calibration in UBEM

Urban Building Energy modelling (UBEM) has emerged in the last decade as an important tool to accelerate energy transition in the building sector. To fulfil one of its major purposes - forecasting energy savings for potential energy conservation measures at an urban scale, several challenges are still to be addressed. Two key challenges include: 1) the need to calibrate models with a large number of unknown parameters across numerous buildings (either individually or through archetype representation); 2) the limited availability of high-resolution measured data, which raises concerns about calibrated models based solely on yearly values for accurate energy savings forecast. This study addresses these challenges using a case study of 35 buildings in a district in Stockholm, Sweden. Firstly, a new iterative Approximate Bayesian Computation (ABC) method for calibration is proposed, incorporating a copula-based sampling process at each iteration. Secondly, the new calibration process is applied with three different time resolutions to examine the impact of data resolution on forecasted energy usage, particularly when applied to a classical energy conservation measure. Results demonstrate the efficiency of the new method across the 35 buildings, facilitating the rapid population of a final joint distribution for the nine unknown parameters considered in each building. While the marginals may be strongly influenced by the time resolution, the forecasted energy consumption remains identical across the three analysed time resolutions. However, a noticeable difference is observed when the ECM pertains to a formerly unknown or known parameter.

Data-driven Stochastic Model for Quantifying the Interplay Between Amyloid-beta and Calcium Levels in Alzheimer's Disease.

The abnormal aggregation of extracellular amyloid- in senile plaques resulting in calcium dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in the past to better understand the underlying molecular mechanisms driving deposition and dysregulation. Importantly, synaptic impairments, neuronal loss, and cognitive failure in AD patients are all related to the buildup of intraneuronal accumulation. Moreover, increasing evidence show a feed-forward loop between and levels, i.e. disrupts neuronal levels, which in turn affects the formation of . To better understand this interaction, we report a novel stochastic model where we analyze the positive feedback loop between and using ADNI data. A good therapeutic treatment plan for AD requires precise predictions. Stochastic models offer an appropriate framework for modelling AD since AD studies are observational in nature and involve regular patient visits. The etiology of AD may be described as a multi-state disease process using the approximate Bayesian computation method. So, utilizing ADNI data from 2-year visits for AD patients, we employ this method to investigate the interplay between and levels at various disease development phases. Incorporating the ADNI data in our physics-based Bayesian model, we discovered that a sufficiently large disruption in either metabolism or intracellular homeostasis causes the relative growth rate in both and , which corresponds to the development of AD. The imbalance of ions causes disorders by directly or indirectly affecting a variety of cellular and subcellular processes, and the altered homeostasis may worsen the abnormalities of ion transportation and deposition. This suggests that altering the balance or the balance between and by chelating them may be able to reduce disorders associated with AD and open up new research possibilities for AD therapy.

A MCMC method based on surrogate model and Gaussian process parameterization for infinite Bayesian PDE inversion

This work focuses on an inversion problem derived from parametric partial differential equations (PDEs) with an infinite-dimensional parameter, represented as a coefficient function. The objective is to estimate this coefficient function accurately despite having only noisy measurements of the PDE solution at sparse input points. Conventional methods for inversion require numerous calls to a refined PDE solver, resulting in significant computational complexity, especially for challenging PDE problems, making the inference of the coefficient function practically infeasible. To address this issue, we propose a MCMC method that combines an deep learning-based surrogate and Gaussian process parameterization to efficiently infer the posterior of the coefficient function. The surrogate model is a combination of a cost-effective coarse PDE solver and a neural network-based transformation which provides an approximate solution derived from the refined PDE solver but based on the coarse PDE solution. The coefficient function is represented by Gaussian process with finite number of spatially dependent parameters and this parametric representation will be beneficial for the preconditioned Crank-Nicolson (pCN) Markov chain Monte Carlo method to sample efficiently from the posterior distribution. Approximate Bayesian computation method is used for constructing an informative dataset for the transformation learning. Our numerical examples demonstrate the effectiveness of this approach in accurately estimating the coefficient function while significantly reducing the computational burden associated with traditional inversion techniques.

