Effects of immigration on some stochastic logistic models: a cumulant truncation analysis.

This paper uses a new cumulant truncation methodology to investigate the stochastic power law logistic model with immigration, and illustrates the model with parameter values used to describe the growth of muskrat populations in the Netherlands. This model has a stable equilibrium distribution. The incorporation of immigration into the model, therefore, simplifies the qualitative nature of the stochastic solution. The (unconditional) cumulant functions for the transient and the equilibrium population size distributions are obtained, from which the distributions are shown to be near-normal at all times for the parameter values of interest. Approximating cumulant functions, which are relatively easy to find in practice, are derived and shown to be quite accurate, except for the case of massive immigration. As the level of immigration increases, the mean value rises more rapidly initially, as expected; however, the variance and the skewness of both the transient and the equilibrium distributions are reduced.     

Neotyphodium endophyte infection frequency in annual grass populations: relative importance of mutualism and transmission efficiency

Persistence and ubiquity of vertically transmitted Neotyphodium endophytes in grass populations is puzzling because infected plants do not consistently exhibit increased fitness. Using an annual grass population model, we show that the problems for matching endophyte infection and mutualism are likely to arise from difficulties in detecting small mutualistic effects, variability in endophyte transmission efficiency and an apparent prevalence of non-equilibrium in the dynamics of infection. Although endophytes would ultimately persist only if the infection confers some fitness increase to the host plants, such an increase can be very small, as long as the transmission efficiency is sufficiently high. In addition, imperfect transmission limits effectively the equilibrium infection level if the infected plants exhibit small or large reproductive advantage. Under frequent natural conditions, the equilibrium infection level is very sensitive to small changes in transmission efficiency and host reproductive advantage, while convergence to such an equilibrium is slow. As a consequence, seed immigration and environmental fluctuation are likely to keep local infection levels away from equilibrium. Transient dynamics analysis suggests that, when driven by environmental fluctuation, infection frequency increases would often be larger than decreases. By contrast, when due to immigration, overrepresentation of infected individuals tends to vanish faster than equivalent overrepresentation of non-infected individuals.     

Dynamic Modeling of Herpes Simplex Virus Type-2 (HSV-2) Transmission: Issues in Structural Uncertainty

The sexually transmitted infection (STI) Herpes simplex virus type-2 (HSV-2) is of public health concern because it is a very common frequently unrecognized lifelong infection, which may facilitate HIV transmission. Within HIV/STI modeling, structural uncertainty has received less attention than parametric uncertainty. By merging the compartments of a “complex” model, a “simple” HSV-2 model is developed. Sexual interactions between female sex workers (FSWs) and clients are modeled using data from India. Latin Hypercube Sampling selects from parameter distributions and both models are run for each of the 10,000 parameter sets generated. Outputs are compared (except for 2,450 unrealistic simulations). The simple model is a good approximation to the complex model once the HSV-2 epidemic has reached 60% of the equilibrium prevalence (95% of the 7,550 runs produced <10% relative error). The simple model is a reduced version of the complex model that retains details implicitly. For late-stage epidemics, the simple model gives similar prevalence trends to the complex model. As HSV-2 epidemics in many populations are advanced, the simple model is accurate in most instances, although the complex model may be preferable for early epidemics. The analysis highlights the issue of structural uncertainty and the value of reducing complexity.     

Host-pathogen interactions, insect outbreaks, and natural selection for disease resistance

The theory of insect population dynamics has shown that heterogeneity in natural-enemy attack rates is strongly stabilizing. We tested the usefulness of this theory for outbreaking insects, many of which are attacked by infectious pathogens. We measured heterogeneity among gypsy moth larvae in their risk of infection with a nucleopolyhedrovirus, which is effectively heterogeneity in the pathogen's attack rate. Our data show that heterogeneity in infection risk in this insect is so high that it leads to a stable equilibrium in the models, which is inconsistent with the outbreaks seen in North American gypsy moth populations. Our data further suggest that infection risk declines after epidemics, in turn suggesting that the model assumption of constant infection risk is incorrect. We therefore constructed an alternative model in which natural selection drives fluctuations in infection risk, leading to reductions after epidemics because of selection for resistance and increases after epidemics because of a cost of resistance. This model shows cycles even for high heterogeneity, and experiments confirm that infection risk is indeed heritable. The model is very general, and so we argue that natural selection for disease resistance may play a role in many insect outbreaks.     

