Approximate Bayesian Computation Approach Research Articles

A strong east–west Mediterranean divergence supports a new phylogeographic history of the carob tree (Ceratonia siliqua, Leguminosae) and multiple domestications from native populations

AbstractAimPhylogeography of fruit trees is challenging due to recurrent exchanges between domesticated and wild populations. Here we tested the eastern refugium hypothesis (ERH) for the carob tree, Ceratonia siliqua, which supports its natural and domestication origins in the eastern Mediterranean and a feral origin in the west.LocationMediterranean basin.TaxonCeratonia siliqua L., Leguminosae.MethodsA phylogenetic reconstruction based on two nuclear and one plastid sequences was performed to estimate the divergence time between the carob tree and its sister species, Ceratonia oreothauma. Variation from four plastid regions and 17 nuclear microsatellite loci were used to decipher genetic structure in the carob tree and to test coalescent‐based models by an Approximate Bayesian computation (ABC) approach. We assessed our hypotheses by examining palaeobotanical records and hindcasting the past distribution of the carob tree at Mid‐Holocene, Last Glacial Maximum (LGM) and Last Interglacial (LIG) using species distribution modelling.ResultsThe split between C. oreothauma and C. siliqua was estimated at 6.4 Ma, and a first divergence within C. siliqua at 1.3 Ma. After a continuous presence since the Oligocene, Ceratonia was rarely found in the fossil record during the Pleistocene but present in the western and the eastern Mediterranean. Plastid and nuclear markers, characterized by low allelic richness, revealed a strong west‐east genetic structuring. ABC analyses rejected the ERH.Main conclusionsOur study supports a severe population decline during LIG. The strong west–east divergence and the occurrence of four lineages within C. siliqua provided support for a new hypothesis of multiple domestications of the carob tree from native populations throughout the Mediterranean basin.

AKL-ABC: An Automatic Approximate Bayesian Computation Approach Based on Kernel Learning

Bayesian statistical inference under unknown or hard to asses likelihood functions is a very challenging task. Currently, approximate Bayesian computation (ABC) techniques have emerged as a widely used set of likelihood-free methods. A vast number of ABC-based approaches have appeared in the literature; however, they all share a hard dependence on free parameters selection, demanding expensive tuning procedures. In this paper, we introduce an automatic kernel learning-based ABC approach, termed AKL-ABC, to automatically compute posterior estimations from a weighting-based inference. To reach this goal, we propose a kernel learning stage to code similarities between simulation and parameter spaces using a centered kernel alignment (CKA) that is automated via an Information theoretic learning approach. Besides, a local neighborhood selection (LNS) algorithm is used to highlight local dependencies over simulations relying on graph theory. Attained results on synthetic and real-world datasets show our approach is a quite competitive method compared to other non-automatic state-of-the-art ABC techniques.

Fast likelihood-free cosmology with neural density estimators and active learning

Abstract Likelihood-free inference provides a framework for performing rigorous Bayesian inference using only forward simulations, properly accounting for all physical and observational effects that can be successfully included in the simulations. The key challenge for likelihood-free applications in cosmology, where simulation is typically expensive, is developing methods that can achieve high-fidelity posterior inference with as few simulations as possible. Density-estimation likelihood-free inference (DELFI) methods turn inference into a density estimation task on a set of simulated data-parameter pairs, and give orders of magnitude improvements over traditional Approximate Bayesian Computation approaches to likelihood-free inference. In this paper we use neural density estimators (NDEs) to learn the likelihood function from a set of simulated datasets, with active learning to adaptively acquire simulations in the most relevant regions of parameter space on-the-fly. We demonstrate the approach on a number of cosmological case studies, showing that for typical problems high-fidelity posterior inference can be achieved with just $\mathcal {O}(10^3)$ simulations or fewer. In addition to enabling efficient simulation-based inference, for simple problems where the form of the likelihood is known, DELFI offers a fast alternative to MCMC sampling, giving orders of magnitude speed-up in some cases. Finally, we introduce pydelfi – a flexible public implementation of DELFI with NDEs and active learning – available at https://github.com/justinalsing/pydelfi.