Probabilistic Offline Policy Ranking with Approximate Bayesian Computation

In practice, it is essential to compare and rank candidate policies offline before real-world deployment for safety and reliability. Prior work seeks to solve this offline policy ranking (OPR) problem through value-based methods, such as Off-policy evaluation (OPE). However, they fail to analyze special case performance (e.g., worst or best cases), due to the lack of holistic characterization of policies’ performance. It is even more difficult to estimate precise policy values when the reward is not fully accessible under sparse settings. In this paper, we present Probabilistic Offline Policy Ranking (POPR), a framework to address OPR problems by leveraging expert data to characterize the probability of a candidate policy behaving like experts, and approximating its entire performance posterior distribution to help with ranking. POPR does not rely on value estimation, and the derived performance posterior can be used to distinguish candidates in worst-, best-, and average-cases. To estimate the posterior, we propose POPR-EABC, an Energy-based Approximate Bayesian Computation (ABC) method conducting likelihood-free inference. POPR-EABC reduces the heuristic nature of ABC by a smooth energy function, and improves the sampling efficiency by a pseudo-likelihood. We empirically demonstrate that POPR-EABC is adequate for evaluating policies in both discrete and continuous action spaces across various experiment environments, and facilitates probabilistic comparisons of candidate policies before deployment.

A wall-time minimizing parallelization strategy for approximate Bayesian computation.

Approximate Bayesian Computation (ABC) is a widely applicable and popular approach to estimating unknown parameters of mechanistic models. As ABC analyses are computationally expensive, parallelization on high-performance infrastructure is often necessary. However, the existing parallelization strategies leave computing resources unused at times and thus do not optimally leverage them yet. We present look-ahead scheduling, a wall-time minimizing parallelization strategy for ABC Sequential Monte Carlo algorithms, which avoids idle times of computing units by preemptive sampling of subsequent generations. This allows to utilize all available resources. The strategy can be integrated with e.g. adaptive distance function and summary statistic selection schemes, which is essential in practice. Our key contribution is the theoretical assessment of the strategy of preemptive sampling and the proof of unbiasedness. Complementary, we provide an implementation and evaluate the strategy on different problems and numbers of parallel cores, showing speed-ups of typically 10-20% and up to 50% compared to the best established approach, with some variability. Thus, the proposed strategy allows to improve the cost and run-time efficiency of ABC methods on high-performance infrastructure.

Flexible Bayesian inference on partially observed epidemics.

Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and heterogeneity of realistic contact dynamics. In this article, we consider Bayesian inference on the spreading parameters of an SIR contagion on a known, static network, where information regarding individual disease status is known only from a series of tests (positive or negative disease status). When the contagion model is complex or information such as infection and removal times is missing, the posterior distribution can be difficult to sample from. Previous work has considered the use of Approximate Bayesian Computation (ABC), which allows for simulation-based Bayesian inference on complex models. However, ABC methods usually require the user to select reasonable summary statistics. Here, we consider an inference scheme based on the Mixture Density Network compressed ABC, which minimizes the expected posterior entropy in order to learn informative summary statistics. This allows us to conduct Bayesian inference on the parameters of a partially observed contagious process while also circumventing the need for manual summary statistic selection. This methodology can be extended to incorporate additional simulation complexities, including behavioural change after positive tests or false test results.

Approximate Bayesian computational methods to estimate the strength of divergent selection in population genomics models

