Novel moment closure approximations in stochastic epidemics

Moment closure approximations are used to provide analytic approximations to non-linear stochastic population models. They often provide insights into model behaviour and help validate simulation results. However, existing closure schemes typically fail in situations where the population distribution is highly skewed or extinctions occur. In this study we address these problems by introducing novel second-and third-order moment closure approximations which we apply to the stochastic SI and SIS epidemic models. In the case of the SI model, which has a highly skewed distribution of infection, we develop a second-order approximation based on the beta-binomial distribution. In addition, a closure approximation based on mixture distribution is developed in order to capture the behaviour of the stochastic SIS model around the threshold between persistence and extinction. This mixture approximation comprises a probability distribution designed to capture the quasi-equilibrium probabilities of the system and a probability mass at 0 which represents the probability of extinction. Two third-order versions of this mixture approximation are considered in which the log-normal and the beta-binomial are used to model the quasi-equilibrium distribution. Comparison with simulation results shows: (1) the beta-binomial approximation is flexible in shape and matches the skewness predicted by simulation as shown by the stochastic SI model and (2) mixture approximations are able to predict transient and extinction behaviour as shown by the stochastic SIS model, in marked contrast with existing approaches. We also apply our mixture approximation to approximate a likehood function and carry out point and interval parameter estimation.     

Moments and order statistics of extinction times in multitype branching processes and their relation to random selection models

We investigate the circumstances under which the moments of the order statistics of the extinction times of a set of independent branching processes exist. This extends a result of Schuster and Sigmund,Bull. math. Biol. 46, 11–17, 1984, which was found in a special random selection model. Furthermore we discussed existence of the expectation of extinction times of multitype branching processes and extend well known results for irreducible processes to the reducible case.     

A modeled time-varying density function for the incubation period of AIDS

Building on the Weibull distribution, we develop a modeled time-varying density function of the incubation time between exposure to HIV infection and full-blown AIDS. This approach leads to a series of cohort-specific density functions that take into account the increasing impact of new therapies such as zidovudine (AZT). The resulting modeled density functions are studied in detail, particularly with regard to their modes and medians. The mode is sensitive to changes in the period incubation time distribution, with even a possibility of a bimodal distribution for certain combinations of the parameters that determine the rate at which the period median incubation time changes. An important substantive result is that when a period median incubation period slowly increases to some leveling off value, say m(x _c ), then it is surprisingly early on that cohorts of infected individuals have a median incubation period very close to that ultimate value m(x _c ).     

Report of the Alpine Section, 1958

Background: Over 10,000 island endemic angiosperms are highly threatened by extinction. Yet, few of these species have the temporal change in their range documented and quantified, particularly within a potentially informative context of a long period of botanical study.

Aim: Here, we used Roussea simplex a mono-specific genus endemic to Mauritius, itself an island with long botanical history and advanced habitat destruction extent, to investigate how the distribution and population of this model oceanic island plant changed through time.

Methods: All known localities and population size estimates were compiled from published literature, herbarium specimens, surveys and personal communications to estimate changes in population size, extent of occurrence and area of occupancy and investigate main distribution patterns.

Results: Roussea simplex survives in nine high elevation sites. Since the 1930s, its range halved relative to its maximum known distribution and its population size decreased much faster than direct habitat loss would predict. It now qualifies as Endangered according to the IUCN Red List categories.

Conclusions: Even in an extremely deforested island, endemic plant population decline may be driven more by diminishing habitat quality than diminishing habitat extent. This renders habitat protection alone insufficient, therefore addressing ecological interactions is vital to stem population decline.     

THE BARRED MINNOWS (TELEOSTEI: CYPRINIDAE) OF ZIMBABWE: IS THERE CAUSE FOR CONCERN?

Summary

Two species of barred minnow, Opsaridium zambezense and O. peringueyi, occur in Zimbabwe. The former is widely distributed in the Zambezi basin and some other rivers but is now absent from Lake Kariba and possibly some of its tributaries. The latter, which was only recently recognised as a distinct species and admitted to the Zimbabwean list, is much scarcer. It occurs in the Save and Limpopo catchments and there are only four specimens in the Natural History Museum of Zimbabwe collection. These specimens are all more than 40 years old and the lack of more recent ones suggest that O. peringueyi may be extinct, or close to extinction, in Zimbabwe. This situation may have come about through habitat alteration and drought, and emphasises the need for further monitoring of the current occurrence/distribution of fish species in the country.     