Using a continuum model to decipher the mechanics of embryonic tissue spreading from time-lapse image sequences: An approximate Bayesian computation approach

Advanced imaging techniques generate large datasets capable of describing the structure and kinematics of tissue spreading in embryonic development, wound healing, and the progression of many diseases. These datasets can be integrated with mathematical models to infer biomechanical properties of the system, typically identifying an optimal set of parameters for an individual experiment. However, these methods offer little information on the robustness of the fit and are generally ill-suited for statistical tests of multiple experiments. To overcome this limitation and enable efficient use of large datasets in a rigorous experimental design, we use the approximate Bayesian computation rejection algorithm to construct probability density distributions that estimate model parameters for a defined theoretical model and set of experimental data. Here, we demonstrate this method with a 2D Eulerian continuum mechanical model of spreading embryonic tissue. The model is tightly integrated with quantitative image analysis of different sized embryonic tissue explants spreading on extracellular matrix (ECM) and is regulated by a small set of parameters including forces on the free edge, tissue stiffness, strength of cell-ECM adhesions, and active cell shape changes. We find statistically significant trends in key parameters that vary with initial size of the explant, e.g., for larger explants cell-ECM adhesion forces are weaker and free edge forces are stronger. Furthermore, we demonstrate that estimated parameters for one explant can be used to predict the behavior of other similarly sized explants. These predictive methods can be used to guide further experiments to better understand how collective cell migration is regulated during development.

Global childhood cancer survival estimates and priority-setting: a simulation-based analysis.

Accurate childhood cancer survival estimates are crucial for policy makers and clinicians for priority-setting and planning decisions. However, observed survival estimates are lacking for many countries, and when available, wide variation in outcomes is reported. Understanding the barriers to optimising survival can help improve childhood cancer outcomes. We aimed to provide estimates of global childhood cancer survival, accounting for the impact of multiple factors that affect cancer outcomes in children. We developed a microsimulation model to simulate childhood cancer survival for 200 countries and territories worldwide, accounting for clinical and epidemiologic factors, including country-specific treatment variables, such as availability of chemotherapy, radiation, and surgery. To ensure model results were consistent with reported survival data, we calibrated the model to estimates from the CONCORD-2 and CONCORD-3 studies using an Approximate Bayesian Computation approach. We estimated 5-year net survival for diagnosed cases of childhood cancer in each country and territory and estimated potential survival gains of seven policy interventions focused on improving treatment availability and delivery (ie, increasing the availability of chemotherapy, radiation, general surgery, neurosurgery, or ophthalmic surgery, reducing treatment abandonment, and improving the quality of care to the mean of high-income countries) implemented in isolation or as packages. Our model estimated that, for diagnosed cases, global 5-year net childhood cancer survival is currently 37·4% (95% uncertainty interval 34·7-39·8), with large variation by region, ranging from 8·1% (4·4-13·7) in eastern Africa to 83·0% (81·6-84·4) in North America. Among the seven policy interventions modelled, each individually provided small gains, increasing global 5-year net survival to between 38·4% (35·8-40·9) and 44·6% (41·7-47·4). 5-year net survival increased more substantially when policy interventions were bundled into packages that improved service delivery (5-year net survival 50·2% [47·3-53·0]) or that expanded treatment access (54·1% [50·1-58·5]). A comprehensive systems approach consisting of all policy interventions yielded superadditive gains with a global 5-year net survival of 53·6% (51·5-55·6) at 50% scale-up and 80·8% (79·5-82·1) at full implementation. Childhood cancer survival varies widely by region, with especially poor survival in Africa. Although expanding access to treatment (chemotherapy, radiation, and surgery) and addressing financial toxicity are essential, investments that improve the quality of care, at both the health-system and facility level, are needed to improve childhood cancer outcomes globally. Boston Children's Hospital, Dana-Farber Cancer Institute, Harvard TH Chan School of Public Health, Harvard Medical School, National Cancer Institute, SickKids, St Jude Children's Research Hospital, Union for International Cancer Control, Children with Cancer UK Davidson and O'Gorman Fellowship.

