The fossilized birth–death process for coherent calibration of divergence-time estimates

Time-calibrated species phylogenies are critical for addressing a wide range of questions in evolutionary biology, such as those that elucidate historical biogeography or uncover patterns of coevolution and diversification. Because molecular sequence data are not informative on absolute time, external data—most commonly, fossil age estimates—are required to calibrate estimates of species divergence dates. For Bayesian divergence time methods, the common practice for calibration using fossil information involves placing arbitrarily chosen parametric distributions on internal nodes, often disregarding most of the information in the fossil record. We introduce the “fossilized birth–death” (FBD) process—a model for calibrating divergence time estimates in a Bayesian framework, explicitly acknowledging that extant species and fossils are part of the same macroevolutionary process. Under this model, absolute node age estimates are calibrated by a single diversification model and arbitrary calibration densities are not necessary. Moreover, the FBD model allows for inclusion of all available fossils. We performed analyses of simulated data and show that node age estimation under the FBD model results in robust and accurate estimates of species divergence times with realistic measures of statistical uncertainty, overcoming major limitations of standard divergence time estimation methods. We used this model to estimate the speciation times for a dataset composed of all living bears, indicating that the genus Ursus diversified in the Late Miocene to Middle Pliocene.A phylogenetic analysis of species has two goals: to infer the evolutionary relationships and the amount of divergence among species. Preferably, divergence is estimated in units proportional to time, thus revealing the times at which speciation events occurred. Once orthologous DNA sequences from the species have been aligned, both goals can be accomplished by assuming that nucleotide substitutions occur at the same rate in all lineages [the “molecular clock” assumption (1)] and that the time of at least one speciation event on the tree is known, i.e., one speciation event acts to “calibrate” the substitution rate.The goal of reconstructing rooted, time-calibrated phylogenies is complicated by substitution rates changing over the tree and by the difficulty of determining the date of any speciation event. Substitution rate variation among lineages is pervasive and has been accommodated in several ways. The most widely used method to account for rate heterogeneity is to assign an independent parameter to each branch of the tree. Branch lengths, then, are the product of substitution rate and time, and usually measured in units of expected number of substitutions per site. This solution allows estimation of the tree topology—which is informative about interspecies relationships—but does not attempt to estimate the rate and time separately. Thus, under this “unconstrained” parameterization, molecular sequence data allow inference of phylogenetic relationships and genetic distances among species, but the timing of speciation events is confounded in the branch-length parameter (2–4). Under a “relaxed-clock” model, substitution rates change over the tree in a constrained manner, thus separating the rate and time parameters associated with each branch and allowing inference of lineage divergence times. A considerable amount of effort has been directed at modeling lineage-specific substitution rate variation, with many different relaxed-clock models described in the literature (5–19). When such models are coupled with a model on the distribution of speciation events over time [e.g., the Yule model (20) or birth–death process (21)], molecular sequence data can inform the relative rates and node ages in a phylogenetic analysis.Estimates of branch lengths in units of absolute time (e.g., millions of years) are required for studies investigating comparative or biogeographical questions (e.g., refs. 22, 23). However, because commonly used diversification priors are imprecise on node ages, external information is required to infer the absolute timing of speciation events. Typically, a rooted time tree is calibrated by constraining the ages of a set of internal nodes. Age constraints may be derived from several sources, but the most common and reliable source of calibration information is the fossil record (24, 25). Despite the prevalence of these data in divergence time analyses, the problem of properly calibrating a phylogenetic tree has received less consideration than the problem of accommodating rate variation. Moreover, various factors may lead to substantial errors in parameter estimates (26–31). When estimating node ages, a calibration node must be identified for each fossil. For a given fossil, the calibration node is the node in the extant species tree that represents the most recent common ancestor (MRCA) of the fossil and a set of extant species. Based on the fossil, the calibration node’s age is estimated on an absolute timescale. Thus, fossil data typically can provide valid minimum-age constraints only on these nodes (24, 27), and erroneous conclusions may result if the calibration node is not specified properly (26).Bayesian inference methods are well adapted to accommodating uncertainty in calibration times by assuming that the age of the calibrated node is a random variable drawn from some parametric probability distribution (10, 14, 29, 31–35). Although this Bayesian approach properly propagates uncertainty in the calibration times through the analysis (reflected in the credible intervals on uncalibrated node ages), two problems remain unresolved.First, these approaches, as they commonly are applied, induce a probability distribution on the age of each calibrated node that comes from both the node-specific calibration prior and the tree-wide prior on node ages, leading to an incoherence in the model of branching times on the tree (35, 36). Typically, a birth–death process of cladogenesis is considered as the generating model for the tree and speciation times (20, 21, 37–40), serving as the tree-wide prior distribution on branch times in a Bayesian analysis. The speciation events acting as calibrations then are considered to be drawn from an additional, unrelated probability distribution intended to model uncertainty in the calibration time. This procedure results in overlaying two prior distributions for a calibration node: one from the tree prior and one from the calibration density (35, 41). Importantly, this incoherence is avoided by partitioning the nodes and applying a birth–death process to uncalibrated nodes conditioned on the calibrated nodes (32), although many divergence time methods do not use this approach. Nevertheless, a single model that acts as a prior on the speciation times for both calibrated and uncalibrated nodes is a better representation of the lineage diversification process and preferable as a prior on branching times when using fossil data.Second, the probability distributions used to model uncertainty in calibration times are poorly motivated. The standard practice in Bayesian divergence time methods is to model uncertainty in calibrated node ages by using simple probability distributions, such as the uniform, log-normal, gamma, or exponential distributions (29). When offset by a minimum age, these “calibration densities” (35) simply seek to characterize the age of the node with respect to its descendant fossil. However, the selection and parameterization of calibration priors rarely are informed by any biological process or knowledge of the fossil record (except see refs. 42–44). A probability model that acts as a fossil calibration prior should have parameters relevant to the preservation history of the group, such as the rate at which fossils occur in the rock record, a task that likely is difficult for most groups without an abundant fossil record (43, 45). Consequently, most biologists are faced with the challenge of choosing and parameterizing calibration densities without an explicit way to describe their prior knowledge about the calibration time. Thus, calibration priors often are specified based on arbitrary criteria or ad hoc validation methods (46), and ultimately, this may lead to arbitrary or ad hoc estimates of divergence times.We provide an alternative method for calibrating phylogenies with fossils. Because fossils and molecular sequences from extant species are different observations of the same diversification process, we use an explicit speciation–extinction–fossilization model to describe the distribution of speciation times and recovered fossils. This model—the fossilized birth–death (FBD) process—acts as a prior for divergence time dating. The parameters of the model—the speciation rate, extinction rate, fossil recovery rate, and proportion of sampled extant species—interact to inform the amount of uncertainty for every speciation event on the tree. These four parameters are the only quantities requiring prior assumptions, compared with assuming separate calibration densities for each fossil. Analyses of simulated data under the FBD model result in reliable estimates of absolute divergence times with realistic measures of statistical uncertainty. Moreover, node age estimates are robust to several biased sampling strategies of fossils and extant species—strategies that may be common practice or artifacts of fossil preservation but heavily violate assumptions of the model.     

