Integrating Pool-seq uncertainties into demographic inference.

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1-28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

The ever-increasing availability of high-throughput DNA sequences and the development of numerous computational methods have led to considerable advances in our understanding of the evolutionary and demographic history of populations. Several demographic inference methods have been developed to take advantage of these massive genomic data. Simulation-based approaches, such as approximate Bayesian computation (ABC), have proved particularly efficient for complex demographic models. However, taking full advantage of the comprehensive information contained in massive genomic data remains a challenge for demographic inference methods, which generally rely on partial information from these data. Using advanced computational methods, such as machine learning, is valuable for efficiently integrating more comprehensive information. Here, we showed how simulation-based supervised machine learning methods applied to an extensive range of summary statistics are effective in inferring demographic parameters for connected populations. We compared three machine learning (ML) methods: a neural network, the multilayer perceptron (MLP), and two ensemble methods, random forest (RF) and the gradient boosting system XGBoost (XGB), to infer demographic parameters from genomic data under a standard isolation with migration model and a secondary contact model with varying population sizes. We showed that MLP outperformed the other two methods and that, on the basis of permutation feature importance, its predictions involved a larger combination of summary statistics. Moreover, they outperformed all three tested ABC algorithms. Finally, we demonstrated how a method called SHAP, from the field of explainable artificial intelligence, can be used to shed light on the contribution of summary statistics within the ML models.

Wastewater production, like many other engineered and environmental processes, is inherent stochastic in nature and requires the use of complex stochastic models, for example, to predict realistic patterns of down-the-drain chemicals or pharmaceuticals and personal care products. Up until now, a formal method of statistical inference has been lacking for many of those models, where explicit likelihood functions were intractable. In this Article, we investigate Approximate Bayesian Computation (ABC) methods to infer important parameters of stochastic environmental models. ABC methods have been recently suggested to perform model-based inference in a Bayesian setting when model likelihoods are analytically or computationally intractable and have not been applied to environmental systems analysis or water quality modeling before. In a case study, we investigate the performance of three different algorithms to infer the number of wastewater pulses contained in three high-resolution data series of benzotriazole and total nitrogen loads in sewers. We find that all algorithms perform well and that the uncertainty in the inferred number of corresponding wastewater pulses varies between 6% and 28%. In our case, the results are more sensitive to substance characteristics than to catchment properties. Although the application of ABC methods requires careful tuning and attention to detail, they have a great general potential to update stochastic model parameters with monitoring data and improve their predictive capabilities.

The skyline plot is a graphical representation of historical effective population sizes as a function of time. Past population sizes for these plots are estimated from genetic data, without a priori assumptions on the mathematical function defining the shape of the demographic trajectory. Because of this flexibility in shape, skyline plots can, in principle, provide realistic descriptions of the complex demographic scenarios that occur in natural populations. Currently, demographic estimates needed for skyline plots are estimated using coalescent samplers or a composite likelihood approach. Here, we provide a way to estimate historical effective population sizes using an Approximate Bayesian Computation (ABC) framework. We assess its performance using simulated and actual microsatellite datasets. Our method correctly retrieves the signal of contracting, constant and expanding populations, although the graphical shape of the plot is not always an accurate representation of the true demographic trajectory, particularly for recent changes in size and contracting populations. Because of the flexibility of ABC, similar approaches can be extended to other types of data, to multiple populations, or to other parameters that can change through time, such as the migration rate.

Probabilistic logic programming formalisms permit the definition of potentially very complex probability distributions. This complexity can often make learning hard, even when structure is fixed and learning reduces to parameter estimation. In this paper an approximate Bayesian computation (ABC) method is presented which computes approximations to the posterior distribution over PRISM parameters. The key to ABC approaches is that the likelihood function need not be computed, instead a 'distance' between the observed data and synthetic data generated by candidate parameter values is used to drive the learning. This makes ABC highly appropriate for PRISMprograms which can have an intractable likelihood function, but from which synthetic data can be readily generated. The algorithm is experimentally shown to work well on an easy problem but further work is required to produce acceptable results on harder ones.

