Spatial and phylogenetic patterns reveal hidden infection sources of Bacillus anthracis in an anthrax outbreak in Son La province, Vietnam

Bacillus anthracis, the bacterial cause of anthrax, is a zoonosis affecting livestock and wildlife often spilling over into humans. In Vietnam, anthrax has been nationally reportable since 2015 with cases occurring annually, mostly in the northern provinces. In April 2022, an outbreak was reported in Son La province following the butchering of a water buffalo, Bubalus bubalis. A total of 137 humans from three villages were likely exposed to contaminated meat from the animal. Early epidemiological investigations suggested a single animal was involved in all exposures. Five B. anthracis isolates were recovered from human clinical cases along with one from the buffalo hide, another from associated maggots, and one from soil at the carcass site. The isolates were whole genome sequenced, allowing global, regional, and local molecular epidemiological analyses of the outbreak strains. All recovered B. anthracis belong to the A.Br.001/002 lineage based on canonical single nucleotide polymorphism analysis (canSNP). Although not previously identified in Vietnam, this lineage has been identified in the nearby countries of China, India, Indonesia, Thailand, as well as Australia. A twenty-five marker multi-locus variable number tandem repeat analysis (MLVA-25) was used to investigate the relationship between human, soil, and buffalo strains. Locally, four MLVA-25 genotypes were identified from the eight isolates. This level of genetic diversity is unusual for the limited geography and timing of cases and differs from past literature using MLVA-25. The coupled spatial and phylogenetic data suggest this outbreak originated from multiple, likely undetected, animal sources. These findings were further supported by local news reports that identified at least two additional buffalo deaths beyond the initial animal sampled in response to the human cases. Future outbreak response should include intensive surveillance for additional animal cases and additional molecular epidemiological traceback to identify pathogen sources.

Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications

Scope and Goals of the Special Issue: There is a growing realization that despite being the essential tool of modern data-based scientific discovery and model testing, statistics has major problems [...].

Anthrax Surveillance and the Limited Overlap Between Obligate Scavengers and Endemic Anthrax Zones in the United States

Anthrax is a zoonosis caused by the spore-forming bacterium Bacillus anthracis, with potential for high fatality rate, especially in herbivores. Upon host death, spores can enter the soil surrounding the carcass and be ingested by other animals feeding in the same location. Accordingly, surveillance to quickly identify and decontaminate anthrax carcasses is crucial to outbreak prevention. In endemic anthrax areas such as Texas and Africa, vultures are used as a surveillance tool for identifying presence and location of dead animals. However, many anthrax outbreaks in the United States have occurred in areas outside the ranges of both black and turkey vultures. Here, we used a longitudinal camera trap survey at carcass sites in southwestern Montana to investigate the utility of facultative avian scavengers on disease and carcass surveillance in a reemerging anthrax risk zone. From August 2016 to September 2018, camera traps at 11 carcass sites were triggered 1996 times by avian scavengers. While the majority were facultative avian scavengers such as corvids and eagles, our results suggest that facultative scavengers cannot replace vultures as a surveillance tool in this ecosystem due to their absence during the anthrax risk period (June to August), reduced search efficiency, or low flight patterns. We found that the conditions in Montana likely parallel systems elsewhere in the continental United States. Using ecological niche models of B. anthracis distribution overlaid with relative abundance maps of turkey vultures, we found that much of North Dakota, South Dakota, Minnesota, Wyoming, Nebraska, and Iowa have areas of anthrax risk, but low or absent turkey vulture populations. Without vultures in these areas, surveillance capacity is reduced, and it becomes more difficult to identify anthrax cases, meaning fewer carcasses are decontaminated, and consequently, outbreaks could become more frequent or severe.

