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1AbstractZoonotic pathogens spread by wildlife continue to spill into human populations and threaten human lives. A potential way to reduce this threat is by vaccinating wildlife species that harbor pathogens that are infectious to humans. Unfortunately, even in cases where vaccines can be distributed en masse as edible baits, achieving levels of vaccine coverage sufficient for pathogen elimination is rare. Developing vaccines that self-disseminate may help solve this problem by magnifying the impact of limited direct vaccination. Although models exist that quantify how well these self-disseminating vaccines will work when introduced into temporally stable wildlife populations, how well they will perform when introduced into populations with pronounced seasonal population dynamics remains unknown. Here we develop and analyze mathematical models of fluctuating wildlife populations that allow us to study how reservoir ecology, vaccine design, and vaccine delivery interact to influence vaccine coverage and opportunities for pathogen elimination. Our results demonstrate that the timing of vaccine delivery can make or break the success of vaccination programs. As a general rule, the effectiveness of self-disseminating vaccines is optimized by introducing after the peak of seasonal reproduction when the number of susceptible animals is near its maximum.

The ecology and life history of wild animals influences their potential to harbour infectious disease. This observation has motivated studies identifying empirical relationships between traits of wild animals and historical patterns of spillover and emergence into humans. Although these studies have identified compelling broad-scale patterns, they are generally agnostic with respect to underlying mechanisms. Here, we develop mathematical models that couple reservoir population ecology with viral epidemiology and evolution to clarify existing verbal arguments and pinpoint the conditions that favour spillover and emergence. Our results support the idea that average lifespan influences the likelihood of an animal serving as a reservoir for human infectious disease. At the same time, however, our results show that the magnitude of this effect is sensitive to the rate of viral mutation. Our results also demonstrate that viral pathogens causing persistent infections or a transient immune response within the reservoir are more likely to fuel emergence. Genetically explicit stochastic simulations enrich these mathematical results by identifying relationships between the genetic basis of transmission and the risk of spillover and emergence. Together, our results clarify the scope of applicability for existing hypotheses and refine our understanding of emergence risk.

Background and objectivesGenetic engineering combined with CRISPR technology has developed to the point that gene drives can, in theory, be engineered to cause extinction in countless species. Success of extinction programs now rests on the possibility of resistance evolution, which is largely unknown. Depending on the gene-drive technology, resistance may take many forms, from mutations in the nuclease target sequence (e.g. for CRISPR) to specific types of non-random population structures that limit the drive (that may block potentially any gene-drive technology).MethodologyWe develop mathematical models of various deviations from random mating to consider escapes from extinction-causing gene drives. A main emphasis here is sib mating in the face of recessive-lethal and Y-chromosome drives.ResultsSib mating easily evolves in response to both kinds of gene drives and maintains mean fitness above 0, with equilibrium fitness depending on the level of inbreeding depression. Environmental determination of sib mating (as might stem from population density crashes) can also maintain mean fitness above 0. A version of Maynard Smith’s haystack model shows that pre-existing population structure can enable drive-free subpopulations to be maintained against gene drives.Conclusions and implicationsTranslation of mean fitness into population size depends on ecological details, so understanding mean fitness evolution and dynamics is merely the first step in predicting extinction. Nonetheless, these results point to possible escapes from gene-drive-mediated extinctions that lie beyond the control of genome engineering.Lay summaryRecent gene drive technologies promise to suppress and even eradicate pests and disease vectors. Simple models of gene-drive evolution in structured populations show that extinction-causing gene drives can be thwarted both through the evolution of sib mating as well as from purely demographic processes that cluster drive-free individuals.

Understanding the evolutionary dynamics of microbial communities is a key step towards the goal of predicting and manipulating microbiomes to promote beneficial states. While interactions within microbiomes and between microbes and their environment collectively determine the community composition and population dynamics, we are often concerned with traits or functions of a microbiome that link more directly to host health. To study how traits of a microbiome are impacted by eco-evolutionary dynamics, we recast a classic resource-mediated population dynamic model into a population genetic framework which incorporates traits. The relative fitness of each group of microbes can be explicitly written in terms of population dynamic parameters, and corresponding evolutionary dynamics emerge. Using several example systems, we demonstrate how natural selection, mutation, and shifts in the environment work together to produce changes in traits over time.