Approximate Bayesian estimation of coevolutionary arms races.

Exaggerated traits involved in species interactions have long captivated the imagination of evolutionary biologists and inspired the durable metaphor of the coevolutionary arms race. Despite decades of research, however, we have only a handful of examples where reciprocal coevolutionary change has been rigorously established as the cause of trait exaggeration. Support for a coevolutionary mechanism remains elusive because we lack generally applicable tools for quantifying the intensity of coevolutionary selection. Here we develop an approximate Bayesian computation (ABC) approach for estimating the intensity of coevolutionary selection using population mean phenotypes of traits mediating interspecific interactions. Our approach relaxes important assumptions of a previous maximum likelihood approach by allowing gene flow among populations, variable abiotic environments, and strong coevolutionary selection. Using simulated data, we show that our ABC method accurately infers the strength of coevolutionary selection if reliable estimates are available for key background parameters and ten or more populations are sampled. Applying our approach to the putative arms race between the plant Camellia japonica and its seed predatory weevil, Curculio camelliae, provides support for a coevolutionary hypothesis but fails to preclude the possibility of unilateral evolution. Comparing independently estimated selection gradients acting on Camellia pericarp thickness with values simulated by our model reveals a correlation between predicted and observed selection gradients of 0.941. The strong agreement between predicted and observed selection gradients validates our method.

A simple spatially explicit neutral model explains the range size distribution of reef fishes

AbstractAimThe great variation in range sizes among species has fascinated ecologists for decades. Reef‐associated fish species live in highly spatially structured habitats and adopt a wide range of dispersal strategies. We consequently expect species with greater dispersal ability to occupy larger ranges. However, empirical evidence for such a positive relationship between dispersal and range size remains scarce. Here, we unveil the role of dispersal on the range size distribution of reef‐associated fishes using empirical data and a novel spatially explicit model.LocationTropical Eastern Pacific.Major taxa studiedReef‐associated fishes.Time periodUnderlying records are from the 20th and 21st centuries.MethodsWe estimated range size distributions for all reef‐associated fishes separated into six guilds, each with different dispersal abilities. We used a one‐dimensional spatially explicit neutral model, which simulates the distribution of species along a linear and contiguous coastline, to explore the effect of dispersal, speciation and sampling on the distribution of range sizes. Our model incorporates biologically important long‐distance dispersal events with a fat‐tailed dispersal kernel and also adopts a more realistic gradual “protracted” speciation process than originally used in neutral theory. We fitted the model to the empirical data using an approximate Bayesian computation approach, with a sequential Monte Carlo algorithm.ResultsStochastic birth, death, speciation and dispersal events alone can accurately explain empirical range size distributions for six different guilds of tropical, reef‐associated fishes. Variation in range size distributions among guilds are explained purely by differences in dispersal ability with the best dispersers being distributed over larger ranges.Main conclusionsNeutral processes and guild‐specific dispersal ability provide a general explanation for both within‐ and across‐guild range size variation. Our results support the theoretically expected, but empirically much debated, hypothesis that high dispersal capacity promotes the establishment of large range size.

Phylogeography of lethal male fighting in a social spider mite.

When males fight for access to females, such conflict rarely escalates into lethal fight because the risks and costs involved, that is, severe injury or death, are too high. The social spider mite, Stigmaeopsis miscanthi, does exhibit lethal male fights, and this male–male aggressiveness varies among populations. To understand the evolution of lethal fighting, we investigated aggressiveness in 42 populations and phylogenetic relationships in 47 populations along the Japanese archipelago. By analysis of the male weapon morph, a proxy for aggressiveness, we confirmed the existence of a mildly aggressive (ML) form, besides the low aggression (LW) and high aggression (HG) forms reported earlier. To evaluate demographic history of these three forms, we employed the approximate Bayesian computation approach using mtCOI sequences and taking into consideration the postlast glacial expansion history of the host plant, Miscanthus sinensis. As results, hierarchical split models are more likely to explain the observed genetic pattern than admixture models, and the ML form in the subtropical region was considered the ancestral group. The inferred demographic history was consistent with the one reconstructed for the host plant in a previous study. The LW form was split from the ML form during the last glacial period (20,000–40,000 years BP), and subsequently, the HG form was split from the ML form at the end of or after the last glacial period (5,494–10,988 years BP). The results also suggest that the mite invaded Japan more than once, resulting in the present parapatric distribution of LW and HG forms in eastern Japan.