Efectividad de una intervención educativa breve en pacientes con insomnio en atención primaria

ObjetiveTo evaluate the effectiveness of providing an educational intervention in primary care (PC) alongside a pharmacological treatment for insomnia.DesignSingle blinded non randomised clinical trial.LocationTwo urban primary health centers in Gijón (Asturias, Spain).ParticipantsPatients who consulted for insomnia between July 2012-January 2013 and met the inclusion criteria (n = 50) were assigned systematically to the control group (CG) or intervention group (IG). All patients initiated treatment with lorazepam 1 mg in the evenings and had four weekly 15 min visits plus a follow-up visit after another month.InterventionsThe IG received training for control of stimuli, sleep hygiene and respiration and relaxation techniques in the four visits. The CG had only non invasive measures taken.MeasurementsConsidering as cured those who reached a Pittsburgh Sleep Quality Index PSQI < 6 or a 50% reduction from baseline level. It was also analyzed the change in the PSQI from baseline to final visit and to follow-up visit, and voluntary interruption of lorazepam. Analysis by Bayesian inference.ResultsTwelve out of recoveries after intervention against one out of 24 among control group. Mean change in PSQI to final visit and follow-up visit was: –4.7 (95%CrI:–5.9 to –3.5) and –6,3 (95%ICred: –7.5 to –5.1) in IG; –1.8 (95%ICred: –3 to –0.5) and –1.7 (95%ICred: –2.9 to –0.4) in CG. Interruption of lorazepan: in 4 controls (16,7%) and 9 (34,6%) in IG. Twenty nine patients in GI and 17 in GC completed the trial. Per protocol analysis showed similar results.ConclusionsThe educational intervention in PC improves sleep quality and reduces the need of treatment with benzodiacepines.     