Factors influencing scavenger guilds and scavenging efficiency in Southwestern Montana

Scavenging of carrion shapes ecological landscapes by influencing scavenger population demography, increasing inter- and intra-specific interactions, and generating ecosystem services such as nutrient cycling and disease moderation. Previous research found the cues promoting, or the constraints limiting, an individual's propensity or ability to scavenge vary widely, depending on anthropogenic and environmental factors. Here we investigated differences in scavenging patterns in a complex scavenger guild in Southwestern Montana. We used camera traps established at 13 carcass sites to monitor carcass detection, visitation, and consumption times, during 2016-2018 and generalized linear models to explore the influence of carcass characteristics, habitat features, and seasonality, on carcass selection and scavenging efficiency. We found that scavenger species diversity was higher at higher elevations and in grassland habitats. Scavenging efficiency was influenced inter alia by seasonality, distance to water, and elevation. We found that most carcass consumption was via facultative scavengers (bears, wolves, magpies, Corvus spp.) rather than turkey vultures, the only obligate scavengers in the study area. However, growing populations of turkey vultures may lead to increased competition with facultative scavengers over carrion, and could have cascading effects on food webs in this ecosystem.

Ungulate use of locally infectious zones in a re-emerging anthrax risk area

Environmentally mediated indirect pathogen transmission is linked to host movement and foraging in areas where pathogens are maintained in the environment. In the case of anthrax, spores of the causative bacterium Bacillus anthracis are released into the environment following host death and create locally infectious zones (LIZs) around carcass sites; by grazing at LIZs, herbivores are potentially exposed to spores. Here, we used camera traps to assess how ungulate species use carcass sites in southwestern Montana and evaluated how these behaviours may promote indirect anthrax transmission, thus providing, to our knowledge, the first detailed documentation and study of the fine-scale mechanisms underlying foraging-based disease transmission in this ecosystem. We found that carcasses at LIZs significantly increased aboveground biomass of vegetation and concentrations of sodium and phosphorus, potentially making these sites more appealing to grazers. Host behavioural responses to LIZs varied depending on species, sex, season and carcass age; but, overall, our results demonstrated that carcasses or carcass sites serve as an attractant to herbivores in this system. Attraction to LIZs probably represents an increased risk of exposure to B. anthracis and, consequently, increased anthrax transmission rates. Accordingly, continued anthrax surveillance and control strategies are critical in this system.

Coalescence modeling of intrainfection Bacillus anthracis populations allows estimation of infection parameters in wild populations

Bacillus anthracis, the etiological agent of anthrax, is a well-established model organism. For B. anthracis and most other infectious diseases, knowledge regarding transmission and infection parameters in natural systems, in large part, comprises data gathered from closely controlled laboratory experiments. Fatal, natural anthrax infections transmit the bacterium through new host-pathogen contacts at carcass sites, which can occur years after death of the previous host. For the period between contact and death, all of our knowledge is based upon experimental data from domestic livestock and laboratory animals. Here we use a noninvasive method to explore the dynamics of anthrax infections, by evaluating the terminal diversity of B. anthracis in anthrax carcasses. We present an application of population genetics theory, specifically, coalescence modeling, to intrainfection populations of B. anthracis to derive estimates for the duration of the acute phase of the infection and effective population size converted to the number of colony-forming units establishing infection in wild plains zebra (Equus quagga). Founding populations are small, a few colony-forming units, and infections are rapid, lasting roughly between 1 d and 3 d in the wild. Our results closely reflect experimental data, showing that small founding populations progress acutely, killing the host within days. We believe this method is amendable to other bacterial diseases from wild, domestic, and human systems.

Model Projections in Model Space: A Geometric Interpretation of the AIC Allows Estimating the Distance Between Truth and Approximating Models

Information criteria have had a profound impact on modern ecological science. They allow researchers to estimate which probabilistic approximating models are closest to the generating process. Unfortunately, information criterion comparison does not tell how good the best model is. In this work, we show that this shortcoming can be resolved by extending the geometric interpretation of Hirotugu Akaike's original work. Standard information criterion analysis considers only the divergences of each model from the generating process. It is ignored that there are also estimable divergence relationships amongst all of the approximating models. We then show that using both sets of divergences and an estimator of the negative self entropy, a model space can be constructed that includes an estimated location for the generating process. Thus, not only can an analyst determine which model is closest to the generating process, she/he can also determine how close to the generating process the best approximating model is. Properties of the generating process estimated from these projections are more accurate than those estimated by model averaging. We illustrate in detail our findings and our methods with two ecological examples for which we use and test two different neg-selfentropy estimators. The applications of our proposed model projection in model space extend to all areas of science where model selection through information criteria is done.

