Stochastic Extinction Research Articles

Multiscale Immune Selection and the Transmission-Diversity Feedback in Antigenically Diverse Pathogen Systems.

Antigenic diversity is commonly used by pathogens to enhance their transmission success. Within-host clonal antigenic variation helps to maintain long infectious periods, whereas high levels of allelic diversity at the population level significantly expand the pool of susceptible individuals. Diversity, however, is not necessarily a static property of a pathogen population but in many cases is generated by the very act of infection and transmission, and it is therefore expected to respond dynamically to changes in transmission and immune selection. We hypothesized that this coupling creates a positive feedback whereby infection and disease transmission promote the generation of diversity, which itself facilitates immune evasion and further infections. To investigate this link in more detail, we considered the human malaria parasite Plasmodium falciparum, one of the most important antigenically diverse pathogens. We developed an individual-based model in which antigenic diversity emerges as a dynamic property from the underlying transmission processes. Our results show that the balance between stochastic extinction and the generation of new antigenic variants is intrinsically linked to within-host and between-host immune selection. This in turn determines the level of diversity that can be maintained in a given population. Furthermore, the transmission-diversity feedback can lead to temporal lags in the response to natural or intervention-induced perturbations in transmission rates. Our results therefore have important implications for monitoring and assessing the effectiveness of disease control efforts.

Comparative phylogeography of parasitic Laelaps mites contribute new insights into the specialist-generalist variation hypothesis (SGVH)

BackgroundThe specialist-generalist variation hypothesis (SGVH) in parasites suggests that, due to patchiness in habitat (host availability), specialist species will show more subdivided population structure when compared to generalist species. In addition, since specialist species are more prone to local stochastic extinction events with their hosts, they will show lower levels of intraspecific genetic diversity when compared to more generalist.ResultsTo test the wider applicability of the SGVH we compared 337 cytochrome oxidase I mitochondrial DNA and 268 nuclear tropomyosin DNA sequenced fragments derived from two co-distributed Laelaps mite species and compared the data to 294 COI mtDNA sequences derived from the respective hosts Rhabdomys dilectus, R. bechuanae, Mastomys coucha and M. natalensis. In support of the SGVH, the generalist L. muricola was characterized by a high mtDNA haplotypic diversity of 0.97 (±0.00) and a low level of population differentiation (mtDNA Fst = 0.56, p < 0.05; nuDNA Fst = 0.33, P < 0.05) while the specialist L. giganteus was overall characterized by a lower haplotypic diversity of 0.77 (±0.03) and comparatively higher levels of population differentiation (mtDNA Fst = 0.87, P < 0.05; nuDNA Fst = 0.48, P < 0.05). When the two specialist L. giganteus lineages, which occur on two different Rhabdomys species, are respectively compared to the generalist parasite, L. muricola, the SGVH is not fully supported. One of the specialist L. giganteus species occurring on R. dilectus shows similar low levels of population differentiation (mtDNA Fst = 0.53, P < 0.05; nuDNA Fst = 0.12, P < 0.05) than that found for the generalist L. muricola. This finding can be correlated to differences in host dispersal: R. bechuanae populations are characterized by a differentiated mtDNA Fst of 0.79 (P < 0.05) while R. dilectus populations are less structured with a mtDNA Fst = 0.18 (P < 0.05).ConclusionsThese findings suggest that in ectoparasites, host specificity and the vagility of the host are both important drivers for parasite dispersal. It is proposed that the SGHV hypothesis should also incorporate reference to host dispersal since in our case only the specialist species who occur on less mobile hosts showed more subdivided population structure when compared to generalist species.