Predicting severity of pathological scarring due to burn injuries: a clinical decision making tool using Bayesian networks

It is important for clinicians to understand which are the clinical signs, the patient characteristics and the procedures that are related with the occurrence of hypertrophic burn scars in order to carry out a possible prognostic assessment. Providing clinicians with an easy‐to‐ use tool for predicting the risk of pathological scars. A total of 703 patients with 2440 anatomical burn sites who were admitted to the Department of Plastic and Reconstructive Surgery, Burn Center of the Traumatological Hospital in Torino between January 1994 and May 2006 were included in the analysis. A Bayesian network (BN) model was implemented. The probability of developing a hypertrophic scar was evaluated on a number of scenarios. The error rate of the BN model was assessed internally and it was equal to 24·83%. While classical statistical method as logistic models can infer only which variables are related to the final outcome, the BN approach displays a set of relationships between the final outcome (scar type) and the explanatory covariates (patient's age and gender, burn surface area, full‐thickness burn surface area, burn anatomical area and wound‐healing time; burn treatment options such as advanced dressings, type of surgical approach, number of surgical procedures, type of skin graft, excision and coverage timing). A web‐based interface to handle the BN model was developed on the website www.pubchild.org (burns header). Clinicians who registered at the website could submit their data in order to get from the BN model the predicted probability of observing a pathological scar type.     

Bayesian age–period–cohort models with versatile interactions and long‐term predictions: mortality and population in Finland 1878–2050

Age–period–cohort (APC) models are widely used for studying time trends of disease incidence or mortality. Model identifiability has become less of a problem with Bayesian APC models. These models are usually based on random walk (RW1, RW2) smoothing priors. For long and complex time series and for long predicted periods, these models as such may not be adequate. We present two extensions for the APC models. First, we introduce flexible interactions between the age, period and cohort effects based on a two‐dimensional conditional autoregressive smoothing prior on the age/period plane. Our second extension uses autoregressive integrated (ARI) models to provide reasonable long‐term predictions. To illustrate the utility of our model framework, we provide stochastic predictions for the Finnish male and female population, in 2010–2050. For that, we first study and forecast all‐cause male and female mortality in Finland, 1878–2050, showing that using an interaction term is needed for fitting and interpreting the observed data. We then provide population predictions using a cohort component model, which also requires predictions for fertility and migration. As our main conclusion, ARI models have better properties for predictions than the simple RW models do, but mixing these prediction models with RW1 or RW2 smoothing priors for observed periods leads to a model that is not fully consistent. Further research with our model framework will concentrate on using a more consistent model for smoothing and prediction, such as autoregressive integrated moving average models with state‐space methods or Gaussian process priors. Copyright © 2013 John Wiley & Sons, Ltd.     

Augmented mixed beta regression models for periodontal proportion data

Continuous (clustered) proportion data often arise in various domains of medicine and public health where the response variable of interest is a proportion (or percentage) quantifying disease status for the cluster units, ranging between zero and one. However, because of the presence of relatively disease‐free as well as heavily diseased subjects in any study, the proportion values can lie in the interval [0,1]. While beta regression can be adapted to assess covariate effects in these situations, its versatility is often challenged because of the presence/excess of zeros and ones because the beta support lies in the interval (0,1). To circumvent this, we augment the probabilities of zero and one with the beta density, controlling for the clustering effect. Our approach is Bayesian with the ability to borrow information across various stages of the complex model hierarchy and produces a computationally convenient framework amenable to available freeware. The marginal likelihood is tractable and can be used to develop Bayesian case‐deletion influence diagnostics based on q‐divergence measures. Both simulation studies and application to a real dataset from a clinical periodontology study quantify the gain in model fit and parameter estimation over other ad hoc alternatives and provide quantitative insight into assessing the true covariate effects on the proportion responses. Copyright © 2014 John Wiley & Sons, Ltd.     

An approach for modelling multiple correlated outcomes in a network of interventions using odds ratios

A multivariate meta‐analysis of two or more correlated outcomes is expected to improve precision compared with a series of independent, univariate meta‐analyses especially when there are studies reporting some but not all outcomes. Multivariate meta‐analysis requires estimates of the within‐study correlations, which are seldom available. Existing methods for analysing multiple outcomes simultaneously are limited to pairwise treatment comparisons. We propose a model for a joint, simultaneous synthesis of multiple dichotomous outcomes in a network of interventions and introduce a simple way to elicit expert opinion for the within‐study correlations by utilizing a set of conditional probability parameters. We implement our multiple‐outcomes network meta‐analysis model within a Bayesian framework, which allows incorporation of expert information. As an example, we analyse two correlated dichotomous outcomes, response to the treatment and dropout rate, in a network of pharmacological interventions for acute mania. The produced estimates have narrower confidence intervals compared with the simple network meta‐analysis. We conclude that the proposed model and the suggested prior elicitation method for correlations constitute a useful framework for performing network meta‐analysis for multiple outcomes. Copyright © 2014 John Wiley & Sons, Ltd.     