Errors in Statistical Inference Under Model Misspecification: Evidence, Hypothesis Testing, and AIC

The methods for making statistical inferences in scientific analysis have diversified even within the frequentist branch of statistics, but comparison has been elusive. We approximate analytically and numerically the performance of Neyman-Pearson hypothesis testing, Fisher significance testing, information criteria, and evidential statistics (Royall, 1997). This last approach is implemented in the form of evidence functions: statistics for comparing two models by estimating, based on data, their relative distance to the generating process (i.e., truth) (Lele, 2004). A consequence of this definition is the salient property that the probabilities of misleading or weak evidence, error probabilities analogous to Type 1 and Type 2 errors in hypothesis testing, all approach 0 as sample size increases. Our comparison of these approaches focuses primarily on the frequency with which errors are made, both when models are correctly specified, and when they are misspecified, but also considers ease of interpretation. The error rates in evidential analysis all decrease to 0 as sample size increases even under model misspecification. Neyman-Pearson testing on the other hand, exhibits great difficulties under misspecification. The real Type 1 and Type 2 error rates can be less, equal to, or greater than the nominal rates depending on the nature of model misspecification. Under some reasonable circumstances, the probability of Type 1 error is an increasing function of sample size that can even approach 1! In contrast, under model misspecification an evidential analysis retains the desirable properties of always having a greater probability of selecting the best model over an inferior one and of having the probability of selecting the best model increase monotonically with sample size. We show that the evidence function concept fulfills the seeming objectives of model selection in ecology, both in a statistical as well as scientific sense, and that evidence functions are intuitive and easily grasped. We find that consistent information criteria are evidence functions but the MSE minimizing (or efficient) information criteria (e.g., AIC, AICc, TIC) are not. The error properties of the MSE minimizing criteria switch between those of evidence functions and those of Neyman-Pearson tests depending on models being compared.

Modeling R₀ for Pathogens with Environmental Transmission: Animal Movements, Pathogen Populations, and Local Infectious Zones

How a disease is transmitted affects our ability to determine R₀, the average number of new cases caused by an infectious host at the onset of an epidemic. R₀ becomes progressively more difficult to compute as transmission varies from directly transmitted diseases to diseases that are vector-borne to environmentally transmitted diseases. Pathogens responsible for diseases with environmental transmission are typically maintained in environmental reservoirs that exhibit a complex spatial distribution of local infectious zones (LIZs). Understanding host encounters with LIZs and pathogen persistence within LIZs is required for an accurate R₀ and modeling these contacts requires an integrated geospatial and dynamical systems approach. Here we review how interactions between host and pathogen populations and environmental reservoirs are driven by landscape-level variables, and synthesize the quantitative framework needed to formulate outbreak response and disease control.

Decoupling environmental effects and host population dynamics for anthrax, a classic reservoir-driven disease

Quantitative models describing environmentally-mediated disease transmission rarely focus on the independent contribution of recruitment and the environment on the force of infection driving outbreaks. In this study we attempt to investigate the interaction between external factors and host’s population dynamics in determining the outbreaks of some indirectly transmitted diseases. We first built deterministic and stochastic compartmental models based on anthrax which were parameterized using information from literature and complemented with field observations. Our force of infection function was derived modeling the number of successful transmission encounters as a pure birth process that depends on the pathogen’s dispersion effort. After accounting for individual heterogeneity in pathogen’s dispersion effort, we allowed the force of infection to vary seasonally according to external factors recreating a scenario in which disease transmission increases in response to an environmental variable. Using simulations we demonstrate that anthrax disease dynamics in mid-latitude grasslands is decoupled from hosts population dynamics. When seasonal forcing was ignored, outbreaks matched hosts reproductive events, a scenario that is not realistic in nature. Instead, when allowing the force of infection to vary seasonally, outbreaks were only present in years were environmental variables were appropriate for the outbreaks to develop. We used the stochastic formulation of the force of infection to derive R₀ under scenarios with different assumptions. The derivation of R₀ allowed us to conclude that during epizootic years, pathogen contribution to disease persistence is nearly independent of dispersion. In endemic years, only pathogens with high dispersion significantly prevent disease extinction. Finally, we used our model in a maximum likelihood framework to estimate the parameters that determined a significant anthrax outbreak in Montana in 2008. Our study highlights the importance of the environment in determining anthrax outbreak intensity and could be useful to predict future events that could result in significant wildlife and domestic livestock losses.

