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Phylogenetic trees of present-day species allow investigation of the rate of evolution that led to the present-day diversity. A recent analysis of the mammalian phylogeny challenged the view of explosive mammalian evolution after the Cretaceous-Tertiary (K/T) boundary (65 Mya). However, due to lack of appropriate methods, the diversification (speciation minus extinction) rates in the more recent past of mammalian evolution could not be determined. In this paper, I provide a method that reveals that the tempo of mammalian evolution did not change until

Divergence time estimation on an absolute timescale requires external calibration information, which typically is derived from the fossil record. The common practice in Bayesian divergence time estimation involves applying calibration densities to individual nodes. Often, these priors are arbitrarily chosen and specified yet have an excessive impact on estimates of absolute time. We introduce the fossilized birth–death process—a fossil calibration method that unifies extinct and extant species with a single macroevolutionary model, eliminating the need for ad hoc calibration priors. Compared with common calibration density approaches, Bayesian inference under this mechanistic model yields more accurate node age estimates while providing a coherent measure of statistical uncertainty. Furthermore, unlike calibration densities, our model accommodates all the reliable fossils for a given phylogenetic dataset. 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.

Host population structure has a major influence on epidemiological dynamics. However, in particular for sexually transmitted diseases, quantitative data on population contact structure are hard to obtain. Here, we introduce a new method that quantifies host population structure based on phylogenetic trees, which are obtained from pathogen genetic sequence data. Our method is based on a maximum-likelihood framework and uses a multi-type branching process, under which each host is assigned to a type (subpopulation). In a simulation study, we show that our method produces accurate parameter estimates for phylogenetic trees in which each tip is assigned to a type, as well for phylogenetic trees in which the type of the tip is unknown. We apply the method to a Latvian HIV-1 dataset, quantifying the impact of the intravenous drug user epidemic on the heterosexual epidemic (known tip states), and identifying superspreader dynamics within the men-having-sex-with-men epidemic (unknown tip states).

Phylogenetic trees can be used to infer the processes that generated them. Here, we introduce a model, the Bayesian birth-death skyline plot which explicitly estimates the rate of transmission, recovery, and sampling and thus allows inference of the effective reproductive number directly from genetic data. Our method allows these parameters to vary through time in a piecewise fashion and is implemented within the Beast2 software framework. The method is a powerful alternative to the existing coalescent skyline plot providing insight into the differing roles of incidence and prevalence in an epidemic. We apply this method to data from the United Kingdom HIV-1 epidemic and Egyptian hepatitis C virus (HCV) epidemic. The analysis reveals temporal changes of the effective reproductive number that highlight the effect of past public health interventions.

Phylogenetic comparative methods are widely used to understand and quantify the evolution of phenotypic traits, based on phylogenetic trees and trait measurements of extant species. Such analyses depend crucially on the underlying model. Gaussian phylogenetic models like Brownian motion and Ornstein–Uhlenbeck processes are the workhorses of modeling continuous-trait evolution. However, these models fit poorly to big trees, because they neglect the heterogeneity of the evolutionary process in different lineages of the tree. Previous works have addressed this issue by introducing shifts in the evolutionary model occurring at inferred points in the tree. However, for computational reasons, in all current implementations, these shifts are “intramodel,” meaning that they allow jumps in 1 or 2 model parameters, keeping all other parameters “global” for the entire tree. There is no biological reason to restrict a shift to a single model parameter or, even, to a single type of model. Mixed Gaussian phylogenetic models (MGPMs) incorporate the idea of jointly inferring different types of Gaussian models associated with different parts of the tree. Here, we propose an approximate maximum-likelihood method for fitting MGPMs to comparative data comprising possibly incomplete measurements for several traits from extant and extinct phylogenetically linked species. We applied the method to the largest published tree of mammal species with body- and brain-mass measurements, showing strong statistical support for an MGPM with 12 distinct evolutionary regimes. Based on this result, we state a hypothesis for the evolution of the brain–body-mass allometry over the past 160 million y.