When several factors align, pathogens that normally infect wildlife can spill over into the human population. If pathogen transmission within the human population is self-sustaining, or rapidly evolves to be self sustaining, novel human pathogens can emerge. Although many factors influence the likelihood of spillover and emergence, the rate of contact between humans and wildlife is critical. Thus, for those pathogens inhabiting wildlife reservoirs with pronounced seasonal fluctuations in population density, it is broadly recognized that spillover risk also varies with season. What remains unknown, however, is the extent to which seasonal fluctuations in reservoir populations influence the evolutionary dynamics of pathogens in ways that affect the likelihood of emergence. Here, we use mathematical models and stochastic simulations to show that seasonal fluctuations in reservoir population densities lead to seasonal increases in genetic variation within pathogen populations and thus influence the waiting time for mutations capable of sustained human-to-human transmission. These seasonal increases in genetic variation also lead to elevated risk of emergence at predictable times of year.

Population dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research, including predicting how populations change over time, determining how manipulations of microbiomes affect dynamics and designing synthetic microbiomes to perform tasks. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka–Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka–Volterra model. We used structural identifiability analyses to determine the extent to which a time series of relative abundances can be used to parametrize the generalized Lotka–Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Using synthetic data of a simple community for which we know the underlying structure, local practical identifiability analysis showed that modest amounts of both process and measurement error do not fundamentally affect these identifiability properties.

Background and objectives Genetic engineering and similar technologies offer promising new approaches to controlling human diseases by blocking transmission from vectors. However, in spatially structured populations, imperfect coverage of the vector will leave pockets in which the parasite may persist. Movement by humans may disrupt this local persistence and facilitate eradication when these pockets are small, spreading parasite reproduction outside unprotected areas and into areas that block its reproduction. Here, we consider the sensitivity of this process to biological details: do simple generalities emerge that may facilitate interventions? Methodology We develop formal mathematical models of this process similar to standard Ross–Macdonald models, but (i) specifying spatial structure of two patches, with vector transmission blocked in one patch but not in the other, (ii) allowing temporary human movement (travel instead of migration) and (iii) considering two different modes of mosquito biting. Results We find that there is no invariant effect of disrupting spatial structure with travel. For both biting models, travel out of the unprotected patch has different consequences than travel by visitors into the patch, but the effects are reversed between the two biting models. Conclusions and implications Overall, the effect of human travel on the maintenance of vector-borne diseases in structured habitats must be considered in light of the actual biology of mosquito abundances, biting dynamics and human movement patterns. Lay summary: Genetic interventions against pathogens transmitted by insect vectors are promising methods of controlling infectious diseases. These interventions may be imperfect, leaving pockets where the parasite persists. How will human movement between protected and unprotected areas affect persistence? Mathematical models developed here show that the answer is ecology-dependent, depending on vector biting behavior.

Acetaminophen (APAP) overdose is one of the predominant causes of drug induced acute liver injury in the U.S and U.K. Clinical studies show that ingestion of alcohol may increase the risk of APAP induced liver injury. Chronic alcoholism may potentiate APAP hepatotoxicity and this increased risk of APAP toxicity is observed when APAP is ingested even shortly after alcohol is cleared from the body. However, clinical reports also suggest that acute alcohol consumption may have a protective effect against hepatotoxicity by inhibiting microsomal acetaminophen oxidation and thereby reducing N-acetyl-p-benzoquinone imine (NAPQI) production. The aim of this study is to model this dual role of alcohol to determine how the timing of alcohol ingestion affects APAP metabolism and resulting liver injury and identify mechanisms of APAP induced liver injury. The mathematical model is developed to capture condition of a patient of single time APAP overdose who may be an acute or chronic alcohol user. The analysis suggests that the risk of APAP-induced hepatotoxicity is increased if APAP is ingested shortly after alcohol is cleared from the body in chronic alcohol users. A protective effect of acute consumption of alcohol is also observed in patients with APAP overdose. For example, simultaneous ingestion of alcohol and APAP overdose or alcohol intake after or before few hours of APAP overdose may result in less APAP-induced hepatotoxicity when compared to a single time APAP overdose. The rate of hepatocyte damage in APAP overdose patients depends on trade-off between induction and inhibition of CYP enzyme.

