How well can the exponential-growth coalescent approximate constant-rate birth-death population dynamics?
Ontology highlight
ABSTRACT:
SUBMITTER: Stadler T
PROVIDER: S-EPMC4426635 | biostudies-literature | 2015 May
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:Quantifying epidemiological dynamics is crucial for understanding and forecasting the spread of an epidemic. The coalescent and the birth-death model are used interchangeably to infer epidemiological parameters from the genealogical relationships of the pathogen population under study, which in turn are inferred from the pathogen genetic sequencing data. To compare the performance of these widely applied models, we performed a simulation study. We simulated phylogenetic trees under the constant rate birth-death model and the coalescent model with a deterministic exponentially growing infected population. For each tree, we re-estimated the epidemiological parameters using both a birth-death and a coalescent based method, implemented as an MCMC procedure in BEAST v2.0. In our analyses that estimate the growth rate of an epidemic based on simulated birth-death trees, the point estimates such as the maximum a posteriori/maximum likelihood estimates are not very different. However, the estimates of uncertainty are very different. The birth-death model had a higher coverage than the coalescent model, i.e. contained the true value in the highest posterior density (HPD) interval more often (2-13% vs. 31-75% error). The coverage of the coalescent decreases with decreasing basic reproductive ratio and increasing sampling probability of infecteds. We hypothesize that the biases in the coalescent are due to the assumption of deterministic rather than stochastic population size changes. Both methods performed reasonably well when analyzing trees simulated under the coalescent. The methods can also identify other key epidemiological parameters as long as one of the parameters is fixed to its true value. In summary, when using genetic data to estimate epidemic dynamics, our results suggest that the birth-death method will be less sensitive to population fluctuations of early outbreaks than the coalescent method that assumes a deterministic exponentially growing infected population.
| S-EPMC4222655 | biostudies-literature
Project description:Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the birth–death-sampling model (BDM), in the context of estimating population size and birth rates in a population growing exponentially according to the birth–death branching process. For sequences sampled at a single time, we found the coalescent and the BDM gave virtually indistinguishable results in terms of the growth rates and fraction of the population sampled, even when sampling from a small population. For sequences sampled at multiple time points, we find that the birth–death model estimators are subject to large bias if the sampling process is misspecified. Since BDMs incorporate a model of the sampling process, we show how much of the statistical power of BDMs arises from the sequence of sample times and not from the genealogical tree. This motivates the development of a new coalescent estimator, which is augmented with a model of the known sampling process and is potentially more precise than the coalescent that does not use sample time information.
| S-EPMC4223917 | biostudies-literature
Project description:A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by a Brownian dynamics simulation, also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. Building on earlier work, this article completes the development of a robust importance sampling algorithm for Brownian dynamics-i.e., biased Brownian dynamics with weight control-to overcome the high energy and entropy barriers in biomolecular association reactions. The biased Brownian dynamics steers sampling by a bias force, and the weight control algorithm controls sampling by a target weight. This algorithm is optimal if the bias force and the target weight are constructed from the solution of the reaction probability problem. In reality, an approximate reaction probability has to be used to construct the bias force and the target weight. Thus, the performance of the algorithm depends on the quality of the approximation. Given here is a method to calculate a good approximation, which is based on the selection of a reaction coordinate and the variational formulation of the reaction probability problem. The numerically approximated reaction probability is shown by computer experiments to give a factor-of-two speedup over the use of a purely heuristic approximation. Also, the fully developed method is compared to unbiased Brownian dynamics. The tests for human superoxide dismutase, Escherichia coli superoxide dismutase, and antisweetener antibody NC6.8, show speedups of 17, 35, and 39, respectively. The test for reactions between two model proteins with orientations shows speedups of 2578 for one set of configurations and 3341 for another set of configurations.
| S-EPMC1303442 | biostudies-literature
Project description:Estimates of the coalescent effective population size N(e) can be poorly correlated with the true population size. The relationship between N(e) and the population size is sensitive to the way in which birth and death rates vary over time. The problem of inference is exacerbated when the mechanisms underlying population dynamics are complex and depend on many parameters. In instances where nonparametric estimators of N(e) such as the skyline struggle to reproduce the correct demographic history, model-based estimators that can draw on prior information about population size and growth rates may be more efficient. A coalescent model is developed for a large class of populations such that the demographic history is described by a deterministic nonlinear dynamical system of arbitrary dimension. This class of demographic model differs from those typically used in population genetics. Birth and death rates are not fixed, and no assumptions are made regarding the fraction of the population sampled. Furthermore, the population may be structured in such a way that gene copies reproduce both within and across demes. For this large class of models, it is shown how to derive the rate of coalescence, as well as the likelihood of a gene genealogy with heterochronous sampling and labeled taxa, and how to simulate a coalescent tree conditional on a complex demographic history. This theoretical framework encapsulates many of the models used by ecologists and epidemiologists and should facilitate the integration of population genetics with the study of mathematical population dynamics.