Spatial Autocorrelation of Genotypes under Directional Selection

The spatial distributions of genetic variation under selection-mutation equilibrium within populations that have limited dispersal are investigated. The results show that directional selection with moderate strength rapidly reduces the amount of genetic structure and spatial autocorrelations far below that predicted for selectively neutral loci. For the latter, homozygotes are spatially clustered into separate areas or patches, each consisting of several hundred homozygotes. When selection is added the patches of the deleterious homozygotes are much smaller, in the range of 25 to 50 individuals. Selection also reduces temporal correlations. Also investigated are the effects of random replacement processes, such as mutation, immigration, and long-distance migration, on spatial and temporal correlations. The detection of natural selection through spatial pattern analysis is discussed, and applied to data from populations of the morning glory, Ipomoea purpurea.     

Microbial colonization dynamics in temporary aquatic systems

Most studies of community development in insular systems have investigated the colonization dynamics of only a portion of the biotic community using islands that have the benefit of prior biotic modification. Two experiments assessed the predictive ability of equilibrium island theory with regard to the development of the protistan community in temporary aquatic islands (100-1 plastic swimming pools) void of any prior biotic modification. The first experiment ran for 170 d (March–September 1985) and manipulated the access of islands to animals that represent potentially important dispersal pathways for microbes. A second experiment (May–June 1986) investigated in greater detail the early stages of species accrual in the absence of dispersal pathways other than via the atmosphere. Polyurethane foam substrates were used as sampling devices to increase the accuracy and replicability of sampling and provide habitat for colonists. Sampling was determined to be asymptotic. Species accrual was asymptotic in both experiments, although it initially lagged behind that predicted by theory. Autotrophs approached equilibrium faster than heterotrophs, but at a lower species richness. The predicted number of autotroph species at equilibrium was lower in islands that were excluded from contact with birds compared to less exclosed islands. The colonization dynamics of the entire community was not significantly different among islands having different degrees of exclosure. In both experiments, rates of species immigration were nonmonotonic with respect to time and species richness. This relationship appeared to reflect the importance of species interactions during the initial accrual phase before equilibrium. Rates of extinction were positively correlated with both these parameters, although they tended to decrease with time during the equilibrium period in less exclosed islands. Turnover at equilibrium was significant and resulted in directional changes in species composition over time. Assortative processes appeared to be important since later colonists exhibited greater persistence. Colonizing species generally fall into three autecological categories: 1) those that were ubiquitous and had temporally predictable patterns of immigration (successional species); 2) those possessing temporally predictable distributions but not spatially ubiquitous distributions (dispersal limited species); 3) those that showed little temporal or spatial predictability in immigration (transient or allochthonous species). Individual islands exhibited various degrees of fluctuation in species number during the predicted equilibrium which were poorly correlated with exogenous environmental variables and physicochemical habitat parameters. The presence of predacious mosquito larvae(Culex spp.) invariably resulted in a sharp decreases in microbial species richness, while documented contact with rodents was followed by an increase in species number in an island so contaminated. Several aspects of microbial colonization of temporary waters that contradict equilibrium predictions appear to be strongly influenced by microbe-microbe as well as macrobe-microbe interactions.     

Structured models of metapopulation dynamics

I develop models of metapopulation dynamics that describe changes in the numbers of individuals within patches. These models are analogous to structured population models, with patches playing the role of individuals. Single species models which do not include the effect of immigration on local population dynamics of occupied patches typically lead to a unique equilibrium. The models can be used to study the distributions of numbers of individuals among patches, showing that both metapopulations with local outbreaks and metapopulations without outbreaks can occur in systems with no underlying environmental variability. Distributions of local population sizes (in occupied patches) can vary independently of the total population size, so both patterns of distributions of local population sizes are compatible with either rare or common species. Models which include the effect of immigration on local population dynamics can lead to two positive equilibria, one stable and one unstable, the latter representing a threshold between regional extinction and persistence.     