Bayesian Latent Variable Collapsing Model for Detecting Rare Variant Interaction Effect in Twin Study

By analyzing more next‐generation sequencing data, researchers have affirmed that rare genetic variants are widespread among populations and likely play an important role in complex phenotypes. Recently, a handful of statistical models have been developed to analyze rare variant (RV) association in different study designs. However, due to the scarce occurrence of minor alleles in data, appropriate statistical methods for detecting RV interaction effects are still difficult to develop. We propose a hierarchical Bayesian latent variable collapsing method (BLVCM), which circumvents the obstacles by parameterizing the signals of RVs with latent variables in a Bayesian framework and is parameterized for twin data. The BLVCM can tackle nonassociated variants, allow both protective and deleterious effects, capture SNP‐SNP synergistic effect, provide estimates for the gene level and individual SNP contributions, and can be applied to both independent and various twin designs. We assessed the statistical properties of the BLVCM using simulated data, and found that it achieved better performance in terms of power for interaction effect detection compared to the Granvil and the SKAT. As proof of practical application, the BLVCM was then applied to a twin study analysis of more than 20,000 gene regions to identify significant RVs associated with low‐density lipoprotein cholesterol level. The results show that some of the findings are consistent with previous studies, and we identified some novel gene regions with significant SNP–SNP synergistic effects.     

In the Search of Marine Pestiviruses: First Case of Phocoena Pestivirus in a Belt Sea Harbour Porpoise

Pestiviruses are widespread pathogens causing severe acute and chronic diseases among terrestrial mammals. Recently, Phocoena pestivirus (PhoPeV) was described in harbour porpoises (Phocoena phocoena) of the North Sea, expanding the host range to marine mammals. While the role of the virus is unknown, intrauterine infections with the most closely related pestiviruses— Bungowannah pestivirus (BuPV) and Linda virus (LindaV)—can cause increased rates of abortions and deaths in young piglets. Such diseases could severely impact already vulnerable harbour porpoise populations. Here, we investigated the presence of PhoPeV in 77 harbour porpoises, 277 harbour seals (Phoca vitulina), grey seals (Halichoerus grypus) and ringed seals (Pusa hispida) collected in the Baltic Sea region between 2002 and 2019. The full genome sequence of a pestivirus was obtained from a juvenile female porpoise collected along the coast of Zealand in Denmark in 2011. The comparative Bayesian phylogenetic analyses revealed a close relationship between the new PhoPeV sequence and previously published North Sea sequences with a recent divergence from genotype 1 sequences between 2005 and 2009. Our findings provide further insight into the circulation of PhoPeV and expand the distribution from the North Sea to the Baltic Sea region with possible implications for the vulnerable Belt Sea and endangered Baltic Proper harbour porpoise populations.     

The biological basis of the experience and categorization of colour

We used the Land Colour Mondrian experiments in a Bayesian context to test the degree to which subjects vary in categorizing the colour of different patches, when each patch is made to reflect light of the identical wavelength‐energy composition. The brain uses a ratio‐taking mechanism to determine the ratio of light of every waveband reflected from a surface and from its surrounds. Our (Bayesian) hypothesis was that this ratio‐taking mechanism is similar in all humans and therefore leads to a constant categorization of colours that differs little between them. The similarly categorized colours are the initial priors, with initial hues attached to them. Twenty subjects of different ethnic and cultural backgrounds, for all but one of whom English was not the primary language, viewed eight patches of different colour in two Mondrian displays; each patch, when viewed, was made to reflect identical ratios of long‐, middle‐ and short‐wave light. Subjects were asked to match the colour of the viewed patch with that of the Munsell chip coming closest in colour to that of the viewed patch, without using language. In terms of hue, there was less variability in matching warm hues than cool ones. In terms of colour categorization, there was little variability overall. We take the lack of significant variability between subjects in the matches made as a pointer to similar computational mechanisms being employed in different subjects to perceive colours, thus permitting them to assume that their categorization of colours has universal agreement and assent.