Statistical estimation of parameters in large models of evolutionary processes is often too computationally inefficient to pursue using exact model likelihoods, even with single-nucleotide polymorphism (SNP) data, which offers a way to reduce the size of genetic data while retaining relevant information. Approximate Bayesian Computation (ABC) to perform statistical inference about parameters of large models takes the advantage of simulations to bypass direct evaluation of model likelihoods. We develop a mechanistic model to simulate forward-in-time divergent selection with variable migration rates, modes of reproduction (sexual, asexual), length and number of migration-selection cycles. We investigate the computational feasibility of ABC to perform statistical inference and study the quality of estimates on the position of loci under selection and the strength of selection. To expand the parameter space of positions under selection, we enhance the model by implementing an outlier scan on summarized observed data. We evaluate the usefulness of summary statistics well-known to capture the strength of selection, and assess their informativeness under divergent selection. We also evaluate the effect of genetic drift with respect to an idealized deterministic model with single-locus selection. We discuss the role of the recombination rate as a confounding factor in estimating the strength of divergent selection, and emphasize its importance in break down of linkage disequilibrium (LD). We answer the question for which part of the parameter space of the model we recover strong signal for estimating the selection, and determine whether population differentiation-based summary statistics or LD–based summary statistics perform well in estimating selection.

Simulation‐based inference for reliability model selection and parameter calibration: An application to fatigue

AbstractSelecting a “useful” model among a set of competing candidate models is a common problem in many disciplines and particularly in engineering applications. For a modeller, the best model fulfills a certain purpose best (e.g., the ability to accurately predict new data, good interpolation, precise estimates of lower/upper percentiles, etc.), which is typically assessed by comparing model simulations to the observed data. Approximate Bayesian computation (ABC) which is a statistical learning technique is used in this work for reliability model selection and parameter calibration using small/moderate fatigue life data sets. This is always the case in material fatigue due to the high cost and low efficiency of fatigue tests which are bottleneck problem when designing components/structures with regard to fatigue. The ABC is a likelihood‐free based method which means that it needs only a generative model to simulate the data. The proposed method provides a formal rank of the competing reliability models by eliminating gradually the least likely models in a parsimonious manner. It is flexible since it offers the possibility to use different metrics to measure the discrepancy between simulated and observed data. The choice of the appropriate distance function depends essentially on the purpose of model selection. Through various examples, it has been demonstrated that the ABC method has a number of very attractive properties, which makes it especially useful in probabilistic risk assessment and reliability analysis.

Quantifying health risks from ESBL-producing Escherichia coli in Dutch broiler production chains and potential interventions using compartmental models

Extended-spectrum beta-lactamase (ESBL)-producing Escherichia coli (E. coli) in animals are considered a human health threat, because this type of bacteria can serve as a reservoir of antibiotic resistant genes and act as a continuous threat of the emergence of new resistant bacteria, in addition to the direct effect of making infection untreatable. Although the prevalence of ESBL producing bacteria in broilers was drastically reduced in the Netherlands, chicken meat still has the highest prevalence among meat products. Therefore, further control of the ESBL-producing E. coli in the broiler production chain is important to reduce public health risks. The main objectives of this study were to evaluate the effectiveness of intervention scenarios to reduce the transmission of ESBL-producing E. coli in the broiler production chain and to quantitatively estimate the risk to public health. In this study, we developed two different types of transmission models that described the observed time-related decline in prevalence during a production round: one with time-dependent decline in susceptibility and one with partial immunity to phylogenetic groups. Both models incorporated the environmental contamination effect between production rounds and within flocks. The parameter values, including transmission rate and recovery rate, were estimated by Approximate Bayesian computation (ABC) method using data from a longitudinal study in a Dutch organic broiler farm. We applied the models to the three production stages in the broiler production chain, beginning from the Parent Stock (PS) farms, the hatcheries, and to the broiler farms. In our models, eggs were collected from different parent stock farms and transported to the hatchery and from there to a broiler farm.The size of a flock and the number of farms were adjusted to the Dutch situation. Both models were able to describe the observed dynamics within and between the production stages equally well, with estimated ESBL-producing E. coli prevalence of 8.98% and 11.47% in broilers at slaughter and 0.12% and 0.15% in humans due to chicken consumption. Both models indicated that improving farm management to eliminate the bacteria from the environment was the most effective intervention, making this outcome robust. Although chicken meat consumption is not a major risk factor for human carriage of the bacteria according to our models, reducing the bacteria in the PS and broiler farm environment to at least one percent can further decrease the prevalence in humans.