| S-EPMC3249372 | biostudies-literature
Project description:Effective risk management requires accurate assessment of population exposure to volcanic hazards. Assessment of this exposure at the large-scale has often relied on circular footprints of various sizes around a volcano to simplify challenges associated with estimating the directionality and distribution of the intensity of volcanic hazards. However, to date, exposure values obtained from circular footprints have never been compared with modelled hazard footprints. Here, we compare hazard and population exposure estimates calculated from concentric radii of 10, 30 and 100 km with those calculated from the simulation of dome- and column-collapse pyroclastic density currents (PDCs), large clasts, and tephra fall across Volcanic Explosivity Index (VEI) 3, 4 and 5 scenarios for 40 volcanoes in Indonesia and the Philippines. We found that a 10 km radius-considered by previous studies to capture hazard footprints and populations exposed for VEI ≤ 3 eruptions-generally overestimates the extent for most simulated hazards, except for column collapse PDCs. A 30 km radius - considered representative of life-threatening VEI ≤ 4 hazards-overestimates the extent of PDCs and large clasts but underestimates the extent of tephra fall. A 100 km radius encapsulates most simulated life-threatening hazards, although there are exceptions for certain combinations of scenario, source parameters, and volcano. In general, we observed a positive correlation between radii- and model-derived population exposure estimates in southeast Asia for all hazards except dome collapse PDC, which is very dependent upon topography. This study shows, for the first time, how and why concentric radii under- or over-estimate hazard extent and population exposure, providing a benchmark for interpreting radii-derived hazard and exposure estimates.Supplementary informationThe online version contains supplementary material available at 10.1007/s00445-023-01686-5.
| S-EPMC10730679 | biostudies-literature
Project description:SUMMARY:Recent genetic studies as well as recorded history point to massive growth in human population sizes during the recent past. To model and understand this growth accurately we introduce FTEC, an easy-to-use coalescent simulation program capable of simulating haplotype samples drawn from a population that has undergone faster than exponential growth. Samples drawn from a population that has undergone faster than exponential growth show an excess of very rare variation and more rapid LD decay when compared with samples drawn from a population that has maintained a constant size over time. AVAILABILITY:Source code for FTEC is freely available for download from the University of Michigan Center for Statistical Genetics Wiki at http://genome.sph.umich.edu/wiki/FTEC
| S-EPMC3338023 | biostudies-literature
Project description:Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman's coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late Quaternary period were related to climate change. [Coalescent; effective population size; Gaussian Markov random fields; phylodynamics; phylogenetics; population genetics.
| S-EPMC5066065 | biostudies-literature
Project description:MotivationEfficient simulation of population genetic samples under a given demographic model is a prerequisite for many analyses. Coalescent theory provides an efficient framework for such simulations, but simulating longer regions and higher recombination rates remains challenging. Simulators based on a Markovian approximation to the coalescent scale well, but do not support simulation of selection. Gene conversion is not supported by any published coalescent simulators that support selection.ResultsWe describe cosi2, an efficient simulator that supports both exact and approximate coalescent simulation with positive selection. cosi2 improves on the speed of existing exact simulators, and permits further speedup in approximate mode while retaining support for selection. cosi2 supports a wide range of demographic scenarios, including recombination hot spots, gene conversion, population size changes, population structure and migration. cosi2 implements coalescent machinery efficiently by tracking only a small subset of the Ancestral Recombination Graph, sampling only relevant recombination events, and using augmented skip lists to represent tracked genetic segments. To preserve support for selection in approximate mode, the Markov approximation is implemented not by moving along the chromosome but by performing a standard backwards-in-time coalescent simulation while restricting coalescence to node pairs with overlapping or near-overlapping genetic material. We describe the algorithms used by cosi2 and present comparisons with existing selection simulators.Availability and implementationA free C++ implementation of cosi2 is available at http://broadinstitute.org/mpg/cosi2.
| S-EPMC4296154 | biostudies-literature
Project description:The stress-induced mutagenesis hypothesis postulates that in response to stress, bacteria increase their genome-wide mutation rate, in turn increasing the chances that a descendant is able to better withstand the stress. This has implications for antibiotic treatment: exposure to subinhibitory doses of antibiotics has been reported to increase bacterial mutation rates and thus probably the rate at which resistance mutations appear and lead to treatment failure. More generally, the hypothesis posits that stress increases evolvability (the ability of a population to generate adaptive genetic diversity) and thus accelerates evolution. Measuring mutation rates under stress, however, is problematic, because existing methods assume there is no death. Yet subinhibitory stress levels may induce a substantial death rate. Death events need to be compensated by extra replication to reach a given population size, thus providing more opportunities to acquire mutations. We show that ignoring death leads to a systematic overestimation of mutation rates under stress. We developed a system based on plasmid segregation that allows us to measure death and division rates simultaneously in bacterial populations. Using this system, we found that a substantial death rate occurs at the tested subinhibitory concentrations previously reported to increase mutation rate. Taking this death rate into account lowers and sometimes removes the signal for stress-induced mutagenesis. Moreover, even when antibiotics increase mutation rate, we show that subinhibitory treatments do not increase genetic diversity and evolvability, again because of effects of the antibiotics on population dynamics. We conclude that antibiotic-induced mutagenesis is overestimated because of death and that understanding evolvability under stress requires accounting for the effects of stress on population dynamics as much as on mutation rate. Our goal here is dual: we show that population dynamics and, in particular, the numbers of cell divisions are crucial but neglected parameters in the evolvability of a population, and we provide experimental and computational tools and methods to study evolvability under stress, leading to a reassessment of the magnitude and significance of the stress-induced mutagenesis paradigm.
| S-EPMC5966242 | biostudies-literature
Project description:We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of selection are graphs for which the fixation probability is increased for advantageous mutants and decreased for disadvantageous mutants. A few examples of such amplifiers have been developed, but so far it is unclear how many such structures exist and how to construct them. Here, we show that almost any undirected random graph is an amplifier of selection for Birth-death updating, where an individual is selected to reproduce with probability proportional to its fitness and one of its neighbors is replaced by that offspring at random. If we instead focus on death-Birth updating, in which a random individual is removed and its neighbors compete for the empty spot, then the same ensemble of graphs consists of almost only suppressors of selection for which the fixation probability is decreased for advantageous mutants and increased for disadvantageous mutants. Thus, the impact of population structure on evolutionary dynamics is a subtle issue that will depend on seemingly minor details of the underlying evolutionary process.
| S-EPMC4636432 | biostudies-literature