Impact of colored cross-correlated noises on stochastic resonance and mean extinction rate for a metapopulation system with a multiplicative periodic signal

In this paper, we aim to explore the mean extinction rate and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by a multiplicative periodic signal, colored cross-correlated multiplicative and additive Gaussian noises. By use of the fast descent method and the adiabatic approximation theory for the signal-to-noise ratio, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results indicate that the various SR phenomena occur in the metapopulation system due to the variation of the noise terms and the correlation time. Specifically, the noise correlation always plays a critical role in motivating the SR phenomenon, while the multiplicative noise exerts the inhibition effect on the SR. Interestingly, the weak additive noise can stimulate the resonant peak of the SNR, while the further increase of the noise intensity will lead to the reduction of the SR effect. On the other hand, the noise correlation time τ plays antipodal roles in motivating the SR phenomenon under different circumstances. With regard to the mean extinction rate of the population from the boom state to the extinction one, by performing the numerical calculations, it is found that the additive noise always accelerate the extinction of the population, while the correlation noise will slow down the decline for the population. The role that the noise correlation time plays in the population extinction depends on the values that λ takes.

Differential temporal beta‐diversity patterns of native and non‐native arthropod species in a fragmented native forest landscape

An important factor that hinders the management of non‐native species is a general lack of information regarding the biogeography of non‐natives, and, in particular, their rates of turnover. Here, we address this research gap by analysing differences in temporal beta‐diversity (using both pairwise and multiple‐time dissimilarity metrics) between native and non‐native species, using a novel time‐series dataset of arthropods sampled in native forest fragments in the Azores. We use a null model approach to determine whether temporal beta‐diversity was due to deterministic processes or stochastic colonisation and extinction events, and linear modelling selection to assess the factors driving variation in temporal beta‐diversity between plots. In accordance with our predictions, we found that the temporal beta‐diversity was much greater for non‐native species than for native species, and the null model analyses indicated that the turnover of non‐native species was due to stochastic events. No predictor variables were found to explain the turnover of native or non‐native species. We attribute the greater turnover of non‐native species to source‐sink processes and the close proximity of anthropogenic habitats to the fragmented native forest plots sampled in our study. Thus, our findings point to ways in which the study of turnover can be adapted for future applications in habitat island systems. The implications of this for biodiversity conservation and management are significant. The high rate of stochastic turnover of non‐native species indicates that attempts to simply reduce the populations of non‐native species in situ within native habitats may not be successful. A more efficient management strategy would be to interrupt source‐sink dynamics by improving the harsh boundaries between native and adjacent anthropogenic habitats.

A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process

In this paper, based on the results of Gray et al. (2011), we propose a new SDE SIS model incorporating mean-reverting Ornstein–Uhlenbeck process, and prove that the stochastic basic reproduction number R0s can be used to identify the stochastic extinction and persistence for the SDE mode: if R0s<1 under mild extra conditions, the disease will be extinct a.s., while if R0s>1, the disease will persist a.s. Epidemiologically, we find that smaller speed of reversion or bigger intensity of volatility can suppress the disease outbreak. Thus, in order to control the spread of the disease, we must decrease the speed of reversion or increase the intensity of volatility.

A stochastic Feline immunodeficiency virus model with vertical transmission

In this paper, we formulate a stochastic Feline immunodeficiency virus (FIV) model with vertical transmission to investigate the effect of environmental fluctuations on the FIV dynamics. We prove that the threshold parameter R0s can be used to identify the stochastic extinction and persistence of the FIV: if R0s<1, the FIV will be extinct a.s., while if R0s>1, the FIV will persist a.s. Epidemiologically, we find that large environmental fluctuations can suppress the outbreak of FIV, and the vertical transmission may be beneficial to the persistence of the FIV. Thus, in order to control the spread of the FIV, we must decrease the vertical transmission.

Environmental variability in a stochastic epidemic model

In this paper, we investigate the stochastic dynamics of a simple epidemic model incorporating the mean-reverting Ornstein–Uhlenbeck process analytically and numerically. We define two threshold parameters, the stochastic demographic reproduction number Rds and the stochastic basic reproduction number R0s, to utilize in identifying the stochastic extinction and persistence of the disease. We find that the stochastic disease dynamics can be determined by the environment fluctuations which measured by the intensity of volatility and the speed of reversion: the larger intensity of volatility or the smaller speed of reversion can suppress the outbreak of the disease, the smaller intensity of volatility or the the higher speed of reversion can enhance the outbreak of the disease. Furthermore, via numerical simulations, we find that the stochastic model has an endemic stationary distribution which leads to the stochastic persistence of the disease. Our results show that mean-reverting process is a well-established way of introducing stochastic environmental noise into biologically realistic population dynamic models.