Modelling Trait-dependent Speciation with Approximate Bayesian Computation

Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The field's progression is hampered by the lack of robust software to estimate the numerous parameters of the speciation process. In this work we present an R package, pcmabc, based on Approximate Bayesian Computations, that implements three novel phylogenetic algorithms for trait-dependent speciation modelling. Our phylogenetic comparative methodology takes into account both the simulated traits and phylogeny, attempting to estimate the parameters of the processes generating the phenotype and the trait. The user is not restricted to a predefined set of models and can specify a variety of evolutionary and branching models. We illustrate the software with a simulation-reestimation study focused around the branching Ornstein-Uhlenbeck process, where the branching rate depends non-linearly on the value of the driving Ornstein-Uhlenbeck process. Included in this work is a tutorial on how to use the software.

A preferential attachment model for the stellar initial mass function

Accurate specification of a likelihood function is becoming increasingly difficult in many inference problems in astronomy. As sample sizes resulting from astronomical surveys continue to grow, deficiencies in the likelihood function lead to larger biases in key parameter estimates. These deficiencies result from the oversimplification of the physical processes that generated the data, and from the failure to account for observational limitations. Unfortunately, realistic models often do not yield an analytical form for the likelihood. The estimation of a stellar initial mass function (IMF) is an important example. The stellar IMF is the mass distribution of stars initially formed in a given cluster of stars, a population which is not directly observable due to stellar evolution and other disruptions and observational limitations of the cluster. There are several difficulties with specifying a likelihood in this setting since the physical processes and observational challenges result in measurable masses that cannot legitimately be considered independent draws from an IMF. This work improves inference of the IMF by using an approximate Bayesian computation approach that both accounts for observational and astrophysical effects and incorporates a physically-motivated model for star cluster formation. The methodology is illustrated via a simulation study, demonstrating that the proposed approach can recover the true posterior in realistic situations, and applied to observations from astrophysical simulation data.

Parameter estimates of the 2016-2017 Zika outbreak in Costa Rica: An Approximate Bayesian Computation (ABC) approach

In Costa Rica, the first known cases of Zika were reported in 2016. We looked at the 2016-2017 Zika outbreak and explored the transmission dynamics using weekly reported data. A nonlinear differential equation single-outbreak model with sexual transmission, as well as host availability for vector-feeding was used to estimate key parameters, fit the data and compute the basic reproductive number, R₀, distribution. Furthermore, a sensitivity and elasticity analysis was computed based on the R₀ parameters.

90‐90‐90 by 2020? Estimation and projection of the adult HIV epidemic and ART programme in Zimbabwe – 2017 to 2020