Probabilistic model updating of civil structures with a decentralized variational inference approach

The quantification of uncertainties in civil structures poses a significant challenge due to the need to update a large number of unknown parameters, which can significantly increase the computational workload. A potential solution to this problem is the use of Approximate Bayesian Computation (ABC) approaches, which have gained attention in recent years. However, most existing ABC methods are limited in their ability to handle a large number of unknowns. To address this limitation, this study proposes a decentralized approach for uncertainty quantification in civil structures. In this approach, the structure is divided into several parts, and the uncertainties in each part are estimated independently. The proposed method utilizes the wavelet domain technique to eliminate the interfacial force of the target part and employs a recently developed variational inference approach to quantify the uncertainty in the target substructure. A three-span beam, a 2D truss, and an eight-story building were tested to evaluate the efficiency and feasibility of this approach. The results show that uncertainties in large structures can be estimated and that the proposed method is robust to high levels of measurement noise.

Global stability and parameter analysis reinforce therapeutic targets of PD-L1-PD-1 and MDSCs for glioblastoma

Glioblastoma (GBM) is an aggressive primary brain cancer that currently has minimally effective treatments. Like other cancers, immunosuppression by the PD-L1-PD-1 immune checkpoint complex is a prominent axis by which glioma cells evade the immune system. Myeloid-derived suppressor cells (MDSCs), which are recruited to the glioma microenviroment, also contribute to the immunosuppressed GBM microenvironment by suppressing T cell functions. In this paper, we propose a GBM-specific tumor-immune ordinary differential equations model of glioma cells, T cells, and MDSCs to provide theoretical insights into the interactions between these cells. Equilibrium and stability analysis indicates that there are unique tumorous and tumor-free equilibria which are locally stable under certain conditions. Further, the tumor-free equilibrium is globally stable when T cell activation and the tumor kill rate by T cells overcome tumor growth, T cell inhibition by PD-L1-PD-1 and MDSCs, and the T cell death rate. Bifurcation analysis suggests that a treatment plan that includes surgical resection and therapeutics targeting immune suppression caused by the PD-L1-PD1 complex and MDSCs results in the system tending to the tumor-free equilibrium. Using a set of preclinical experimental data, we implement the approximate Bayesian computation (ABC) rejection method to construct probability density distributions that estimate model parameters. These distributions inform an appropriate search curve for global sensitivity analysis using the extended fourier amplitude sensitivity test. Sensitivity results combined with the ABC method suggest that parameter interaction is occurring between the drivers of tumor burden, which are the tumor growth rate and carrying capacity as well as the tumor kill rate by T cells, and the two modeled forms of immunosuppression, PD-L1-PD-1 immune checkpoint and MDSC suppression of T cells. Thus, treatment with an immune checkpoint inhibitor in combination with a therapeutic targeting the inhibitory mechanisms of MDSCs should be explored.

Approximate Bayesian computation with semiparametric density ratio model

Approximate Bayesian computation (ABC) is a likelihood-free inference method commonly employed for statistical inference in models with unknown or complex likelihood functions. ABC estimates the posterior distributions of model parameters by comparing summary statistics of the simulated and observed data. However, the selection of informative summary statistics can be challenging in practice. In this study, we propose a summary-statistic-free method called ABC with semiparametric empirical likelihood ratio (ABC-SELR). This method utilises the empirical likelihood within the framework of the semiparametric density ratio model to assess the simulated parameters via testing whether the simulated and observed data conform to the same distribution. By eliminating the need for choosing summary statistics, our approach avoids potential information loss. Furthermore, the proposed method captures the shared characteristics between the simulated and observed data, leading to improved efficiency. We demonstrate the accuracy and efficiency of ABC-SELR by comparing with existing ABC methods through numerical simulations.