Persistence of host and parasite populations subject to experimental size-selective removal

Predators have the potential to limit the spread of pathogens not only by selecting infected prey but also by shaping prey demographics. We tested this idea with an epidemiological experiment in which we simulated variable levels of size-selective predation on zooplankton hosts and monitored the persistence of host and parasite populations. In the absence of simulated predation, the virulent protozoan Caullerya mesnili frequently drove its host Daphnia galeata to extinction. Uninfected control populations showed lower extinction rates and higher average densities than infected populations in the absence of simulated predation (all of the latter went extinct or remained infected). With a weak removal rate of the largest hosts, the proportion of populations in which the parasite drove the host to extinction decreased, while the number of populations in which the host persisted and the parasite went extinct increased. Host-parasite coexistence was also observed in some cases. With intermediate levels of removal, most of the parasite populations went extinct, while the host populations persisted. With an even higher removal rate, Daphnia were driven to extinction as well. Thus, variation in one factor, size-selective mortality, resulted in four different patterns of population dynamics. Our results highlight the potential role of predation in shaping the epidemiology and community structure of host-parasite systems.     

Fifteenth annual research symposium University of Glasgow, 1975

Background: All human land use (LU) affects the distribution of plant species; however, the impacts vary with the type/intensity of LU. For managing ecosystems, it is therefore essential to understand the effects of LU types on the distribution of plant species on a macroscale.

Aims: The objectives of our study were to quantify the effects of various LU types on the distribution of vascular plant species in Japan and to determine in particular the extent to which LU was an important factor for the distribution of common species.

Methods: Based on a logistic regression model and variation partitioning being applied to each plant species, we evaluated the partial deviance by six LU types, four climatic types and three topographic and geological factors for 647 plant species at 14,412 sites in Japan.

Results: The effect of LU was significant for species present at multiple sites. Of the six LU types, secondary vegetation and plantation were the most important factors determining species distribution for many species.

Conclusions: Our results suggest that distribution of the common species is largely affected by LU on macroscale. The design of LU relating to secondary vegetation and plantations will thus be important in determining changes in the vegetation composition within Japan.     

Responses of Metapopulation Dynamics to Two Different Kinds of Habitat Destruction Caused by Human Activities

Habitat destruction can be classified into instantaneous destruction and continuous destruction by the different ways of human destroying habitat. Previous studies, however, always focused on instantaneous destruction. In this study, we develop a universal model, Multi-time scale N-species model, to study and compare the responses of metapopulation dynamics to both kinds of habitat destruction. The model explores that: (1) under instantaneous habitat destruction, species extinction is determined by the proportion of habitat destruction (D) and the structure of metapopulation (q). When D>q, species will go extinct ranked from the best competitor to the worst. When D≤ q, no species will go extinct, but the equilibrium abundances of odd-ranked competitors will decrease, and the equilibrium abundances of even-ranked competitors will increase; (2) under continuous destruction, species extinction is dependent on the speed of habitat destruction and the metapopulation structure. The higher the speed of habitat destruction and the bigger q are, the earlier species go extinct. Usually, there are two possible mechanisms of species extinction: one is that all species go extinct collectively following complete destruction, and the other is that species go extinct in ranked competitive order from best to worst, and the survivals, if they exist, will go extinct collectively following complete destruction. The oscillation amplitudes of inferior competitors are so large as to increase the probability of stochastic extinction under instantaneous destruction. Therefore, it is relatively propitious for the persistence of rare species under slow and continuous destruction, especially when continuous destruction stops.     

Interactions leading to persistence in predator-prey systems with group defence

In previous work (Freedman and Wolkowicz, 1986;Bull. math. Biol. 48, 493–508) it was shown that in a predator-prey system where the prey population exhibits group defence, it is possible that enrichment of the environment could lead to extinction of the predator population. In this paper a third population is introduced and criteria are derived under which persistence of all populations will occur. In particular, criteria for a superpredator and for a competitor to stabilize the system in the sense of persistence are analyzed. Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A 4823. This research was carried out while the author was a visiting scholar at the University of Alberta.     

Potential distribution under different climatic scenarios of climate change of the vulnerable Caucasian salamander (<Emphasis Type="Italic">Mertensiella caucasica</Emphasis>): A case study of the Caucasus Hotspot

Amphibians are strongly affected by climate change like many vertebrate animals. To address this problematic situation, we examined the potential effect of climate change on the distribution of Mertensiella caucasica (Waga, 1876) that is the best known species in Caucasus hotspot using future distribution modelling (average for 2041–2060 and 2061–2080) under RCP 4.5 and RCP 8.5 emission scenarios. According to our model, the future distribution showed a remarkable expansion towards the northwest part of the Greater Caucasus whereas it indicated a regression from the West of the western Lesser Caucasus up to the Greater Caucasus. Our results indicated that most habitat loss seems to occur in the West Lesser Caucasus including the northeast of Turkey and the East Lesser Caucasus. Moreover, habitat suitability for M. caucasica showed trends towards local extinction in the future. In the Caucasus hotspot, the expected distribution range of M. caucasica will decrease with the risk of local extinction. Therefore, we recommend that its status in IUCN Red List should be reconsidered again.     