Phylogenetic analyses which include fossils or molecular sequences that are sampled through time require models that allow one sample to be a direct ancestor of another sample. As previously available phylogenetic inference tools assume that all samples are tips, they do not allow for this possibility. We have developed and implemented a Bayesian Markov Chain Monte Carlo (MCMC) algorithm to infer what we call sampled ancestor trees, that is, trees in which sampled individuals can be direct ancestors of other sampled individuals. We use a family of birth-death models where individuals may remain in the tree process after sampling, in particular we extend the birth-death skyline model [Stadler et al., 2013] to sampled ancestor trees. This method allows the detection of sampled ancestors as well as estimation of the probability that an individual will be removed from the process when it is sampled. We show that even if sampled ancestors are not of specific interest in an analysis, failing to account for them leads to significant bias in parameter estimates. We also show that sampled ancestor birth-death models where every sample comes from a different time point are non-identifiable and thus require one parameter to be known in order to infer other parameters. We apply our phylogenetic inference accounting for sampled ancestors to epidemiological data, where the possibility of sampled ancestors enables us to identify individuals that infected other individuals after being sampled and to infer fundamental epidemiological parameters. We also apply the method to infer divergence times and diversification rates when fossils are included along with extant species samples, so that fossilisation events are modelled as a part of the tree branching process. Such modelling has many advantages as argued in the literature. The sampler is available as an open-source BEAST2 package (https://github.com/CompEvol/sampled-ancestors).

The time-varying effective reproduction number R t is a widely used indicator of transmission dynamics during infectious disease outbreaks. Timely estimates of R t can be obtained from reported cases counted by their date of symptom onset, which is generally closer to the time of infection than the date of report. Case counts by date of symptom onset are typically obtained from line list data, however these data can have missing information and are subject to right truncation. Previous methods have addressed these problems independently by first imputing missing onset dates, then adjusting truncated case counts, and finally estimating the effective reproduction number. This stepwise approach makes it difficult to propagate uncertainty and can introduce subtle biases during real-time estimation due to the continued impact of assumptions made in previous steps. In this work, we integrate imputation, truncation adjustment, and R t estimation into a single generative Bayesian model, allowing direct joint inference of case counts and R t from line list data with missing symptom onset dates. We then use this framework to compare the performance of nowcasting approaches with different stepwise and generative components on synthetic line list data for multiple outbreak scenarios and across different epidemic phases. We find that under reporting delays realistic for hospitalization data (50% of reports delayed by more than a week), intermediate smoothing, as is common practice in stepwise approaches, can bias nowcasts of case counts and R t , which is avoided in a joint generative approach due to shared regularization of all model components. On incomplete line list data, a fully generative approach enables the quantification of uncertainty due to missing onset dates without the need for an initial multiple imputation step. In a real-world comparison using hospitalization line list data from the COVID-19 pandemic in Switzerland, we observe the same qualitative differences between approaches. The generative modeling components developed in this work have been integrated and further extended in the R package epinowcast, providing a flexible and interpretable tool for real-time surveillance.

The effective reproductive number R e is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of R e , applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated R e dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated R e . Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent R e estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of R e estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data. Over the past two and a half years, countries around the globe have struggled to control the transmission of the SARS-CoV-2 virus within their borders. To manage the situation, it is important to have an accurate picture of how fast the virus is spreading. This can be achieved by calculating the effective reproductive number (Re), which describes how many people, on average, someone with COVID-19 is likely to infect. If the Re is greater than one, the virus is infecting increasingly more people, but if it is smaller than one, the number of cases is declining. Scientists use various strategies to estimate the Re, which each have their own strengths and weaknesses. One of the main difficulties is that infections are typically recorded only when people test positive for COVID-19, are hospitalized with the virus, or die. This means that the data provides a delayed representation of when infections are happening. Furthermore, changes in these records occur later than measures that change the infection dynamics. As a result, researchers need to take these delays into account when estimating Re. Here, Huisman, Scire et al. have developed a new method for estimating the Re based on available data records, statistically taking into account the above-mentioned delays. An online dashboard with daily updates was then created so that policy makers and the population could monitor the values over time. For over two years, Huisman, Scire et al. have been applying their tool and dashboard to COVID-19 data from 170 countries. They found that public health interventions, such as mask requirements and lockdowns, did help reduce the Re in Europe. But the effects were not uniform across the globe, likely because of variations in how restrictions were implemented and followed during the pandemic. In early 2020, the Re only dropped below one after countries put lockdowns or other severe measures in place. The Re values added to the dashboard over the last two years have been used pro-actively to inform public health policies in Switzerland and to monitor the spread of SARS-CoV-2 in South Africa. The team has also recently released programming software based on this method that can be used to track future disease outbreaks, and extended the method to estimate the Re using SARS-CoV-2 levels in wastewater.

Estimation of the effective reproductive number R t is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using R t to assess the effectiveness of interventions and to inform policy. However, estimation of R t from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of R t , we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t , such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting R t estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in R t estimation.