The obligate intracellular bacterial pathogen Chlamydia trachomatis (Ctr) is reliant on an unusual developmental cycle consisting of two cell forms termed the elementary body (EB) and the reticulate body (RB). The EB is infectious and utilizes a type III secretion system and preformed effector proteins during invasion, but does not replicate. The RB replicates in the host cell but is non-infectious. This developmental cycle is central to chlamydial pathogenesis. In this study we developed mathematical models of the chlamydial developmental cycle that account for potential factors influencing the timing of RB to EB cell type switching during infection. Our models predicted that two broad categories of regulatory signals for RB to EB development could be differentiated experimentally; an “intrinsic” cell autonomous program inherent to each RB or an “extrinsic” environmental signal to which RBs respond. To experimentally differentiate between these hypotheses, we tracked the expression of Ctr developmental specific promoters using fluorescent reporters and live cell imaging. These experiments indicated that EB production was not influenced by increased MOI or by superinfection, suggesting the cycle follows an intrinsic program that is not influenced by environmental factors. Additionally, live cell imaging of these promoter constructs revealed that EB development is a multistep process linked to RB growth rate and cell division. The formation of EBs followed a cell type gene expression progression with the promoters for euo and ihtA active in RBs, while the promoter for hctA was active in early EBs/intermediate cells and finally the promoters for the true late genes, hctB, scc2, and tarp active in the maturing EB.ImportanceChlamydia trachomatis is an obligate intracellular bacteria that can cause trachoma, cervicitis, urethritis, salpingitis, and pelvic inflammatory disease. To establish infection in host cells Chlamydia must complete a multi cell type developmental cycle. The developmental cycle consists of two specialized cells; the EB which mediates infection of new cells and the RB which replicates and eventually produces more EB cells to mediate the next round of infection. By developing and testing mathematical models to discriminate between two competing hypotheses for the nature of the signal controlling RB to EB cell type switching. We demonstrate that RB to EB development follows a cell autonomous program that does not respond to environmental cues. Additionally, we show that RB to EB development is a function of cell growth and cell division. This study serves to further our understanding of the chlamydial developmental cycle that is central to the bacterium’s pathogenesis.

Forecasting the risk of pathogen spillover from reservoir populations of wild or domestic animals is essential for the effective deployment of interventions such as wildlife vaccination or culling. Due to the sporadic nature of spillover events and limited availability of data, developing and validating robust, spatially explicit, predictions is challenging. Recent efforts have begun to make progress in this direction by capitalizing on machine learning methodologies. An important weakness of existing approaches, however, is that they generally rely on combining human and reservoir infection data during the training process and thus conflate risk attributable to the prevalence of the pathogen in the reservoir population with the risk attributed to the realized rate of spillover into the human population. Because effective planning of interventions requires that these components of risk be disentangled, we developed a multi-layer machine learning framework that separates these processes. Our approach begins by training models to predict the geographic range of the primary reservoir and the subset of this range in which the pathogen occurs. The spillover risk predicted by the product of these reservoir specific models is then fit to data on realized patterns of historical spillover into the human population. The result is a geographically specific spillover risk forecast that can be easily decomposed and used to guide effective intervention. Applying our method to Lassa virus, a zoonotic pathogen that regularly spills over into the human population across West Africa, results in a model that explains a modest but statistically significant portion of geographic variation in historical patterns of spillover. When combined with a mechanistic mathematical model of infection dynamics, our spillover risk model predicts that 897,700 humans are infected by Lassa virus each year across West Africa, with Nigeria accounting for more than half of these human infections., Author summary The 2019 emergence of SARS-CoV-2 is a grim reminder of the threat animal-borne pathogens pose to human health. Even prior to SARS-CoV-2, the spillover of pathogens from animal reservoirs was a persistent problem, with pathogens such as Ebola, Nipah, and Lassa regularly but unpredictably causing outbreaks. Machine-learning models that anticipate when and where pathogen transmission from animals to humans is likely to occur would help guide surveillance efforts and preemptive countermeasures like information campaigns or vaccination programs. We develop a novel machine learning framework that uses datasets describing the distribution of a virus within its host and the range of its animal host, along with data on spatial patterns of human immunity, to infer rates of animal-to-human transmission across a region. By training the model on data from the animal host alone, our framework allows rigorous validation of spillover predictions using human data. We apply our framework to Lassa fever, a viral disease of West Africa that is spread to humans by rodents, and use the predictions to update estimates of Lassa virus infections in humans. Our results suggest that Nigeria is most at risk for the emergence of Lassa virus, and should be prioritized for outbreak-surveillance.