Analysis of a stochastic cooperation-competition model

In this paper, we explore dynamic properties of a stochastic cooperation-competition model. Some sufficient conditions are established for stochastic persistence and stochastic extinction of species. Studies suggest that the noise may have a positive effect on the persistence of species. We also analyze global asymptotic stability of positive solutions and give a stationary distribution of this stochastic model which has the ergodic property. Finally, some numerical simulations are presented to illustrate or complement our mathematical findings.

Local biodiversity erosion in south Brazilian grasslands under moderate levels of landscape habitat loss

Abstract Habitat loss is one of the greatest threats to biodiversity, exerting negative effects on the ecological viability of natural vegetation remnants. The south Brazilian grasslands belong to one of the largest temperate grassland regions in the world, but have lost 50% of their natural extent in the past 35 years. To date, there is no empirical evidence for the effects of habitat loss on these grasslands' biological diversity, undermining their conservation. Using data from a large‐scale biodiversity survey, we asked if local plant communities respond to levels of habitat loss representative of the entire region (≤50%). Vegetation in grassland remnants was sampled in 24 landscapes at three localities each, using nine plots per locality. To investigate whether species losses were a consequence of stochastic or nonrandom local extinctions and whether plant communities became more homogenized, we evaluated species richness, beta‐diversity components (spatial turnover and nestedness), and phylogenetic diversity, in respect to landscape change. In part of the landscapes, arthropods were sampled to investigate if loss of plant diversity had a cascading effect on other trophic levels. We evaluated generic richness of ants, an omnivore group with high levels of plant associations, in respect to a plant community's phylogenetic diversity. Local plant communities in landscapes with less grassland cover had fewer species, less spatial turnover, increased nestedness and lower phylogenetic diversity. Our results suggest that the observed species loss can be linked to taxonomic homogenization and is nonrandom, decreasing evolutionary diversity within the community. Furthermore, ant richness declined by 50% in plant communities with the lowest phylogenetic diversity, suggesting that effects of habitat loss propagate to higher trophic levels. Policy implications. We conclude that the biological diversity of south Brazilian grasslands, at the producer and consumer level, is at risk under the current rate of land‐use conversion, even at habitat losses below 50%. To avoid substantial biodiversity loss, conservation and more restrictive policies for conversion of native grasslands to different land uses in South Brazil are urgently needed.

Permanence and asymptotic behaviors of stochastic predator–prey system with Markovian switching and Lévy noise

This paper concerns the dynamics of a stochastic predator–prey system with Markovian switching and Lévy noise. First, the existence and uniqueness of global positive solution to the system is proved. Then, by combining stochastic analytical techniques with M-matrix analysis, sufficient conditions of stochastic permanence and extinction are obtained. Furthermore, for the stochastic permanence case, by means of four constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems, both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated. Finally, our conclusions are illustrated through an example.

Extinction time of a stochastic predator–prey model by the generalized cell mapping method

The stochastic response and extinction time of a predator–prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

How do patch quality and spatial context affect invertebrate communities in a natural moss microlandscape?