Selection of models and parameter estimation for monitoring the COVID-19 epidemic in Brazil via Bayesian inference

In 2019, a new strain of coronavirus led to an outbreak of disease cases named COVID-19, evolving rapidly into a pandemic. In Brazil, delayed decision making and lack of knowledge have resulted in an alarming increase in daily transmission and deaths. In this context, researchers used mathematical models to assist in determining the parameters that act in the spread of diseases, revealing containment measures. However, numerous mathematical models exist in the literature, each with specific parameters to be specified, leading to an important question about which model best represents the pandemic behavior. In this regard, this work aims to apply the Approximate Bayesian Computation method to select the best model and simultaneously estimate the parameters to resolve the abovementioned issue. The models adopted were susceptible-infected-recovered (SIR), susceptible-exposed-infected-recovered (SEIR), susceptible-infected-recovered-susceptible (SIRS), and susceptible-exposed-infected-recovered-susceptible (SEIRS). Approximate Bayesian Computation Monte Carlo Sequencing (ABC-SMC) was used to select among four competing models to represent the number of infected individuals and to estimate the model parameters based on three periods of Brazil COVID-19 data. A forecasting test was performed to test the ABC-SMC algorithm and the selected models for two months. The result was compared with the actual number of infected that were reported. Among the teste models, it was found that the ABC-SMC algorithm had a promising performance, since the data were noisy and the models could not predict all parameters.

Parameter estimation for fractional power type diffusion: A hybrid Bayesian-deep learning approach

. In this article, we consider the problem of parameter estimation in a power-type diffusion driven by fractional Brownian motion with Hurst parameter in . To estimate the parameters of the process, we use an approximate bayesian computation method. Also, a particular case is addressed by means of variations and wavelet-type methods. Several theoretical properties of the process are studied and numerical examples are provided in order to show the small sample behavior of the proposed methods.

Conditional density estimation using population Monte Carlo based approximate Bayesian computation

Most statistical methods require likelihood evaluation to draw a statistical inference. However, in some situations, likelihood evaluation becomes difficult analytically or computationally. Different likelihood-free methods are available that eliminate the need to compute the likelihood function. Approximate Bayesian Computation (ABC) is a framework that implements likelihood-free inference and replaces the likelihood evaluation with simulations by using forward modeling. The goal of ABC methods is to approximate the posterior distribution. However, posterior approximation via ABC methods is still considerably expensive for high dimensions. ABC requires many simulations that become computationally infeasible for complex models. Here, a technique is proposed that combines a somewhat more efficient form of ABC (Population Monte Carlo, PMC) with a Conditional Density Estimation (CDE) approach. The proposed framework provides an estimation of the posterior distribution which is referred to as PMC-CDE. A simulation study is performed that provides empirical evidence to show the efficiency of PMC-CDE in terms of integrated squared error loss. Furthermore, real-life datasets manifest the application of the proposed method.

Ghost introgression facilitates genomic divergence of a sympatric cryptic lineage in Cycas revoluta.

A cryptic lineage is a genetically diverged but morphologically unrecognized variant of a known species. Clarifying cryptic lineage evolution is essential for quantifying species diversity. In sympatric cryptic lineage divergence compared with allopatric divergence, the forces of divergent selection and mating patterns override geographical isolation. Introgression, by supplying preadapted or neutral standing genetic variations, can promote sympatric cryptic lineage divergence via selection. However, most studies concentrated on extant species introgression, ignoring the genetic legacy of introgression from extinct or unsampled lineages ("ghost introgression"). Cycads are an ideal plant for studying the influence of ghost introgression because of their common interspecific gene flow and past high extinction rate. Here, we utilized reference-based ddRADseq to clarify the role of ghost introgression in the evolution of a previously identified sympatric cryptic lineage in Cycas revoluta. After re-evaluating the evolutionary independency of cryptic lineages, the group-wise diverged single-nucleotide polymorphisms among sympatric and allopatric lineages were compared and functionally annotated. Next, we employed an approximate Bayesian computation method for hypothesis testing to clarify the cryptic lineage evolution and ghost introgression effect. SNPs with the genomic signatures of ghost introgression were further annotated. Our results reconfirmed the evolutionary independency of cryptic lineage among C. revoluta and demonstrated that ghost introgression to the noncryptic lineage facilitated their divergence. Gene function related to heat stress and disease resistance implied ecological adaptation of the main extant populations of C. revoluta.