A working group at the National Institute for Mathematical and Biological Synthesis (NIMBioS) explored the feasibility of integrating 2 complementary approaches relevant to ecological risk assessment. Adverse outcome pathway (AOP) models provide "bottom-up" mechanisms to predict specific toxicological effects that could affect an individual's ability to grow, reproduce, and/or survive from a molecular initiating event. Dynamic energy budget (DEB) models offer a "top-down" approach that reverse engineers stressor effects on growth, reproduction, and/or survival into modular characterizations related to the acquisition and processing of energy resources. Thus, AOP models quantify linkages between measurable molecular, cellular, or organ-level events, but they do not offer an explicit route to integratively characterize stressor effects at higher levels of organization. While DEB models provide the inherent basis to link effects on individuals to those at the population and ecosystem levels, their use of abstract variables obscures mechanistic connections to suborganismal biology. To take advantage of both approaches, we developed a conceptual model to link DEB and AOP models by interpreting AOP key events as measures of damage-inducing processes affecting DEB variables and rates. We report on the type and structure of data that are generated for AOP models that may also be useful for DEB models. We also report on case studies under development that merge information collected for AOPs with DEB models and highlight some of the challenges. Finally, we discuss how the linkage of these 2 approaches can improve ecological risk assessment, with possibilities for progress in predicting population responses to toxicant exposures within realistic environments. Integr Environ Assess Manag 2018;14:615-624. © 2018 SETAC.

Transmissible vaccines have the potential to revolutionize infectious disease control by reducing the vaccination effort required to protect a population against a disease. Recent efforts to develop transmissible vaccines focus on recombinant transmissible vaccine designs (RTVs) because they pose reduced risk if intra-host evolution causes the vaccine to revert to its vector form. However, the shared antigenicity of the vaccine and vector may confer vaccine-immunity to hosts infected with the vector, thwarting the ability of the vaccine to spread through the population. We build a mathematical model to test whether a RTV can facilitate disease management in instances where reversion is likely to introduce the vector into the population or when the vector organism is already established in the host population, and the vector and vaccine share perfect cross-immunity. Our results show that a RTV can autonomously eradicate a pathogen, or protect a population from pathogen invasion, when cross-immunity between vaccine and vector is absent. If cross-immunity between vaccine and vector exists, however, our results show that a RTV can substantially reduce the vaccination effort necessary to control or eradicate a pathogen only when continuously augmented with direct manual vaccination. These results demonstrate that estimating the extent of cross-immunity between vector and vaccine is a critical step in RTV design, and that herpesvirus vectors showing facile reinfection and weak cross-immunity are promising.

Lassa virus is a significant burden on human health throughout its endemic region in West Africa, with most human infections the result of spillover from the primary rodent reservoir of the virus, the natal multimammate mouse,M. natalensis. Here we develop a Bayesian methodology for estimating epidemiological parameters of Lassa virus within its rodent reservoir and for generating probabilistic predictions for the efficacy of rodent vaccination programs. Our approach uses Approximate Bayesian Computation (ABC) to integrate mechanistic mathematical models, remotely-sensed precipitation data, and Lassa virus surveillance data from rodent populations. Using simulated data, we show that our method accurately estimates key model parameters, even when surveillance data are available from only a relatively small number of points in space and time. Applying our method to previously published data from two villages in Guinea estimates the time-averagedR0of Lassa virus to be 1.658 and 1.453 for rodent populations in the villages of Bantou and Tanganya, respectively. Using the posterior distribution for model parameters derived from these Guinean populations, we evaluate the likely efficacy of vaccination programs relying on distribution of vaccine-laced baits. Our results demonstrate that effective and durable reductions in the risk of Lassa virus spillover into the human population will require repeated distribution of large quantities of vaccine.Author SummaryLassa virus is a chronic source of illness throughout West Africa, and is considered to be a threat for widespread emergence. Because most human infections result from contact with infected rodents, interventions that reduce the number of rodents infected with Lassa virus represent promising opportunities for reducing the public health burden of this disease. Evaluating how well alternative interventions are likely to perform is complicated by our relatively poor understanding of viral epidemiology within the reservoir population. Here we develop a novel statistical approach that couples mathematical models and viral surveillance data from rodent populations to robustly estimate key epidemiological parameters. Applying our method to existing data from Guinea yields well-resolved parameter estimates and allows us to simulate a variety of rodent vaccination programs. Together, our results demonstrate that rodent vaccination alone is unlikely to be an effective tool for reducing that public health burden of Lassa fever within West Africa.