Asynchronization of local population dynamics and persistence of a metapopulation: a lesson from an endangered composite plant, Aster kantoensis

Fragmentation of a large habitat makes local populations less linked to others, and a whole population structure changes to a metapopulation. The smaller a local population is, the more strengthened extinction factors become. Then, frequent extinctions of local populations threaten persistence of the metapopulation unless recolonizations occur rapidly enough after local extinctions. Spatially structured models have been more widely used for predicting future population dynamics and for assessing the extinction risk of a metapopulation. In this article, we first review such spatially structured models that have been applied to conservation biology, focusing on effects of asynchronization among local population dynamics on persistence of the whole metapopulation. Second, we introduce our ongoing project on extinction risk assessment of an endangered composite biennial plant, Aster kantoensis, in the riverside habitat, based on a lattice model for describing its spatiotemporal population dynamics. The model predicted that the extinction risk of A. kantoensis depends on both the frequency of flood occurrence and the time to coverage of a local habitat by other competitively stronger perennials. Finally, we present a measure (Hassell and Pacala's CV ²) for quantifying the effect of asynchronization among local population dynamics on the persistence of a whole metapopulation in conservation ecology. Received: January 12, 2000 / Accepted: February 8, 2000     

Comparative studies on the changes of total soluble proteins and protease activity in Georgian commercial peanuts contaminated by Aspergillus flavus

The presence of Aspergillus species is an indicator of storage conditions, which also suggests the possibility of several biochemical changes in grains. A comparative change in total soluble proteins and protease activity was determined in commercial peanut seeds collected from Georgia State. Protein contents of healthy peanuts, naturally contaminated peanuts and then artificially inoculated peanut seeds with A. flavus were estimated by Bradford method, and protease activity was also determined by using the Protease Detection Kits. Protein contents and the protease activity of the peanuts varied from sample to sample. The soluble protein content of seeds was significantly higher in healthy peanuts than in artificially inoculated or naturally infected peanuts with A. flavus. Protease activity was found to be higher in artificially inoculated seeds than in either naturally infected or healthy peanuts. Level of soluble proteins in buffer extracts of contaminated seeds decreased with incubation time, and protease activity increased with incubation time. These changes may be attributed to host response due to infection, contribution by A. flavus or due to biochemical alterations that occur naturally during the transition from endosperm to seedling during incubation period.     

Synchronization of the behaviour within nests of the antLeptothorax acervorum (Fabricius)—II. Modelling the phenomenon and predictions from the model

Observations on activity of ants of the speciesLeptothorax acervorum show that ants within the nest are inactive for about 72% of their time (Frankset al., 1990.Bull. math. Biol.,52, 597–612). By examination of the activity of individual ants it is demonstrated that activity bouts of individuals are highly synchronized. The bursts of activity detected by Frankset al. occurred three to four times per hour. In this paper we develop a model to describe the phenomenon. As a result of the interdependence of the number of active ants within the nest and the high level of community activity some predictions are made, which are supported by experimental data in a quantitative way. In case of starvation the number of active ants will increase and no rhythms should occur. When proportionally more brood is present the rhythms should occur with a higher frequency. Eventually the rhythm breaks down and a stable equilibrium is reached.     

The potential distribution of German wasps (Vespula germanica) in Argentina

Abstract

In the early 1980s, the German wasp (Vespula germanica) arrived in Argentina and became established in northern Patagonia. We use an ecoclimatic computer‐based program (CLIMEX) to predict the potential spread of wasps to other areas of the country. The model suggests that much of Argentina does not appear to be very suitable for the species’ establishment. However, more suitable areas than those currently colonised by the wasp occur in the centre of the country. Based on CLIMEX results, we suggest that, if the wasps ever break through the barrier of unfavourable habitat that surrounds their current distribution, they will continue dispersing to those areas. Notwithstanding this, factors other than climate may explain why German wasps are firmly established in areas otherwise considered to be inhospitable for the species.     