Integrating Pool-seq uncertainties into demographic inference.

Next-generation sequencing of pooled samples (Pool-seq) is a popular method to assess genome-wide diversity patterns in natural and experimental populations. However, Pool-seq is associated with specific sources of noise, such as unequal individual contributions. Consequently, using Pool-seq for the reconstruction of evolutionary history has remained underexplored. Here we describe a novel Approximate Bayesian Computation (ABC) method to infer demographic history, explicitly modelling Pool-seq sources of error. By jointly modelling Pool-seq data, demographic history and the effects of selection due to barrier loci, we obtain estimates of demographic history parameters accounting for technical errors associated with Pool-seq. Our ABC approach is computationally efficient as it relies on simulating subsets of loci (rather than the whole-genome) and on using relative summary statistics and relative model parameters. Our simulation study results indicate Pool-seq data allows distinction between general scenarios of ecotype formation (single versus parallel origin) and to infer relevant demographic parameters (e.g. effective sizes and split times). We exemplify the application of our method to Pool-seq data from the rocky-shore gastropod Littorina saxatilis, sampled on a narrow geographical scale at two Swedish locations where two ecotypes (Wave and Crab) are found. Our model choice and parameter estimates show that ecotypes formed before colonization of the two locations (i.e. single origin) and are maintained despite gene flow. These results indicate that demographic modelling and inference can be successful based on pool-sequencing using ABC, contributing to the development of suitable null models that allow for a better understanding of the genetic basis of divergent adaptation.

On a class of prior distributions that accounts for uncertainty in the data

A new class of prior distributions that can be used to assess the sensitivity of the Bayesian posterior inference to uncertainty in the data is proposed. This class is derived starting from an initial prior distribution and the likelihood function. We establish the mathematical properties of this class and the conditions under which ordering can be established within this class. We show how the sensitivity analysis can be performed using a standard MCMC procedure for any model whose likelihood, or an approximation, is available in a closed form and illustrate using examples. We also discuss how the proposed class is connected to the main ideas behind the Approximate Bayesian Computation (ABC) method. For this reason, we choose to call the new class of prior distributions as the ABC class of prior distributions. Finally, we close by sketching further possible extensions to this work.

Speciation in Coastal Basins Driven by Staggered Headwater Captures: Dispersal of a Species Complex, Leporinus bahiensis, as Revealed by Genome-wide SNP Data.

Past sea level changes and geological instability along watershed boundaries have largely influenced fish distribution across coastal basins, either by dispersal via palaeodrainages now submerged or by headwater captures, respectively. Accordingly, the South American Atlantic coast encompasses several small and isolated drainages that share a similar species composition, representing a suitable model to infer historical processes. Leporinus bahiensis is a freshwater fish species widespread along adjacent coastal basins over narrow continental shelf with no evidence of palaeodrainage connections at low sea level periods. Therefore, this study aimed to reconstruct its evolutionary history to infer the role of headwater captures in the dispersal process. To accomplish this, we employed molecular-level phylogenetic and population structure analyses based on Sanger sequences (5 genes) and genome-wide SNP data. Phylogenetic trees based on Sanger data were inconclusive, but SNPs data did support the monophyletic status of L. bahiensis. Both COI and SNP data revealed structured populations according to each hydrographic basin. Species delimitation analyses revealed from 3 (COI) to 5 (multilocus approach) MOTUs, corresponding to the sampled basins. An intricate biogeographic scenario was inferred and supported by Approximate Bayesian Computation (ABC) analysis. Specifically, a staggered pattern was revealed and characterized by sequential headwater captures from basins adjacent to upland drainages into small coastal basins at different periods. These headwater captures resulted in dispersal throughout contiguous coastal basins, followed by deep genetic divergence among lineages. To decipher such recent divergences, as herein represented by L. bahiensis populations, we used genome-wide SNPs data. Indeed, the combined use of genome-wide SNPs data and ABC method allowed us to reconstruct the evolutionary history and speciation of L. bahiensis. This framework might be useful in disentangling the diversification process in other neotropical fishes subject to a reticulate geological history.