Genetic engineering combined with CRISPR technology has developed to the point that gene drives can, in theory, be engineered to cause extinction in countless species. Success of extinction programs now rests on the possibility of resistance evolution, which is largely unknown. For CRISPR technology, resistance may take many forms, from mutations in the nuclease target sequence to specific types of non-random population structures that limit the drive. We develop mathematical models of various deviations from random mating to consider escapes from extinction-causing gene drives. We use a version of Maynard Smith’s haystack model to show that population structure can enable drive-free subpopulations to be maintained against gene drives. Our main emphasis, however, is sib mating in the face of recessive-lethal and Y-chromosome drives. Sib mating easily evolves in response to both kinds of gene drives and maintains mean fitness above 0, with equilibrium fitness depending on the level of inbreeding depression. Environmental determination of sib mating (as might stem from population density crashes) can also maintain mean fitness above 0. Translation of mean fitness into population size depends on ecological details, so understanding mean fitness evolution and dynamics is merely the first step in predicting extinction. Nonetheless, these results point to possible escapes from gene drive-mediated extinctions that lie beyond the control of genome engineering.

Stable isotopes are being used for forensic science studies, with applications to both natural and manufactured products. In this review we discuss how scientific evidence can be used in the legal context and where the scientific progress of hypothesis revisions can be in tension with the legal expectations of widely used methods for measurements. Although this review is written in the context of US law, many of the considerations of scientific reproducibility and acceptance of relevant scientific data span other legal systems that might apply different legal principles and therefore reach different conclusions. Stable isotopes are used in legal situations for comparing samples for authenticity or evidentiary considerations, in understanding trade patterns of illegal materials, and in understanding the origins of unknown decedents. Isotope evidence is particularly useful when considered in the broad framework of physiochemical processes and in recognizing regional to global patterns found in many materials, including foods and food products, drugs, and humans. Stable isotopes considered in the larger spatial context add an important dimension to forensic science.

While microbiologists often make the simplifying assumption that genotype determines phenotype in a given environment, it is becoming increasingly apparent that phenotypic heterogeneity (in which one genotype generates multiple phenotypes simultaneously even in a uniform environment) is common in many microbial populations. The importance of phenotypic heterogeneity has been demonstrated in a number of model systems involving binary phenotypic states (e.g., growth/non-growth); however, less is known about systems involving phenotype distributions that are continuous across an environmental gradient, and how those distributions change when the environment changes. Here, we describe a novel instance of phenotypic diversity in tolerance to a metabolic toxin within wild-type populations of Methylobacterium extorquens, a ubiquitous phyllosphere methylotroph capable of growing on the methanol periodically released from plant leaves. The first intermediate in methanol metabolism is formaldehyde, a potent cellular toxin that is lethal in high concentrations. We have found that at moderate concentrations, formaldehyde tolerance in M. extorquens is heterogeneous, with a cell’s minimum tolerance level ranging between 0 mM and 8 mM. Tolerant cells have a distinct gene expression profile from non-tolerant cells. This form of heterogeneity is continuous in terms of threshold (the formaldehyde concentration where growth ceases), yet binary in outcome (at a given formaldehyde concentration, cells either grow normally or die, with no intermediate phenotype), and it is not associated with any detectable genetic mutations. Moreover, tolerance distributions within the population are dynamic, changing over time in response to growth conditions. We characterized this phenomenon using bulk liquid culture experiments, colony growth tracking, flow cytometry, single-cell time-lapse microscopy, transcriptomics, and genome resequencing. Finally, we used mathematical modeling to better understand the processes by which cells change phenotype, and found evidence for both stochastic, bidirectional phenotypic diversification and responsive, directed phenotypic shifts, depending on the growth substrate and the presence of toxin. Author Summary Scientists tend to appreciate microbes for their simplicity and predictability: a population of genetically identical cells inhabiting a uniform environment is expected to behave in a uniform way. However, counter-examples to this assumption are frequently being discovered, forcing a re-examination of the relationship between genotype and phenotype. In most such examples, bacterial cells are found to split into two discrete populations, for instance growing and non-growing. Here, we report the discovery of a novel example of microbial phenotypic heterogeneity in which cells are distributed along a gradient of phenotypes, ranging from low to high tolerance of a toxic chemical. Furthermore, we demonstrate that the distribution of phenotypes changes in different growth conditions, and we use mathematical modeling to show that cells may change their phenotype either randomly or in a particular direction in response to the environment. Our work expands our understanding of how a bacterial cell’s genome, family history, and environment all contribute to its behavior, with implications for the diverse situations in which we care to understand the growth of any single-celled populations.

