The impacts of spatial-temporal heterogeneity of human-to-human contacts on the extinction probability of infectious disease from branching process model.

In this study, we focus on the impacts of spatial-temporal heterogeneity of human-to-human contacts on the spread of infectious diseases and develop a multi-type branching process model by introducing random human-to-human contact mode into a structured population. We provide the general formulas of the generation size, extinction probability, and basic reproduction number of the proposed branching process model. The result shows that the natural temporal heterogeneity (i.e. random contacts over time) can lead to a higher extinction probability while remains the same basic reproduction number and generation size. This is also numerically verified by choosing the real contact distributions from different circumstances of four countries. In addition, we observe a non-monotonic pattern of the differences, against the transmission probability and the mean contact rate, between the extinction probabilities under the constant and random contact patterns. Given the spatial heterogeneity, we show that it can contribute to the increase of basic reproduction number, but also increase the extinction probability of the infectious disease. This study adds novel insights to the course of the impact of heterogeneity on the transmission dynamics and also provides additional evidence for the limited role of reproduction numbers.

Stochastic bacterial population dynamics restrict the establishment of antibiotic resistance from single cells.

A better understanding of how antibiotic exposure impacts the evolution of resistance in bacterial populations is crucial for designing more sustainable treatment strategies. The conventional approach to this question is to measure the range of concentrations over which resistant strain(s) are selectively favored over a sensitive strain. Here, we instead investigate how antibiotic concentration impacts the initial establishment of resistance from single cells, mimicking the clonal expansion of a resistant lineage following mutation or horizontal gene transfer. Using two Pseudomonas aeruginosa strains carrying resistance plasmids, we show that single resistant cells have <5% probability of detectable outgrowth at antibiotic concentrations as low as one-eighth of the resistant strain's minimum inhibitory concentration (MIC). This low probability of establishment is due to detrimental effects of antibiotics on resistant cells, coupled with the inherently stochastic nature of cell division and death on the single-cell level, which leads to loss of many nascent resistant lineages. Our findings suggest that moderate doses of antibiotics, well below the MIC of resistant strains, may effectively restrict de novo emergence of resistance even though they cannot clear already-large resistant populations.

Impact of multiple small and persistent threats on extinction risk.

Many species may face multiple distinct and persistent drivers of extinction risk, yet theoretical and empirical studies tend to focus on the single largest driver. This means that existing approaches potentially underestimate and mischaracterize future risks to biodiversity. We synthesized existing knowledge on how multiple drivers of extinction can interact to influence a species' overall extinction probability in a probabilistic model of extinction risk that incorporated the impacts of multiple drivers of extinction risk, their interactions, and their accumulative effects through time. We then used this model framework to explore how different threats, interactions between them, and time trends may affect a species' overall extinction probability. Multiple small threats together had potential to pose a large cumulative extinction risk; for example, 10 individual threats posed a 1% extinction risk each and cumulatively posed a 9.7% total extinction risk. Interactions among drivers resulted in escalated risk in some cases, and persistent threats with a small (1%) extinction risk each decade ultimately posed large extinction risk over 100 (9.6% total extinction risk) to 200 years (18.2% total extinction risk). By estimating long-term extinction risk posed by several different factors and their interactions, this approach provides a framework to identify drivers of extinction risk that could be proactively targeted to help prevent species currently of least concern from becoming threatened with extinction.

Muchas especies pueden enfrentarse a múltiples impulsores distintivos y persistentes del riesgo de extinción, aunque los estudios teóricos y empíricos tienden a enfocarse en el impulsor más relevante. Esto significa que las estrategias existentes tienen el potencial de subestimar y caracterizar erróneamente los riesgos para la biodiversidad en el futuro. Sintetizamos el conocimiento existente sobre cómo los múltiples impulsores de la extinción pueden interactuar para influir sobre la probabilidad general de extinción de una especie en un modelo probabilístico del riesgo de extinción, el cual incorporó los impactos de los múltiples impulsores del riesgo de extinción, sus interacciones y sus efectos acumulativos a través del tiempo. Después usamos este modelo para explorar cómo las diferentes amenazas, las interacciones entre ellas y las tendencias temporales pueden afectar la probabilidad general de extinción de una especie. El conjunto de múltiples amenazas pequeñas tuvo el potencial de representar un gran riesgo de extinción acumulativo; por ejemplo, cada una de diez amenazas individuales representó 1% de riesgo de extinción, y acumuladas representaron un riesgo total de extinción de 9.7%. Las interacciones entre los impulsores resultaron en un riesgo escalado en algunos casos, y las amenazas persistentes con un riesgo pequeño (1%) de extinción durante cada década al final representaron un gran riesgo de extinción después de 100 (9.6% del riesgo total de extinción) y 200 años (18.2% del riesgo total de extinción). Mediante la estimación del riesgo de extinción a largo plazo que presentan los diferentes factores y sus interacciones, esta estrategia proporciona un marco para identificar los impulsores del riesgo de extinción que podrían focalizarse proactivamente para ayudar a prevenir que las especies que actualmente están en menor riesgo se conviertan en especies amenazadas.