Testing a key assumption of host‐pathogen theory: density and disease transmission

Conventional disease theory suggests that extinction with density‐dependent transmission is unlikely as the threshold host density (KT) is greater than zero. Extinction may result if transmission is frequency dependent or the pathogen has an environmental reservoir. Given the importance of understanding how pathogens affect species richness and diversity there are few empirical tests of these conclusions. We used an Ambystoma tigrinum–Ambystoma tigrinum virus (ATV) model system in the laboratory to examine disease transmission dynamics. Susceptible A. tigrinum larvae were exposed to three different densities and proportions of infected larvae for 24 h. We then housed susceptible hosts individually for 28 days and monitored them for infection. The density of infected hosts to which susceptible hosts were exposed was the best predictor of infection (p=0.037). There was no effect of host clutch on the probability of becoming infected (p=0.67). Larvae in the highest density treatments died sooner than larvae in lower density treatments (p<0.001). Asymptomatic but infected hosts shed sufficient virus into the water in a 24‐h period to infect susceptible hosts without any direct contact between individuals. ATV transmission was best described by a power function, leading to the prediction that extinction of A. tigrinum as a result of this pathogen is unlikely. Indeed, field observations show that larval salamander populations that experience ATV‐driven epidemics may decrease, but not to extinction, and then recover. Disease is proposed as a possible explanation for the global decline of amphibians. Ranaviruses infect many amphibian populations, but based on our results may not be a general cause of declines to extinction. In contrast, frequency dependent transmission, environmental reservoirs and alternative hosts may be the most likely explanation for the enigmatic decline, at times to extinction, of some amphibian populations as a result of emerging infectious diseases, like the chytrid fungus Batrachochytrium dendrobatidis.     

Ecological niche modeling and geographic distribution of the genus <Emphasis Type="Italic">Polianthes</Emphasis> L. (Agavaceae) in Mexico: using niche modeling to improve assessments of risk status

The genus Polianthes (Agavaceae) is endemic to Mexico and is important at the scientific, economical, and cultural level since prehispanic times. Habitat destruction is one of the main factors affecting populations of Polianthes species, yet little is known about the geographic distribution of this genus, and thus its vulnerability to habitat change. We compared three different approaches to measure the Polianthes species area of distribution to assess the risk of species extinction applying the MER (Method of Evaluation of Risk extinction of wild species for Mexico): area of occupancy, extent of occurrence, and ecological modeling. We also found the richness areas of distribution of this genus. We compared the species distributions with Terrestrial Protected Regions (TPR) and Natural Protected Areas (NPA). Although the three methods used to calculate the species area of distribution agree about the highly restricted nature of Polianthes species. The area of occupancy sub-estimate the species distribution, while the extent of occurrence over-estimate it for species with disjoint distribution. Thus, we recommend the use of ecological modeling to improve the assessment of the current species distribution area to apply the MER. Most Polianthes species are distributed in the Sierra Madre Occidental and Transvolcanic Belt. Three species do not occur in any of the NPA or TPR, one species has suitable habitat in three TPR but has not been recorded there, and one species, P. palustris, is likely extinct.     

牛种布鲁氏菌2308不同途径小鼠感染模型的建立与评估

[背景] 布鲁氏菌可经口、皮肤、黏膜和呼吸道感染人和动物。小鼠是布鲁氏菌研究中最常用的模型动物。[目的] 建立牛种布鲁氏菌2308不同途径和剂量感染BALB/c小鼠的模型,为布鲁氏菌小鼠感染试验提供参考。[方法] 用10¹-10⁵ CFU这5个不同感染剂量,分别经注射、口服和点眼方式感染BALB/c小鼠。在感染后不同时间点采集小鼠血清,检测IgG、IgM、IgA抗体含量、脾脏重量及脾脏含菌量,评价布鲁氏菌经不同途径感染BALB/c小鼠的效果。[结果] 10 CFU是注射感染BALB/c小鼠的最小感染剂量;10⁵ CFU是口服感染BALB/c小鼠的最小感染剂量。10¹-10⁵ CFU这5个不同感染剂量经点眼途径均未能成功感染BALB/c小鼠。在10⁵ CFU感染剂量下,口服与注射感染组小鼠每克脾脏平均含菌量分别为10^5.673 CFU/g和10^5.009 CFU/g,无显著差异（P>0.05）,但口服感染组小鼠脾脏平均重量为0.310 g,显著高于注射感染组0.165 g （P<0.01）。在试验期内,注射感染组和口服感染组小鼠体内IgG抗体的滴度均随感染时间延长而持续升高;整体上,口服感染组IgG抗体峰值显著高于注射感染组;2组IgM抗体变化趋势一致;口服感染组有2只小鼠在感染28 d后产生IgA抗体,注射感染组均未检测到IgA抗体。[结论] 建立了牛种布鲁氏菌2308通过不同途径感染BALB/c小鼠的模型。     