chromploid: An R package for chromosome number evolution across the plant tree of life

PREMISE OF THE STUDY

Polyploidy has profound evolutionary consequences for land plants. Despite the availability of large phylogenetic and chromosomal data sets, estimating the rates of polyploidy and chromosomal evolution across the tree of life remains a challenging, computationally complex problem. We introduce the R package chromploid, which allows scientists to perform inference of chromosomal evolution rates across large phylogenetic trees.

METHODS AND RESULTS

chromploid is an open-source package in the R environment that calculates the likelihood function of models of chromosome evolution. Models of discrete character evolution can be customized using chromploid. We demonstrate the performance of the BiChroM model, testing for associations between rates of chromosome doubling (as a proxy for polyploidy) and a binary phenotypic character, within chromploid using simulations and empirical data from Solanum. In simulations, estimated chromosome-doubling rates were unbiased and the variance decreased with larger trees, but distinguishing small differences in rates of chromosome doubling, even from large data sets, remains challenging. In the Solanum data set, a custom model of chromosome number evolution demonstrated higher rates of chromosome doubling in herbaceous species compared to woody.

CONCLUSIONS

chromploid enables researchers to perform robust likelihood-based inferences using complex models of chromosome number evolution across large phylogenies.

An efficient extension of N-mixture models for multi-species abundance estimation

In this study we propose an extension of the N-mixture family of models that targets an improvement of the statistical properties of rare species abundance estimators when sample sizes are low, yet typical for tropical studies. The proposed method harnesses information from other species in an ecological community to correct each species' estimator. We provide guidance to determine the sample size required to estimate accurately the abundance of rare tropical species when attempting to estimate the abundance of single species.We evaluate the proposed methods using an assumption of 50 m radius plots and perform simulations comprising a broad range of sample sizes, true abundances and detectability values and a complex data generating process. The extension of the N-mixture model is achieved by assuming that the detection probabilities are drawn at random from a beta distribution in a multi-species fashion. This hierarchical model avoids having to specify a single detection probability parameter per species in the targeted community. Parameter estimation is done via Maximum Likelihood.We compared our multi-species approach with previously proposed multi-species N-mixture models, which we show are biased when the true densities of species in the community are less than seven individuals per 100 hectares. The beta N-mixture model proposed here outperforms the traditional Multi-species N-mixture model by allowing the estimation of organisms at lower densities and controlling the bias in the estimation.We illustrate how our methodology can be used to suggest sample sizes required to estimate the abundance of organisms, when these are either rare, common or abundant. When the interest is full communities, we show how the multi-species approaches, and in particular our beta model and estimation methodology, can be used as a practical solution to estimate organism densities from rapid inventory datasets. The statistical inferences done with our model via Maximum Likelihood can also be used to group species in a community according to their detectabilities.

A parametric interpretation of Bayesian Nonparametric Inference from Gene Genealogies: Linking ecological, population genetics and evolutionary processes

Using a nonparametric Bayesian approach Palacios and Minin (2013) dramatically improved the accuracy, precision of Bayesian inference of population size trajectories from gene genealogies. These authors proposed an extension of a Gaussian Process (GP) nonparametric inferential method for the intensity function of non-homogeneous Poisson processes. They found that not only the statistical properties of the estimators were improved with their method, but also, that key aspects of the demographic histories were recovered. The authors' work represents the first Bayesian nonparametric solution to this inferential problem because they specify a convenient prior belief without a particular functional form on the population trajectory. Their approach works so well and provides such a profound understanding of the biological process, that the question arises as to how truly "biology-free" their approach really is. Using well-known concepts of stochastic population dynamics, here I demonstrate that in fact, Palacios and Minin's GP model can be cast as a parametric population growth model with density dependence and environmental stochasticity. Making this link between population genetics and stochastic population dynamics modeling provides novel insights into eliciting biologically meaningful priors for the trajectory of the effective population size. The results presented here also bring novel understanding of GP as models for the evolution of a trait. Thus, the ecological principles foundation of Palacios and Minin (2013)'s prior adds to the conceptual and scientific value of these authors' inferential approach. I conclude this note by listing a series of insights brought about by this connection with Ecology.