IntroductionThe 90‐90‐90 targets set by the United Nations aspire to 73% of people living with HIV (PLHIV) being virally suppressed by 2020. Using the HIV Synthesis Model, we aim to mimic the epidemic in Zimbabwe and make projections to assess whether Zimbabwe is on track to meet the 90‐90‐90 targets and assess whether recently proposed UNAIDS HIV transition metrics are likely to be met.MethodsWe used an approximate Bayesian computation approach to identify model parameter values which result in model outputs consistent with observed data, evaluated using a calibration score. These parameter values were then used to make projections to 2020 to compare with the 90‐90‐90 targets and other key indicators. We also calculated HIV transition metrics proposed by UNAIDS (percentage reduction in new HIV infections and AIDS‐related mortality from 2010 to 2020, absolute rate of new infections and AIDS‐related mortality, incidence–mortality ratio and incidence–prevalence ratios).ResultsAfter calibration, there was general agreement between modelled and observed data. The median predicted outcomes in 2020 were: proportion of PLHIV (aged 15 to 65) diagnosed 0.91 (90% uncertainty range 0.87, 0.94) (0.84 men, 0.95 women); of those diagnosed, proportion on treatment 0.92 (0.90, 0.93); of those receiving treatment, proportion with viral suppression 0.86 (0.81, 0.91). This results in 72% of PLHIV having viral suppression in 2020. We estimated a percentage reduction of 36.5% (13.7% increase to 67.4% reduction) in new infections from 2010 to 2020, and of 30.4% (9.7% increase to 56.6% reduction) in AIDS‐related mortality (UNAIDS target 75%). The modelled absolute rates of HIV incidence and AIDS‐related mortality in 2020 were 5.48 (2.26, 9.24) and 1.93 (1.31, 2.71) per 1000 person‐years respectively. The modelled incidence–mortality ratio and incidence–prevalence ratios in 2020 were 1.05 (0.46, 1.66) and 0.009 (0.004, 0.013) respectively.ConclusionsOur model was able to produce outputs that are simultaneously consistent with an array of observed data and predicted that while the 90‐90‐90 targets are within reach in Zimbabwe, increased efforts are required in diagnosing men in particular. Calculation of the HIV transition metrics suggest increased efforts are needed to bring the HIV epidemic under control.

Phylogeography of the highly invasive sugar beet nematode, Heterodera schachtii (Schmidt, 1871), based on microsatellites.

Plant‐parasitic nematodes (PPNs) threaten crop production worldwide. Yet few studies have examined their intraspecific genetic diversity or patterns of invasion, critical data for managing the spread of these cryptic pests. The sugar beet nematode Heterodera schachtii, a global invader that parasitizes over 200 plant species, represents a model for addressing important questions about the invasion genetics of PPNs. Here, a phylogeographic study using 15 microsatellite markers was conducted on 231 H. schachtii individuals sampled from four continents, and invasion history was reconstructed through an approximate Bayesian computation approach, with emphasis on the origin of newly discovered populations in Korea. Multiple analyses confirmed the existence of cryptic lineages within this species, with the Korean populations comprising one group (group 1) and the populations from Europe, Australia, North America, and western Asia comprising another (group 2). No multilocus genotypes were shared between the two groups, and large genetic distance was inferred between them. Population subdivision was also revealed among the populations of group 2 in both population comparison and STRUCTURE analyses, mostly due to different divergent times between invasive and source populations. The Korean populations showed substantial genetic homogeneity and likely originated from a single invasion event. However, none of the other studied populations were implicated as the source. Further studies with additional populations are needed to better describe the distribution of the potential source population for the East Asian lineage.

Using Approximate Bayesian Computation to infer sex ratios from acoustic data.

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.

Evolution of genomic variation in the burrowing owl in response to recent colonization of urban areas.

When a species successfully colonizes an urban habitat it can be expected that its population rapidly adapts to the new environment but also experiences demographic perturbations. It is, therefore, essential to gain an understanding of the population structure and the demographic history of the urban and neighbouring rural populations before studying adaptation at the genome level. Here, we investigate populations of the burrowing owl (Athene cunicularia), a species that colonized South American cities just a few decades ago. We assembled a high-quality genome of the burrowing owl and re-sequenced 137 owls from three urban–rural population pairs at 17-fold median sequencing coverage per individual. Our data indicate that each city was independently colonized by a limited number of founders and that restricted gene flow occurred between neighbouring urban and rural populations, but not between urban populations of different cities. Using long-range linkage disequilibrium statistics in an approximate Bayesian computation approach, we estimated consistently lower population sizes in the recent past for the urban populations in comparison to the rural ones. The current urban populations all show reduced standing variation in rare single nucleotide polymorphisms (SNPs), but with different subsets of rare SNPs in different cities. This lowers the potential for local adaptation based on rare variants and makes it harder to detect consistent signals of selection in the genome.

Incorporating non-equilibrium dynamics into demographic history inferences of a migratory marine species.