新疆千里光Senecio jacobaea在中国的适生区预测

【背景】菊科植物新疆千里光原产于欧亚大陆,在北美和澳洲为入侵植物,目前在中国只有新疆有分布记录。新疆千里光一旦成为入侵植物,将对农业、畜牧业和人类健康都可能产生危害,所以需要评估其在中国的扩散趋势。【方法】搜集新疆千里光在中国和世界其他地区的分布记录,结合当前和未来(2050年)气候条件下19种生物气候变量,应用Maxent模型和Diva Gis软件,定量预测新疆千里光在中国目前和未来的潜在分布区域;并通过接受者操作特征曲线(ROC)分析法对模型进行精度检验。另外,通过Maxent给出新疆千里光在欧洲(原产地)、北美洲和大洋洲(入侵地)以及中国等4个分布区的年均温度和年均降水量的气候阈值。【结果】用中国和全球分布的数据预测的结果有些差异。前者结果表明除了新疆地区,其他省份几乎没有新疆千里光的适生区;而后者显示在中国其他几个省份也有可能分布,且在甘肃四川交界处有较高适生性。前者模型精确度较高,但2个结果都显示新疆千里光在中国目前和未来的分布区大部分还是在新疆地区。中国分布区年均温度和年均降水量的阈值比其他2个地区都低。【结论与意义】新疆千里光在当前和未来气候条件下在中国未来的扩散趋势较弱,基本局限于新疆地区。用中国分布数据预测优于全球分布数据预测结果,新疆千里光不同分布区的气候阈值的差异揭示分布于中国的新疆千里光与其他地区的种群的生态位有所不同,可能是一个新的亚种,希望未来能进行进一步的研究。     

Consequences of dispersal limitation and habitat fragmentation for the Brazilian heart‐tongued frogs (Phyllodytes spp.)

Poorly known species may be cryptically endangered, especially when they inhabit fragmented and threatened habitats. Heart‐tongued frogs (genus Phyllodytes, family Hylidae, Lophyohylinae) comprise 17 species of poorly known frogs that have obligatory associations with tank bromeliads. The distributions of all species are restricted to a small, extremely fragmented, region of Atlantic Forest in eastern Brazil. We model climate and tank bromeliad distributions to better understand frog distribution limits. Using records from several sources for frogs and bromeliads with climate data from WorldClim, we modelled the distribution of Phyllodytes using maximum entropy. We compared climate and altitude within the distribution and nearby to test how climate may limit distribution. Climate together with bromeliad distributions provided the best model and predicted the smallest suitable area for Phyllodytes that was larger than that occupied, from the state of Paraíba in the north to Rio Grande do Sul in the south. Phyllodytes occurs in lower elevations that are warmer, wetter and less variable than the surrounding regions where it does not occur, and dispersal is apparently limited by the surrounding, inhospitable, region. Dispersal limitation and habitat fragmentation have relegated Phyllodytes to many very small habitat fragments. With many species in this genus being known from a single or few samples, this unfortunate combination of limitation and fragmentation suggests that some or all species of Phyllodytes may be threatened with extinction, especially if habitat fragmentation continues at its present pace in eastern Brazil.     

Extinction times and phase transitions for spatially structured closed epidemics

This paper considers the time to extinction for a stochastic epidemic model of SEIR form without replacement of susceptibles. It first shows how previous rigorous results can be heuristically explained in terms of the more transparent dynamics of an approximating deterministic system. The model is then extended to include a host population structured into patches, with weak nearest-neighbour mixing of infection. It is shown, by considering the approximating deterministic system, that the expected time to extinction in a population of n + 1 patches each of size N is of the form a log N + bn, provided that N > N _c where N _c is a critical patch size below which transits are unlikely to occur. This corresponds to the simple decomposition of the time of an epidemic into the time it takes to spread through one patch plus the time it takes to transit to each of n successive patches. Expressions for this threshold and the coefficients of the time to extinction are given in terms of the transmission parameters of infection and the coupling strength between patches. These expressions are compared with numerical results using parameters relevant to a study of phocine distemper virus in North Sea seals, and the agreement is found to be good for large and small N. In the region when N ≈ N _c , where transits may or may not occur, interesting transitional behaviour is seen, leading to a non-monotonicity of the extinction time as a function of N.