Functional Traits, Flocking Propensity, and Perceived Predation Risk in an Amazonian Understory Bird Community

Within a community, different species might share similar predation risks, and, thus, the ability of species to signal and interpret heterospecific threat information may determine species' associations. We combined observational, experimental, and phylogenetic approaches to determine the extent to which evolutionary history and functional traits determined flocking propensity and perceived predation risk (response to heterospecific alarm calls) in a lowland Amazonian bird community. We predicted that small birds that feed myopically and out in the open would have higher flocking propensities and account for a higher proportion of positive responses to alarms. Using generalized linear models and the incorporation of phylogeny on data from 56 species, our results suggest that phylogenetic relationships alongside body size, foraging height, vegetation density, and response to alarm calls influence flocking propensity. Conversely, phylogenetic relationships did not influence response to heterospecific alarm calls. Among functional traits, however, foraging strategy, foraging density, and flocking propensity partially explained responses to alarm calls. Our results suggest that flocking propensity and perceived predation risk are positively related and that functional ecological traits and evolutionary history may explain certain species' associations.

The red death meets the abdominal bristle: polygenic mutation for susceptibility to a bacterial pathogen in Caenorhabditis elegans

Understanding the genetic basis of susceptibility to pathogens is an important goal of medicine and of evolutionary biology. A key first step toward understanding the genetics and evolution of any phenotypic trait is characterizing the role of mutation. However, the rate at which mutation introduces genetic variance for pathogen susceptibility in any organism is essentially unknown. Here, we quantify the per-generation input of genetic variance by mutation (VM) for susceptibility of Caenorhabditis elegans to the pathogenic bacterium Pseudomonas aeruginosa (defined as the median time of death, LT50). VM for LT50 is slightly less than VM for a variety of life-history and morphological traits in this strain of C. elegans, but is well within the range of reported values in a variety of organisms. Mean LT50 did not change significantly over 250 generations of mutation accumulation. Comparison of VM to the standing genetic variance (VG) implies a strength of selection against new mutations of a few tenths of a percent. These results suggest that the substantial standing genetic variation for susceptibility of C. elegans to P. aeruginosa can be explained by polygenic mutation coupled with purifying selection.

Density-dependent state-space model for population-abundance data with unequal time intervals

The Gompertz state-space (GSS) model is a stochastic model for analyzing time-series observations of population abundances. The GSS model combines density dependence, environmental process noise, and observation error toward estimating quantities of interest in biological monitoring and population viability analysis. However, existing methods for estimating the model parameters apply only to population data with equal time intervals between observations. In the present paper, we extend the GSS model to data with unequal time intervals, by embedding it within a state-space version of the Ornstein-Uhlenbeck process, a continuous-time model of an equilibrating stochastic system. Maximum likelihood and restricted maximum likelihood calculations for the Ornstein-Uhlenbeck state-space model involve only numerical maximization of an explicit multivariate normal likelihood, and so the extension allows for easy bootstrapping, yielding confidence intervals for model parameters, statistical hypothesis testing of density dependence, and selection among sub-models using information criteria. Ecologists and managers previously drawn to models lacking density dependence or observation error because such models accommodated unequal time intervals (for example, due to missing data) now have an alternative analysis framework incorporating density dependence, process noise, and observation error.