BackgroundPopulation dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research; predicting how populations change over time, determining how manipulations of microbiomes affect dynamics, and designing synthetic microbiomes to perform tasks are just a few examples. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka-Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka-Volterra model.ResultsWe used structural identifiability analyses to determine the extent to which time series of relative abundances can be used to parameterize the generalized Lotka-Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Our results also indicate that the relative interaction rates that can be estimated using relative abundance data provide ample information to estimate relative changes of absolute abundance over time. Using synthetic data for which we know the underlying structure, we found our results to be robust to modest amounts of both process and measurement error.ConclusionsFitting the generalized Lotka-Volterra model to time-series sequencing data typically requires either assuming a constant population size or performing additional measurements to obtain absolute abundances. We have found that these assumptions are not strictly necessary because relative abundance data alone contain sufficient information to estimate relative rates of interaction, and thus to infer key drivers of microbial population dynamics.

Reconstructions of dietary composition and trophic level from stable isotope measurements of animal tissue rely on predictable offsets of stable isotope ratios from diet to tissue. Physiological processes associated with metabolism shape tissue stable isotope ratios, and as such the spacing between stable isotope ratios of diet and tissue may be influenced by processes such as growth, nutritional stress, and disease. Here, we develop a model of incorporation stable isotopes in diet to tissues by coupling stable isotope dynamics to a model of macronutrient energy metabolism. We use the model to explore the effect of changes in dietary intake, both composition and amount, and in energy expenditure, on body mass and carbon and nitrogen stable isotope ratios of tissue.

A working group at the National Institute for Mathematical and Biological Synthesis (NIMBioS) explored the feasibility of integrating 2 complementary approaches relevant to ecological risk assessment. Adverse outcome pathway (AOP) models provide "bottom-up" mechanisms to predict specific toxicological effects that could affect an individual's ability to grow, reproduce, and/or survive from a molecular initiating event. Dynamic energy budget (DEB) models offer a "top-down" approach that reverse engineers stressor effects on growth, reproduction, and/or survival into modular characterizations related to the acquisition and processing of energy resources. Thus, AOP models quantify linkages between measurable molecular, cellular, or organ-level events, but they do not offer an explicit route to integratively characterize stressor effects at higher levels of organization. While DEB models provide the inherent basis to link effects on individuals to those at the population and ecosystem levels, their use of abstract variables obscures mechanistic connections to suborganismal biology. To take advantage of both approaches, we developed a conceptual model to link DEB and AOP models by interpreting AOP key events as measures of damage-inducing processes affecting DEB variables and rates. We report on the type and structure of data that are generated for AOP models that may also be useful for DEB models. We also report on case studies under development that merge information collected for AOPs with DEB models and highlight some of the challenges. Finally, we discuss how the linkage of these 2 approaches can improve ecological risk assessment, with possibilities for progress in predicting population responses to toxicant exposures within realistic environments. Integr Environ Assess Manag 2018;14:615-624. © 2018 SETAC.

Ecological risk assessment quantifies the likelihood of undesirable impacts of stressors, primarily at high levels of biological organization. Data used to inform ecological risk assessments come primarily from tests on individual organisms or from suborganismal studies, indicating a disconnect between primary data and protection goals. We know how to relate individual responses to population dynamics using individual-based models, and there are emerging ideas on how to make connections to ecosystem services. However, there is no established methodology to connect effects seen at higher levels of biological organization with suborganismal dynamics, despite progress made in identifying Adverse Outcome Pathways (AOPs) that link molecular initiating events to ecologically relevant key events. This chapter is a product of a working group at the National Center for Mathematical and Biological Synthesis (NIMBioS) that assessed the feasibility of using dynamic energy budget (DEB) models of individual organisms as a “pivot” connecting suborganismal processes to higher level ecological processes. AOP models quantify explicit molecular, cellular or organ-level processes, but do not offer a route to linking sub-organismal damage to adverse effects on individual growth, reproduction, and survival, which can be propagated to the population level through individual-based models. DEB models describe these processes, but use abstract variables with undetermined connections to suborganismal biology. We propose linking DEB and quantitative AOP models by interpreting AOP key events as measures of damage-inducing processes in a DEB model. Here, we present a conceptual model for linking AOPs to DEB models and review existing modeling tools available for both AOP and DEB.