Selective extinctions resulting from random habitat destruction lead to under-estimates of local and regional biodiversity loss in a manipulative field experiment.

Land-use change is a significant cause of anthropogenic extinctions, which are likely to continue and accelerate as habitat conversion proceeds in most biomes. One way to understand the effects of habitat loss on biodiversity is through improved tools for predicting the number and identity of species losses in response to habitat loss. There are relatively few methods for predicting extinctions and even fewer opportunities for rigorously assessing the quality of these predictions. In this paper, we address these issues by applying a new method based on rarefaction to predict species losses after random, but aggregated, habitat loss. We compare predictions from three rarefaction models, individual-based, sample-based, and spatially clustered, to those derived from a commonly used extinction estimation method, the species-area relationship (SAR). We apply each method to a mesocosm experiment, in which we aim to predict species richness and extinctions of arthropods immediately following 50% habitat loss. While each model produced strikingly accurate predictions of species richness immediately after the habitat loss disturbance, each model significantly underestimated the number of extinctions occurring at both the local (within-mesocosm) and regional (treatment-wide) scales. Despite the stochastic nature of our small-scale, short-term, and randomly applied habitat loss experiment, we found surprisingly clear evidence for extinction selectivity, for example, when abundant species with low extinction probabilities were extirpated following habitat loss. The important role played by selective extinction even in this contrived experimental system suggests that ecologically driven, trait-based extinctions play an equally important role to stochastic extinction, even when the disturbance itself has no clear selectivity. As a result, neutrally stochastic null models such as the SAR and rarefaction are likely to underestimate extinctions caused by habitat loss. Nevertheless, given the difficulty of predicting extinctions, null models provide useful benchmarks for conservation planning by providing minimum estimates and probabilities of species extinctions.

Does Counting Different Life Stages Impact Estimates for Extinction Probabilities for Tsetse (Glossina spp)?

As insect populations decline, due to climate change and other environmental disruptions, there has been an increased interest in understanding extinction probabilities. Generally, the life cycle of insects occurs in well-defined stages: when counting insects, questions naturally arise about which life stage to count. Using tsetse flies (vectors of trypanosomiasis) as a case study, we develop a model that works when different life stages are counted. Previous branching process models for tsetse populations only explicitly represent newly emerged adult female tsetse and use that subpopulation to keep track of population growth/decline. Here, we directly model other life stages. We analyse reproduction numbers and extinction probabilities and show that several previous models used for estimating extinction probabilities for tsetse populations are special cases of the current model. We confirm that the reproduction number is the same regardless of which life stage is counted, and show how the extinction probability depends on which life stage we start from. We demonstrate, and provide a biological explanation for, a simple relationship between extinction probabilities for the different life stages, based on the probability of recruitment between stages. These results offer insights into insect population dynamics and provide tools that will help with more detailed models of tsetse populations. Population dynamics studies of insects should be clear about life stages and counting points.

Stochastic models of infectious diseases in a periodic environment with application to cholera epidemics.

Seasonal variation affects the dynamics of many infectious diseases including influenza, cholera and malaria. The time when infectious individuals are first introduced into a population is crucial in predicting whether a major disease outbreak occurs. In this investigation, we apply a time-nonhomogeneous stochastic process for a cholera epidemic with seasonal periodicity and a multitype branching process approximation to obtain an analytical estimate for the probability of an outbreak. In particular, an analytic estimate of the probability of disease extinction is shown to satisfy a system of ordinary differential equations which follows from the backward Kolmogorov differential equation. An explicit expression for the mean (resp. variance) of the first extinction time given an extinction occurs is derived based on the analytic estimate for the extinction probability. Our results indicate that the probability of a disease outbreak, and mean and standard derivation of the first time to disease extinction are periodic in time and depend on the time when the infectious individuals or free-living pathogens are introduced. Numerical simulations are then carried out to validate the analytical predictions using two examples of the general cholera model. At the end, the developed theoretical results are extended to more general models of infectious diseases.

Diffusion dynamics on the coexistence subspace in a stochastic evolutionary game.

Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics with fluctuations due to random drift. A selection advantage which depends on a changing environment will introduce additional possibilities for the dynamics. We analyse a simple model in which a random environment allows competing species to coexist for a long time before a fixation of a single species happens. In our analysis we use stability in a linear combination of competing species to approximate the stochastic dynamics of the system by a diffusion on a one dimensional co-existence region. Our method significantly simplifies approximating the probability of first extinction and its expected time, and demonstrates a rigorous model reduction technique for evaluating quasistationary properties of stochastic evolutionary dynamics.

Effect of stochasticity on coinfection dynamics of respiratory viruses.

BACKGROUND: Respiratory viral infections are a leading cause of mortality worldwide. As many as 40% of patients hospitalized with influenza-like illness are reported to be infected with more than one type of virus. However, it is not clear whether these infections are more severe than single viral infections. Mathematical models can be used to help us understand the dynamics of respiratory viral coinfections and their impact on the severity of the illness. Most models of viral infections use ordinary differential equations (ODE) that reproduce the average behavior of the infection, however, they might be inaccurate in predicting certain events because of the stochastic nature of viral replication cycle. Stochastic simulations of single virus infections have shown that there is an extinction probability that depends on the size of the initial viral inoculum and parameters that describe virus-cell interactions. Thus the coinfection dynamics predicted by the ODE might be difficult to observe in reality. RESULTS: In this work, a continuous-time Markov chain (CTMC) model is formulated to investigate probabilistic outcomes of coinfections. This CTMC model is based on our previous coinfection model, expressed in terms of a system of ordinary differential equations. Using the Gillespie method for stochastic simulation, we examine whether stochastic effects early in the infection can alter which virus dominates the infection. CONCLUSIONS: We derive extinction probabilities for each virus individually as well as for the infection as a whole. We find that unlike the prediction of the ODE model, for similar initial growth rates stochasticity allows for a slower growing virus to out-compete a faster growing virus.

The extinction problem for a distylous plant population with sporophytic self-incompatibility.

In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means absorption at one of the axes. Despite connections with some classical probabilistic models (standard two-type Galton-Watson process, two-urn model), exact formulae for the probabilities of absorption seem to be difficult to come by and one must therefore resort to good approximations. In order to meet this task, we develop potential-theoretic tools and provide various sub- and super-harmonic functions which, for large initial populations, provide bounds which in particular improve those that have appeared earlier in the literature.

Generation studies on benthic amphipod-Quadrivisio bengalensis, Stebbing (Gammaridae) from the Kochin Estuary, Southwest coast of India.

Quadrivisio bengalensis (Stebbing Records of Indian Museum, 1, 159-161, 1907), a eurythermal (26.5-32.2 °C) and euryhaline (0.10-26.2 psu) tropical species, makes a profound contribution as a fodder organism to the benthic biomass of tropical backwaters. Studies on life span, variations in broods, fecundity, sex ratio, brooding behaviour, brood stock assessment, growth rate, antennal segments as an index of growth, moulting frequency, mortality and starvation resistance of Q. bengalensis were made for the first time under controlled laboratory conditions of 12-h photo period for 252 days on 8 pairs of specimens (male and female) collected from the field and their successive broods. The life span of females was found to be higher (maximum 220 days) than males (maximum 175 days). Number of broods varied between 5 and 15, depending on the "status of the brood" (early or late). The maximum number of juveniles in a single brood was 24 and that by a single female over the entire life span was 211. The incubation time varied between 6 and 9 days and the duration of moults (8-18 days) was found to increase with the age of the animals. Maximum growth is usually attained by the offspring arising from the 5th to 7th broods. The 4th to 7th broods were the optimal broods for the maximum number of females attaining maturity. For broods 3 to 7 of the parental set, probability of extinction (ξ) calculated on applying stochastic branching process to generation studies for the first time showed an increasing trend with number of broods while a decreasing trend for ξ for 8th and 9th broods, with least ξ for broods 5 to 7 of the 5th, 6th and 7th generations, suggesting life span and fecundity rates as functions of the "brood status" (early or late). Whether it is true with higher crustaceans remains to be explored.

On the extinction probability in models of within-host infection: the role of latency and immunity.

Not every exposure to virus establishes infection in the host; instead, the small amount of initial virus could become extinct due to stochastic events. Different diseases and routes of transmission have a different average number of exposures required to establish an infection. Furthermore, the host immune response and antiviral treatment affect not only the time course of the viral load provided infection occurs, but can prevent infection altogether by increasing the extinction probability. We show that the extinction probability when there is a time-dependent immune response depends on the chosen form of the model-specifically, on the presence or absence of a delay between infection of a cell and production of virus, and the distribution of latent and infectious periods of an infected cell. We hypothesise that experimentally measuring the extinction probability when the virus is introduced at different stages of the immune response, alongside the viral load which is usually measured, will improve parameter estimates and determine the most suitable mathematical form of the model.