Approximate Bayesian computation (ABC) is used to estimate unknown parameter values, as well as their uncertainties, in Reynolds-averaged Navier–Stokes (RANS) simulations of turbulent flows. The ABC method approximates posterior distributions of model parameters, but does not require the direct computation, or estimation, of a likelihood function. This method thus enables relatively simple and flexible parameter estimation for complex models and a wide range of reference data. This paper describes the ABC approach, including the use of a calibration step, adaptive proposal, and Markov chain Monte Carlo (MCMC) technique to accelerate the parameter estimation, resulting in an ABC approach with improved MCMC, denoted ABC-IMCMC. As a test of the classic ABC rejection algorithm and ABC-IMCMC, parameters are estimated in a nonequilibrium RANS model using reference data from direct numerical simulations of periodically sheared homogeneous turbulence. The use of ABC-IMCMC is then demonstrated to estimate parameters in the Menter shear-stress-transport (SST) model using experimental reference data for an axisymmetric transonic bump. This paper shows that the accuracy of the SST model for this test case can be improved using ABC-IMCMC, indicating that ABC-IMCMC is a promising method for the calibration of RANS models using a wide range of reference data.

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

Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology).

Comparative phylogeographic studies often reveal disparate levels of sequence divergence between lineages spanning a common geographic barrier, leading to the conclusion that isolation was nonsynchronous. However, only rarely do researchers account for the expected variance associated with ancestral coalescence and among-taxon variation in demographic history. We introduce a flexible approximate Bayesian computational (ABC) framework that can test for simultaneous divergence (TSD) using a hierarchical model that incorporates idiosyncratic differences in demographic history across taxon pairs. The method is tested across a range of conditions and is shown to be accurate even with single-locus mitochondrial DNA (mtDNA) data. We apply this method to a landmark dataset of putative simultaneous vicariance, eight geminate echinoid taxon pairs thought to have been split by the Isthmus of Panama 3.1 million years ago. The ABC posterior estimates are not consistent with a history of simultaneous vicariance given these data. Subsequent ABC estimates under a constrained model that assumes two divergence times across the eight taxon pairs suggests simultaneous divergence 3.1 million years ago in seven of the taxon pairs and a more recent divergence in the remaining taxon pair. These ABC estimates on the simultaneous divergence of the seven taxon pairs correspond to a DNA substitution rate of approximately 1.59% per lineage per million years at the mtDNA cytochrome oxidase I gene. This ABC framework can easily be modified to analyze single taxon-pair datasets and/or be expanded to include multiple loci, migration, recombination, and other idiosyncratic demographic histories. The flexible aspect of ABC and its built-in evaluation of estimator bias and statistical power has the potential to greatly enhance statistical rigor in phylogeographic studies.

In time-series analysis, state-space models (SSMs) have been widely used to estimate the conditional probability distributions of hidden variables and parameter values, as well as to understand structures that can generate the data. For example, the Kalman filter is used to analytically calculate the conditional probability distribution on linear SSMs in terms of minimizing the variance, and several extensions, such as the unscented Kalman filter and particle filter, have been applied to calculate the approximate distribution on nonlinear SSMs. Recently, the approximate Bayesian computation (ABC) has been applied to such time-series filtering to handle intractable likelihoods; however, it remains problematic with respect to consistently achieving a reduction of the estimation bias, evaluating the validity of the models, and dealing with replicated observations. To address these problems, in this paper, we propose a novel method combined with the kernel ABC to perform filtering, parameter estimation, and the model evaluation in SSMs. Simulation studies show that the proposed method produces inference that is comparable to other ABC methods, with the advantage of not requiring a careful calibration of the ABC threshold. In addition, we evaluate the performance of the model-selection capability using true and competitive models on synthetic data from nonlinear SSMs. Finally, we apply the proposed method to real data in rat circadian oscillations, and demonstrated the usefulness in practical situations.