As the density of human and domestic animal populations increases, the threat of localized epidemics and global pandemics grows. Although effective vaccines have been developed for a number of threatening pathogens, manufacturing and disseminating vaccines in the face of a rapidly spreading epidemic or pandemic remains a formidable challenge. One potentially powerful solution to this problem is the use of transmissible vaccines. Transmissible vaccines are capable of spreading from one individual to another and are currently being developed for a range of infectious diseases. Here we develop and analyze mathematical models that allow us to quantify the benefits of vaccine transmission in the face of an imminent or ongoing epidemic. Our results demonstrate that even a small amount of vaccine transmission can greatly increase the rate at which a naïve host population can be protected against an anticipated epidemic and substantially reduce the size of unanticipated epidemics if vaccination is initiated shortly after pathogen detection. In addition, our results identify key biological properties and implementation practices that maximize the impact of vaccine transmission on infectious disease.

Many populations are doomed to extinction but little is known about how evolution contributes to their longevity. We address this by modeling an asexual population consisting of genotypes whose abundances change independently according to a system of continuous branching diffusions. Each genotype is characterized by its initial abundance, growth rate, and reproductive variance. The latter two components determine the genotype's ‘risk function’ which describes its per capita probability of extinction at any time. We derive the probability distribution of extinction times for a polymorphic population, which can be expressed in terms of genotypic risk functions. We use this to explore how spontaneous mutation, abrupt environmental change, or population supplementation and removal affect the time to extinction. Results suggest that evolution based on new mutations does little to alter the time to extinction. Abrupt environmental changes that affect all genotypes can have more substantial impact but, curiously, a beneficial change does more to extend the lifetime of thriving than threatened populations of the same initial abundance. Our results can be used to design policies that meet specific conservation goals or management strategies that speed the elimination of agricultural pests or human pathogens. This article is protected by copyright. All rights reserved.

As sequencing technologies have advanced, the amount of information regarding the composition of bacterial communities from various environments (e.g. skin, soil) has grown exponentially. To date, most work has focused on cataloging taxa present in samples and determining whether the distribution of taxa shifts with exogenous covariates. However, important questions regarding how taxa interact with each other and their environment remain open, thus preventing in-depth ecological understanding of microbiomes. Time-series data from 16S rDNA amplicon sequencing are becoming more common within microbial ecology, but given the ‘big data’ nature of these studies, there are currently no methods capable of utilizing the breadth of the data to infer ecological interactions from these longitudinal data. We address this gap by presenting a method of analysis using Poisson regression fit with an elastic-net penalty that 1) takes advantage of the fact that the data are time series; 2) constrains estimates to allow for the possibility of many more interactions than data; and 3) is scalable enough to handle data consisting of thousands of taxa. We test the method on gut microbiome data from white-throated woodrats (Neotoma albigula) that were fed varying amounts of the plant secondary compound oxalate over a period of 22 days to estimate interactions between OTUs and their environment.

The stable isotopic composition of drinking water, diet, and atmospheric oxygen influence the isotopic composition of body water ((2)H/(1)H, (18)O/(16)O expressed as δ(2) H and δ(18)O). In turn, body water influences the isotopic composition of organic matter in tissues, such as hair and teeth, which are often used to reconstruct historical dietary and movement patterns of animals and humans. Here, we used a nonhuman primate system (Macaca fascicularis) to test the robustness of two different mechanistic stable isotope models: a model to predict the δ(2)H and δ(18)O values of body water and a second model to predict the δ(2)H and δ(18)O values of hair. In contrast to previous human-based studies, use of nonhuman primates fed controlled diets allowed us to further constrain model parameter values and evaluate model predictions. Both models reliably predicted the δ(2)H and δ(18)O values of body water and of hair. Moreover, the isotope data allowed us to better quantify values for two critical variables in the models: the δ(2)H and δ(18)O values of gut water and the (18)O isotope fractionation associated with a carbonyl oxygen-water interaction in the gut (α(ow)). Our modeling efforts indicated that better predictions for body water and hair isotope values were achieved by making the isotopic composition of gut water approached that of body water. Additionally, the value of α(ow) was 1.0164, in close agreement with the only other previously measured observation (microbial spore cell walls), suggesting robustness of this fractionation factor across different biological systems.