Extinction probabilities and stationary distributions of mobile genetic elements in prokaryotes: The birth-death-diversification model.

Theoretical approaches are essential to our understanding of the complex dynamics of mobile genetic elements (MGEs) within genomes. Recently, the birth-death-diversification model was developed to describe the dynamics of mobile promoters (MPs), a particular class of MGEs in prokaryotes. A unique feature of this model is that genetic diversification of elements was included. To explore the implications of diversification on the longterm fate of MGE lineages, in this contribution we analyze the extinction probabilities, extinction times and equilibrium solutions of the birth-death-diversification model. We find that diversification increases both the survival and growth rate of MGE families, but the strength of this effect depends on the rate of horizontal gene transfer (HGT). We also find that the distribution of MGE families per genome is not necessarily monotonically decreasing, as observed for MPs, but may have a peak in the distribution that is related to the HGT rate. For MPs specifically, we find that new families have a high extinction probability, and predict that the number of MPs is increasing, albeit at a very slow rate. Additionally, we develop an extension of the birth-death-diversification model which allows MGEs in different regions of the genome, for example coding and non-coding, to be described by different rates. This extension may offer a potential explanation as to why the majority of MPs are located in non-promoter regions of the genome.

How much gene flow is needed to avoid inbreeding depression in wild tiger populations?

The number and size of tiger populations continue to decline owing to habitat loss, habitat fragmentation and poaching of tigers and their prey. As a result, tiger populations have become small and highly structured. Current populations have been isolated since the early 1970s or for approximately seven generations. The objective of this study is to explore how inbreeding may be affecting the persistence of remaining tiger populations and how dispersal, either natural or artificial, may reduce the potentially detrimental effect of inbreeding depression. We developed a tiger simulation model and used published levels of genetic load in mammals to simulate inbreeding depression. Following a 50 year period of population isolation, we introduced one to four dispersing male tigers per generation to explore how gene flow from nearby populations may reduce the negative impact of inbreeding depression. For the smallest populations, even four dispersing male tigers per generation did not increase population viability, and the likelihood of extinction is more than 90% within 30 years. Unless habitat connectivity is restored or animals are artificially introduced in the next 70 years, medium size wild populations are also likely to go extinct, with only four to five of the largest wild tiger populations likely to remain extant in this same period without intervention. To reduce the risk of local extinction, habitat connectivity must be pursued concurrently with efforts to increase population size (e.g. enhance habitat quality, increase habitat availability). It is critical that infrastructure development, dam construction and other similar projects are planned appropriately so that they do not erode the extent or quality of habitat for these populations so that they can truly serve as future source populations.

Vaccination strategies impact the probability of outbreak extinction: A case study of COVID-19 transmission.

Mass vaccination has proven to be an effective control measure for mitigating the transmission of infectious diseases. Throughout history, various vaccination strategies have been employed to control infections and terminate outbreaks. In this study, we utilized the transmission of COVID-19 as a case study and constructed a stochastic age-structured compartmental model to investigate the effectiveness of different vaccination strategies. Our analysis focused on estimating the outbreak extinction probability under different vaccination scenarios in both homogeneous and heterogeneous populations. Notably, we found that population heterogeneity can enhance the likelihood of outbreak extinction at varying levels of vaccine coverage. Prioritizing vaccinations for individuals with higher infection risk was found to maximize outbreak extinction probability and reduce overall infections, while allocating vaccines to those with higher mortality risk has been proven more effective in reducing deaths. Moreover, our study highlighted the significance of booster doses as the vaccine effectiveness wanes over time, showing that they can significantly enhance the extinction probability and mitigate disease transmission.

Increased extinction probability and altered physiological characteristics in pirimicarb-tolerant Daphnia magna.