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ.

Understanding the processes by which new diseases are introduced in previously healthy areas is of major interest in elaborating prevention and management policies, as well as in understanding the dynamics of pathogen diversity at large spatial scale. In this study, we aimed to decipher the dispersal processes that have led to the emergence of the plant pathogenic fungus Microcyclus ulei, which is responsible for the South American Leaf Blight (SALB). This fungus has devastated rubber tree plantations across Latin America since the beginning of the twentieth century. As only imprecise historical information is available, the study of population evolutionary history based on population genetics appeared most appropriate. The distribution of genetic diversity in a continental sampling of four countries (Brazil, Ecuador, Guatemala and French Guiana) was studied using a set of 16 microsatellite markers developed specifically for this purpose. A very strong genetic structure was found (F(st)=0.70), demonstrating that there has been no regular gene flow between Latin American M. ulei populations. Strong bottlenecks probably occurred at the foundation of each population. The most likely scenario of colonization identified by the Approximate Bayesian Computation (ABC) method implemented in DIYABC suggested two independent sources from the Amazonian endemic area. The Brazilian, Ecuadorian and Guatemalan populations might stem from serial introductions through human-mediated movement of infected plant material from an unsampled source population, whereas the French Guiana population seems to have arisen from an independent colonization event through spore dispersal.

Population sex ratios are of high ecological relevance, but are challenging to determine in species lacking conspicuous external cues indicating their sex. Acoustic sexing is an option if vocalizations differ between sexes, but is precluded by overlapping distributions of the values of male and female vocalizations in many species. A method allowing the inference of sex ratios despite such an overlap will therefore greatly increase the information extractable from acoustic data. To meet this demand, we developed a novel approach using Approximate Bayesian Computation (ABC) to infer the sex ratio of populations from acoustic data. Additionally, parameters characterizing the male and female distribution of acoustic values (mean and standard deviation) are inferred. This information is then used to probabilistically assign a sex to a single acoustic signal. We furthermore develop a simpler means of sex ratio estimation based on the exclusion of calls from the overlap zone. Applying our methods to simulated data demonstrates that sex ratio and acoustic parameter characteristics of males and females are reliably inferred by the ABC approach. Applying both the ABC and the exclusion method to empirical datasets (echolocation calls recorded in colonies of lesser horseshoe bats, Rhinolophus hipposideros) provides similar sex ratios as molecular sexing. Our methods aim to facilitate evidence-based conservation, and to benefit scientists investigating ecological or conservation questions related to sex- or group specific behaviour across a wide range of organisms emitting acoustic signals. The developed methodology is non-invasive, low-cost and time-efficient, thus allowing the study of many sites and individuals. We provide an R-script for the easy application of the method and discuss potential future extensions and fields of applications. The script can be easily adapted to account for numerous biological systems by adjusting the type and number of groups to be distinguished (e.g. age, social rank, cryptic species) and the acoustic parameters investigated.

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.

Approximate Bayesian Computation (ABC) methods have a lot of success to accomplish Bayesian inference on the parameters of models for which the calculation of the likelihood is intractable. These algorithms consists in comparing the observed dataset to many simulated datasets. These ones can be generated in different ways. Typically, the rejection ABC scheme consists first of simulating parameters using independent calls to the prior distribution and then, given these values, generating the datasets using independent calls to the model. For such a method, the computation time needed to get a suitable approximation of the posterior distribution can be very long. Also, there exist some sequential Monte Carlo methods replacing simulations from the prior by using successive approximations to the posterior distribution. Here, we recall a sequential simulation algorithm and we compare different parallelization strategies. We notably shown that the parallelization of the sequential ABC sampler is useless when using more than four threads per instance of the program and that the standard rejection ABC sampler has to be used when facing a large number of cores. Indeed, in such a case, the cost of the sequential ABC sampler's parallelization prohibits its use.