Assessing parameter identifiability in phylogenetic models using data cloning

The success of model-based methods in phylogenetics has motivated much research aimed at generating new, biologically informative models. This new computer-intensive approach to phylogenetics demands validation studies and sound measures of performance. To date there has been little practical guidance available as to when and why the parameters in a particular model can be identified reliably. Here, we illustrate how Data Cloning (DC), a recently developed methodology to compute the maximum likelihood estimates along with their asymptotic variance, can be used to diagnose structural parameter nonidentifiability (NI) and distinguish it from other parameter estimability problems, including when parameters are structurally identifiable, but are not estimable in a given data set (INE), and when parameters are identifiable, and estimable, but only weakly so (WE). The application of the DC theorem uses well-known and widely used Bayesian computational techniques. With the DC approach, practitioners can use Bayesian phylogenetics software to diagnose nonidentifiability. Theoreticians and practitioners alike now have a powerful, yet simple tool to detect nonidentifiability while investigating complex modeling scenarios, where getting closed-form expressions in a probabilistic study is complicated. Furthermore, here we also show how DC can be used as a tool to examine and eliminate the influence of the priors, in particular if the process of prior elicitation is not straightforward. Finally, when applied to phylogenetic inference, DC can be used to study at least two important statistical questions: assessing identifiability of discrete parameters, like the tree topology, and developing efficient sampling methods for computationally expensive posterior densities.

Inherent variation in stable isotope values and discrimination factors in two life stages of green turtles

We examine inherent variation in carbon and nitrogen stable isotope values of multiple soft tissues from a population of captive green turtles Chelonia mydas to determine the extent of isotopic variation due to individual differences in physiology. We compare the measured inherent variation in the captive population with the isotopic variation observed in a wild population of juvenile green turtles. Additionally, we measure diet-tissue discrimination factors to determine the offset that occurs between isotope values of the food source and four green turtle tissues. Tissue samples (epidermis, dermis, serum, and red blood cells) were collected from captive green turtles in two life stages (40 large juveniles and 30 adults) at the Cayman Turtle Farm, Grand Cayman, and analyzed for carbon and nitrogen stable isotopes. Multivariate normal models were fit to the isotope data, and the Bayesian Information Criterion was used for model selection. Inherent variation and discrimination factors differed among tissues and life stages. Inherent variation was found to make up a small portion of the isotopic variation measured in a wild population. Discrimination factors not only are tissue and life stage dependent but also appear to vary with diet and sea turtle species, thus highlighting the need for appropriate discrimination factors in dietary reconstructions and trophic-level estimations. Our measures of inherent variation will also be informative in field studies employing stable isotope analysis so that differences in diet or habitat are more accurately identified.

Replicated sampling increases efficiency in monitoring biological populations

Observation or sampling error in population monitoring can cause serious degradation of the inferences, such as estimates of trend or risk, that ecologists and managers frequently seek to make with time-series observations of population abundances. We show that replicating the sampling process can considerably improve the information obtained from population monitoring. At each sampling time the sampling method would be repeated, either simultaneously or within a short time. In this study we examine the potential value of replicated sampling to population monitoring using a density-dependent population model. We modify an existing population time-series model, the Gompertz state-space model, to incorporate replicated sampling, and we develop maximum-likelihood and restricted maximum-likelihood estimates of model parameters. Depending on sampling protocols, replication may or may not entail substantial extra cost. Some sampling programs already have replicated samples, but the samples are aggregated or pooled into one estimate of population abundance; such practice of aggregating samples, according to our model, loses considerable information about model parameters. The gains from replicated sampling are realized in substantially improved statistical inferences about model parameters, especially inferences for sorting out the contributions of process noise and observation error to observed population variability.

Use of stochastic models to assess the effect of environmental factors on microbial growth

We present a novel application of a stochastic ecological model to the study and analysis of microbial growth dynamics as influenced by environmental conditions in an extensive experimental data set. The model proved to be useful in bridging the gap between theoretical ideas in ecology and an applied problem in microbiology. The data consisted of recorded growth curves of Escherichia coli grown in triplicate in a base medium with all 32 possible combinations of five supplements: glucose, NH(4)Cl, HCl, EDTA, and NaCl. The potential complexity of 2(5) experimental treatments and their effects was reduced to 2(2) as just the metal chelator EDTA, the presumed osmotic pressure imposed by NaCl, and the interaction between these two factors were enough to explain the variability seen in the data. The statistical analysis showed that the positive and negative effects of the five chemical supplements and their combinations were directly translated into an increase or decrease in time required to attain stationary phase and the population size at which the stationary phase started. The stochastic ecological model proved to be useful, as it effectively explained and summarized the uncertainty seen in the recorded growth curves. Our findings have broad implications for both basic and applied research and illustrate how stochastic mathematical modeling coupled with rigorous statistical methods can be of great assistance in understanding basic processes in microbial ecology.