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2001. Contributed by Thure E. Cerling, March 3, 2009 (sent for review December 26, 2008) The dietary and movement history of individual animals can be studied using stable isotope records in animal tissues, providing insight into long-term ecological dynamics and a species niche. We provide a 6-year history of elephant diet by examining tail hair collected from 4 elephants in the same social family unit in northern Kenya. Sequential measurements of carbon, nitrogen, and hydrogen isotope rations in hair provide a weekly record of diet and water resources. Carbon isotope ratios were well correlated with satellite-based measurements of the normalized difference vegetation index (NDVI) of the region occupied by the elephants as recorded by the global positioning system (GPS) movement record; the absolute amount of C4 grass consumption is well correlated with the maximum value of NDVI during individual wet seasons. Changes in hydrogen isotope ratios coincided very closely in time with seasonal fluctuations in rainfall and NDVI whereas diet shifts to relatively high proportions of grass lagged seasonal increases in NDVI by 2 weeks. The peak probability of conception in the population occurred 3 weeks after peak grazing. Spatial and temporal patterns of resource use show that the only period of pure browsing by the focal elephants was located in an over-grazed, communally managed region outside the protected area. The ability to extract time-specific longitudinal records on animal diets, and therefore the ecological history of an organism and its environment, provides an avenue for understanding the impact of climate dynamics and land-use change on animal foraging behavior and habitat relations.

Acetaminophen (APAP) overdose is the leading cause of acute liver injury in the USA and the UK. Increasingly, liver injury is caused by sustained overuse rather than a single-time overdose. We have recently developed a mathematical model, the Model of APAP-induced Liver Damage (MALD), to predict the outcome of patients with APAP-induced liver damage. The model is based on a single-time overdose and uses measurable markers of liver injury to estimate time since overdose and overdose amount, two variables critical for survival. Here, we extend the model to study liver injury from chronic APAP use. We find that there is a threshold in the model, such that liver injury occurs rapidly or not at all, even with chronic use. Fits of synthetic data derived from chronic use overdose scenarios to MALD lead to accurate predictions of outcome, even when liver injury is the result of sustained overuse.

Segmental analysis of hair has been used in diverse fields ranging from forensics to ecology to measure the concentration of substances such as drugs and isotopes. Multiple hairs are typically combined into a bundle for segmental analysis to obtain a high-resolution series of measurements. Individual hair strands cycle through multiple phases of growth and grow at different rates when in the growth phase. Variation in growth of hair strands in a bundle can cause misalignment of substance concentration between hairs, attenuating the primary body signal. We developed a mathematical model based on the known physiology of hair growth to describe the signal averaging caused by bundling multiple hairs for segmental analysis. The model was used to form an inverse method to estimate the primary body signal from measurements of a hair bundle. The inverse method was applied to a previously described stable oxygen isotope chronology from the hair of a murder victim and provides a refined interpretation of the data. Aspects of the reconstruction were confirmed when the victim was later identified. Fil: Remien, Christopher H.. University of Tennessee; Estados Unidos Fil: Adler, Frederick R.. University of Utah; Estados Unidos Fil: Chesson, Lesley A.. University of Utah; Estados Unidos Fil: Valenzuela, Luciano Oscar. University of Utah; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Ehleringer, James R.. University of Utah; Estados Unidos Fil: Cerling, Thure E.. University of Utah; Estados Unidos

The role of African savannahs in the evolution of early hominins has been debated for nearly a century. Resolution of this issue has been hindered by difficulty in quantifying the fraction of woody cover in the fossil record. Here we show that the fraction of woody cover in tropical ecosystems can be quantified using stable carbon isotopes in soils. Furthermore, we use fossil soils from hominin sites in the Awash and Omo-Turkana basins in eastern Africa to reconstruct the fraction of woody cover since the Late Miocene epoch (about 7 million years ago). (13)C/(12)C ratio data from 1,300 palaeosols at or adjacent to hominin sites dating to at least 6 million years ago show that woody cover was predominantly less than ∼40% at most sites. These data point to the prevalence of open environments at the majority of hominin fossil sites in eastern Africa over the past 6 million years.

While isotopes are frequently used as tracers in investigations of disease physiology (i.e., 14C labeled glucose), few studies have examined the impact that disease, and disease-related alterations in metabolism, may have on stable isotope ratios at natural abundance levels. The isotopic composition of body water is heavily influenced by water metabolism and dietary patterns and may provide a platform for disease detection. By utilizing a model of streptozotocin (STZ)-induced diabetes as an index case of aberrant water homeostasis, we demonstrate that untreated diabetes mellitus results in distinct combinations, or signatures, of the hydrogen (delta2H) and oxygen (delta18O) isotope ratios in body water. Additionally, we show that the delta2H and delta18O values of body water are correlated with increased water flux, suggesting altered blood osmolality, due to hyperglycemia, as the mechanism behind this correlation. Further, we present a mathematical model describing the impact of water flux on the isotopic composition of body water and compare model predicted values with actual values. These data highlight the importance of factors such as water flux and energy expenditure on predictive models of body water and additionally provide a framework for using naturally occurring stable isotope ratios to monitor diseases that impact water homeostasis.