Globally, moss associated invertebrates remain poorly studied and it is largely unknown to what extent their diversity is driven by local environmental conditions or the landscape context. Here, we investigated small scale drivers of invertebrate communities in a moss landscape in a temperate forest in Western Europe. By comparing replicate quadrats of 5 different moss species in a continuous moss landscape, we found that mosses differed in invertebrate density and community composition. Although, in general, richness was similar among moss species, some invertebrate taxa were significantly linked to certain moss species. Only moss biomass and not relative moisture content could explain differences in invertebrate densities among moss species. Second, we focused on invertebrate communities associated with the locally common moss species Kindbergia praelonga in isolated moss patches on dead tree trunks to look at effects of patch size, quality, heterogeneity and connectivity on invertebrate communities. Invertebrate richness was higher in patches under closed canopies than under more open canopies, presumably due to the higher input of leaf litter and/or lower evaporation. In addition, increased numbers of other moss species in the same patch seemed to promote invertebrate richness in K. praelonga, possibly due to mass effects. Since invertebrate richness was unaffected by patch size and isolation, dispersal was probably not limiting in this system with patches separated by tens of meters, or stochastic extinctions may be uncommon. Overall, we conclude that invertebrate composition in moss patches may not only depend on local patch conditions, in a particular moss species, but also on the presence of other moss species in the direct vicinity.

Nonlatching positive feedback enables robust bimodality by decoupling expression noise from the mean

Fundamental to biological decision-making is the ability to generate bimodal expression patterns where 2 alternate expression states simultaneously exist. Here, we use a combination of single-cell analysis and mathematical modeling to examine the sources of bimodality in the transcriptional program controlling HIV’s fate decision between active replication and viral latency. We find that the HIV transactivator of transcription (Tat) protein manipulates the intrinsic toggling of HIV’s promoter, the long terminal repeat (LTR), to generate bimodal ON-OFF expression and that transcriptional positive feedback from Tat shifts and expands the regime of LTR bimodality. This result holds for both minimal synthetic viral circuits and full-length virus. Strikingly, computational analysis indicates that the Tat circuit’s noncooperative “nonlatching” feedback architecture is optimized to slow the promoter’s toggling and generate bimodality by stochastic extinction of Tat. In contrast to the standard Poisson model, theory and experiment show that nonlatching positive feedback substantially dampens the inverse noise-mean relationship to maintain stochastic bimodality despite increasing mean expression levels. Given the rapid evolution of HIV, the presence of a circuit optimized to robustly generate bimodal expression appears consistent with the hypothesis that HIV’s decision between active replication and latency provides a viral fitness advantage. More broadly, the results suggest that positive-feedback circuits may have evolved not only for signal amplification but also for robustly generating bimodality by decoupling expression fluctuations (noise) from mean expression levels.

Modelling time to population extinction when individual reproduction is autocorrelated

In nature, individual reproductive success is seldom independent from year to year, due to factors such as reproductive costs and individual heterogeneity. However, population projection models that incorporate temporal autocorrelations in individual reproduction can be difficult to parameterise, particularly when data are sparse. We therefore examine whether such models are necessary to avoid biased estimates of stochastic population growth and extinction risk, by comparing output from a matrix population model that incorporates reproductive autocorrelations to output from a standard age-structured matrix model that does not. We use a range of parameterisations, including a case study using moose data, treating probabilities of switching reproductive class as either fixed or fluctuating. Expected time to extinction from the two models is found to differ by only small amounts (under 10%) for most parameterisations, indicating that explicitly accounting for individual reproductive autocorrelations is in most cases not necessary to avoid bias in extinction estimates.

A stochastic model for the probability of malaria extinction by mass drug administration

BackgroundMass drug administration (MDA) has been proposed as an intervention to achieve local extinction of malaria. Although its effect on the reproduction number is short lived, extinction may subsequently occur in a small population due to stochastic fluctuations. This paper examines how the probability of stochastic extinction depends on population size, MDA coverage and the reproduction number under control, Rc. A simple compartmental model is developed which is used to compute the probability of extinction using probability generating functions. The expected time to extinction in small populations after MDA for various scenarios in this model is calculated analytically.ResultsThe results indicate that mass drug administration (Firstly, Rc must be sustained at Rc < 1.2 to avoid the rapid re-establishment of infections in the population. Secondly, the MDA must produce effective cure rates of >95% to have a non-negligible probability of successful elimination. Stochastic fluctuations only significantly affect the probability of extinction in populations of about 1000 individuals or less. The expected time to extinction via stochastic fluctuation is less than 10 years only in populations less than about 150 individuals. Clustering of secondary infections and of MDA distribution both contribute positively to the potential probability of success, indicating that MDA would most effectively be administered at the household level.ConclusionsThere are very limited circumstances in which MDA will lead to local malaria elimination with a substantial probability.