We evaluated the physiological characteristics of chemical-tolerant cladocerans. Over the course of 26 generations (F25), Daphnia magna was continuously exposed to pirimicarb (carbamate) solutions (0, 3.8, 7.5, and 15 µg/L) in sub-lethal or lethal levels. The 48 h EC50 values (29.2-29.9 µg/L) for 7.5 and 15 µg/L exposure groups were found to be nearly two times higher than that in the control (17.2 µg/L). Subsequently, we investigated whether the extinction probability changed when the chemical-tolerant daphnids were fed two different types of food, Chlorella vulgaris and Synechococcus leopoliensis. Furthermore, we ascertained how chemical tolerance influences respiration and depuration rates. The 48 h EC50 value was positively related to the extinction probability when the daphnids were fed S. leopoliensis. Because the measured lipid content of S. leopoliensis was three times lower than that of C. vulgaris, the tolerant daphnids struggled under nutrient-poor conditions. Respiration rates across all pirimicarb treatment groups were higher than those in the control group, suggesting that they may produce large amounts of energy through respiration to maintain the chemical tolerance. Since the pirimicarb depuration rate for 7.5 µg/L exposure groups was higher than that in the control, the altered metabolic/excretion rate may be one factor for acquiring chemical tolerance. These altered physiological characteristics are crucial parameters for evaluating the mechanisms of chemical tolerance and associated fitness costs.

Mathematical modeling in semelparous biological species through two-sex branching processes.

This research focused its interest on the mathematical modeling of the demographic dynamics of semelparous biological species through branching processes. We continued the research line started in previous papers, providing new methodological contributions of biological and ecological interest. We determined the probability distribution associated with the number of generations elapsed before the possible extinction of the population in its natural habitat. We mathematically modeled the phenomenon of populating or repopulating habitats with semelparous species. We also proposed estimates for the offspring parameters governing the reproductive strategies of the species. To this purpose, we used the maximum likelihood and Bayesian estimation methodologies. The statistical results are illustrated through a simulated example contextualized with Labord chameleon (Furcifer labordi) species.

Seabird meta-Population Viability Model (mPVA) methods.

The seabird meta-population viability model (mPVA) uses a generalized approach to project abundance and quasi-extinction risk for 102 seabird species under various conservation scenarios. The mPVA is a stage-structured projection matrix that tracks abundance of multiple populations linked by dispersal, accounting for breeding island characteristics and spatial distribution. Data are derived from published studies, grey literature, and expert review (with over 500 contributions). Invasive species impacts were generalized to stage-specific vital rates by fitting a Bayesian state-space model to trend data from Islands where invasive removals had occurred, while accounting for characteristics of seabird biology, breeding islands and invasive species. Survival rates were estimated using a competing hazards formulation to account for impacts of multiple threats, while also allowing for environmental and demographic stochasticity, density dependence and parameter uncertainty.•The mPVA provides resource managers with a tool to quantitatively assess potential benefits of alternative management actions, for multiple species•The mPVA compares projected abundance and quasi-extinction risk under current conditions (no intervention) and various conservation scenarios, including removal of invasive species from specified breeding islands, translocation or reintroduction of individuals to an island of specified location and size, and at-sea mortality amelioration via reduction in annual at-sea deaths.

Theoretical investigation of stochastic clearance of bacteria: first-passage analysis.

Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations, the stochastic effects become more relevant. Here, we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition, we investigate the effect of fluctuations in population growth rates on the dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters, the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance.

Chance of extinction of populations in food chain model under demographic stochasticity.

The extinction of different species from the earth is increasing at an alarming rate. So, assessment of probability of extinction of different important species in our ecosystem could help us to take proper conservation policy for those population whose chance of extinction is high. In this paper a method is developed to find the probability of extinction of populations in a general n-trophic food chain model under demographic stochasticity. The birth-death process is used to incorporate the demographic stochasticity and the necessary mathematical expressions are obtained. The theoretical finding is validated by numerical simulation for a two dimensional predator-prey system.

The distribution of the time taken for an epidemic to spread between two communities.

Assessing the risk of disease spread between communities is important in our highly connected modern world. However, the impact of disease- and population-specific factors on the time taken for an epidemic to spread between communities, as well as the impact of stochastic disease dynamics on this spreading time, are not well understood. In this study, we model the spread of an acute infection between two communities ('patches') using a susceptible-infectious-removed (SIR) metapopulation model. We develop approximations to efficiently evaluate the probability of a major outbreak in a second patch given disease introduction in a source patch, and the distribution of the time taken for this to occur. We use these approximations to assess how interventions, which either control disease spread within a patch or decrease the travel rate between patches, change the spreading probability and median spreading time. We find that decreasing the basic reproduction number in the source patch is the most effective way of both decreasing the spreading probability, and delaying epidemic spread to the second patch should this occur. Moreover, we show that the qualitative effects of interventions are the same regardless of the approximations used to evaluate the spreading time distribution, but for some regions in parameter space, quantitative findings depend upon the approximations used. Importantly, if we neglect the possibility that an intervention prevents a large outbreak in the source patch altogether, then intervention effectiveness is not estimated accurately.