Understanding how dispersal and gene flow link geographically separated the populations over evolutionary history is challenging, particularly in migratory marine species. In southern right whales (SRWs, Eubalaena australis), patterns of genetic diversity are likely influenced by the glacial climate cycle and recent history of whaling. Here we use a dataset of mitochondrial DNA (mtDNA) sequences (n = 1327) and nuclear markers (17 microsatellite loci, n = 222) from major wintering grounds to investigate circumpolar population structure, historical demography and effective population size. Analyses of nuclear genetic variation identify two population clusters that correspond to the South Atlantic and Indo-Pacific ocean basins that have similar effective breeder estimates. In contrast, all wintering grounds show significant differentiation for mtDNA, but no sex-biased dispersal was detected using the microsatellite genotypes. An approximate Bayesian computation (ABC) approach with microsatellite markers compared the scenarios with gene flow through time, or isolation and secondary contact between ocean basins, while modelling declines in abundance linked to whaling. Secondary-contact scenarios yield the highest posterior probabilities, implying that populations in different ocean basins were largely isolated and came into secondary contact within the last 25,000 years, but the role of whaling in changes in genetic diversity and gene flow over recent generations could not be resolved. We hypothesise that these findings are driven by factors that promote isolation, such as female philopatry, and factors that could promote dispersal, such as oceanographic changes. These findings highlight the application of ABC approaches to infer the connectivity in mobile species with complex population histories and, currently, low levels of differentiation.

Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data-space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper we use massive asymptotically-optimal data compression to reduce the dimensionality of the data-space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (\textsc{delfi}), which learns a parameterized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate Density Estimation Likelihood-Free Inference with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as $\sim 10^4$ simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological datasets.

Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review

BackgroundRigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis.MethodsWe undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios.ResultsFor missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results.ConclusionsMethods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses.

Mitochondrial and nuclear genetic structure in Rhodeus ocellatus (Teleostei: Cyprinidae) with approximate Bayesian computation

The rosy bitterling, Rhodeus ocellatus, is a small freshwater fish belonging to the family Cyprinidae. This species lives in ponds where freshwater mussels are abundant and female lays eggs inside mussels. To understand whether the reproduction mode influenced the phylogeography, our study examined the genetic structure of R. ocellatus using sequences from the mitochondrial DNA (cytochrome b gene and control region) and nuclear DNA (the first intron of ribosomal protein S7 gene). In total, 213 specimens were collected from twelve populations in south of Yangtze River, including Yangtze River, Taiwan and Hainan Islands. The phylogenetic analyses based on mitochondrial and nuclear sequences both showed the lack of a population genetic structure, but all results, including the approximate Bayesian computation approaches, showed that these two markers revealed incongruent historical signals. Our study found that (1) the discordance between these two markers were accounted for admixtures by introduced; (2) the phylogeographic pattern of R. ocellatus and that of other freshwater fish were identical; (3) the reproduction mode was due to that the gene flows among populations were limited; and (4) R. ocellatus colonized in south of the Yangtze River (including) after southeast coastal districts formed and before Taiwan Island reached its present shape by comparing our results with that of the previous studies.

Complex genetic patterns in human arise from a simple range-expansion model over continental landmasses.

Although it is generally accepted that geography is a major factor shaping human genetic differentiation, it is still disputed how much of this differentiation is a result of a simple process of isolation-by-distance, and if there are factors generating distinct clusters of genetic similarity. We address this question using a geographically explicit simulation framework coupled with an Approximate Bayesian Computation approach. Based on six simple summary statistics only, we estimated the most probable demographic parameters that shaped modern human evolution under an isolation by distance scenario, and found these were the following: an initial population in East Africa spread and grew from 4000 individuals to 5.7 million in about 132 000 years. Subsequent simulations with these estimates followed by cluster analyses produced results nearly identical to those obtained in real data. Thus, a simple diffusion model from East Africa explains a large portion of the genetic diversity patterns observed in modern humans. We argue that a model of isolation by distance along the continental landmasses might be the relevant null model to use when investigating selective effects in humans and probably many other species.