Permanence and extinction of stochastic competitive Lotka–Volterra system with Lévy noise

This paper derives sufficient conditions for stochastic permanence and extinction of a stochastic non-autonomous competitive Lotka–Volterra system with Levy noise. For the autonomous case, the results show that stochastic permanence and extinction are characterized by two parameters $$\mathcal {B}_{1}$$ and $$\mathcal {B}_{2}$$ : if $$\mathcal {B}_{1}\mathcal {B}_{2} \ne 0$$ , then the system is either stochastically permanent or extinctive. That is, it is extinctive if and only if $$\mathcal {B}_{1}<0$$ and $$\mathcal {B}_{2}<0$$ ; otherwise, it is stochastically permanent. Some existing results are included as special cases. An example and its simulations are given to support our theoretical results.

Neutral theory of biodiversity: Controversies and a transvaluation of species conservation

The explanation of how the organization of biological communities and the search for an understanding of these patterns occurs has attracted the attention of researchers over several years. Between two existing theories, that sometimes seem to be contradictory; there are the ecological niche theory and the S. P. Hubbell’s neutral theory of biodiversity and biogeography. The niche theory uses the concept that an environment consists of different niches that requires different requirements for the occurrence of the species in a given community. Meanwhile, the neutral theory is based on stochasticity during the formation of a biological community, thus formed over time according to the stochastic immigration, speciation or extinction. However, far from being contradictory, there are situations when both theories are complementary, contributing to a better understanding of biological communities. Even though, there are situations when a possible support to the neutral theory may require a transvaluation of the reasons of species conservation avoiding to fall into a nihilistic abyss of environmental conservation due to the effects of stochasticity in the organization of biological communities. Keywords: environment, evolution, stochasticity.

A stochastic SIS epidemic model with vaccination

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s<1, under some mild extra conditions, there exists a disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s>1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

Transience after disturbance: Obligate species recovery dynamics depend on disturbance duration

After a disturbance event, population recovery becomes an important species response that drives ecosystem dynamics. Yet, it is unclear how interspecific interactions impact species recovery from a disturbance and which role the disturbance duration (pulse or press) plays. Here, we analytically derive conditions that govern the transient recovery dynamics from disturbance of a host and its obligately dependent partner in a two-species metapopulation model. We find that, after disturbance, species recovery dynamics depend on the species’ role (i.e. host or obligately dependent species) as well as the duration of disturbance. Host recovery starts immediately after the disturbance. In contrast, for obligate species, recovery depends on disturbance duration. After press disturbance, which allows dynamics to equilibrate during disturbance, obligate species immediately start to recover. Yet, after pulse disturbance, obligate species continue declining although their hosts have already begun to increase. Effectively, obligate species recovery is delayed until a necessary host threshold occupancy is reached. Obligates’ delayed recovery arises solely from interspecific interactions independent of dispersal limitations, which contests previous explanations. Delayed recovery exerts a two-fold negative effect, because populations continue declining to even smaller population sizes and the phase of increased risk from demographic stochastic extinction in small populations is prolonged. We argue that delayed recovery and its determinants –species interactions and disturbance duration – have to be considered in biodiversity management.

Asymptotic behavior and numerical simulations of a Lotka-Volterra mutualism system with white noises

In the present paper, a stochastic mutualism model subject to white noises is established. We first investigate the existence and uniqueness of globally positive solution of the stochastic model. Then we study its asymptotic behavior, such as stochastic permanence and extinction, and estimate the limit of the average in time of the sample paths of every component. We also show that the stochastic system is globally attractive under some appropriate conditions. Finally, numerical simulations are presented to justify the analytical results.