The effect of superspreading on epidemic outbreak size distributions

Recently, evidence has been presented to suggest that there are significant heterogeneities in the transmission of communicable diseases. Here, a stochastic simulation model of an epidemic process that allows for these heterogeneities is used to demonstrate the potentially considerable effect that heterogeneity of transmission will have on epidemic outbreak size distributions. Our simulation results agree well with approximations gained from the theory of branching processes. Outbreak size distributions have previously been used to infer basic epidemiological parameters. We show that if superspreading does occur then such distributions must be interpreted with care. The simulation results are discussed in relation to measles epidemics in isolated populations and in predominantly urban scenarios. The effect of three different disease control policies on outbreak size distributions are shown for varying levels of heterogeneity and disease control effort.     

Reconciling niche and neutrality: the continuum hypothesis

In this study, we ask if instead of being fundamentally opposed, niche and neutral theories could simply be located at the extremes of a continuum. First, we present a model of recruitment probabilities that combines both niche and neutral processes. From this model, we predict and test whether the relative importance of niche vs. neutral processes in controlling community dynamics will vary depending on community species richness, niche overlap and dispersal capabilities of species (both local and long distance). Results demonstrate that niche and neutrality form ends of a continuum from competitive to stochastic exclusion. In the absence of immigration, competitive exclusion tends to create a regular spacing of niches. However, immigration prevents the establishment of a limiting similarity. The equilibrium community consists of a set of complementary and redundant species, with their abundance determined, respectively, by the distribution of environmental conditions and the amount of immigration.     

Biodiversity and the Lotka-Volterra theory of species interactions: open systems and the distribution of logarithmic densities

Theoretical interest in the distributions of species abundances observed in ecological communities has focused recently on the results of models that assume all species are identical in their interactions with one another, and rely upon immigration and speciation to promote coexistence. Here we examine a one-trophic level system with generalized species interactions, including species-specific intraspecific and interspecific interaction strengths, and density-independent immigration from a regional species pool. Comparisons between results from numerical integrations and an approximate analytic calculation for random communities demonstrate good agreement, and both approaches yield abundance distributions of nearly arbitrary shape, including bimodality for intermediate immigration rates.     

Stochastic and spatial dynamics of nematode parasites in farmed ruminants

Host-parasite systems provide powerful opportunities for the study of spatial and stochastic effects in ecology; this has been particularly so for directly transmitted microparasites. Here, we construct a fully stochastic model of the population dynamics of a macroparasite system: trichostrongylid gastrointestinal nematode parasites of farmed ruminants. The model subsumes two implicit spatial effects: the host population size (the spatial extent of the interaction between hosts) and spatial heterogeneity ('clumping') in the infection process. This enables us to investigate the roles of several different processes in generating aggregated parasite distributions. The necessity for female worms to find a mate in order to reproduce leads to an Allee effect, which interacts nonlinearly with the stochastic population dynamics and leads to the counter-intuitive result that, when rare, epidemics can be more likely and more severe in small host populations. Clumping in the infection process reduces the strength of this Allee effect, but can hamper the spread of an epidemic by making infection events too rare. Heterogeneity in the hosts' response to infection has to be included in the model to generate aggregation at the level observed empirically.     

Equilibrium distributions for deleterious genes in large stationary populations.

In a large population of constant size, there is a unique equilibrium distribution for every deleterious autosomal dominant or deleterious X-linked gene. The purpose of this paper is to determine the mean vector and covariance matrix for such an equilibrium distribution. The theory of branching processes with immigration provides the framework for our investigation. Autosomal dominants can be treated using single-type branching processes; X-linked genes, using two-type branching processes. Application is made to Huntington's chorea and Becker's muscular dystrophy.     

Emergence of non-random structure in local food webs generated from randomly structured regional webs

Previous studies have shown that high-resolution, empirical food webs possess a non-random network structure, typically characterized by uniform or exponential degree distributions. However, the empirical food webs that have been investigated for their structural properties represent local communities that are only a subset of a larger pool of regionally coexisting species. Here, we use a simple model to investigate the effects of regional food web structure on local food webs that are assembled by two simple processes: random immigration of species from a source web (regional food web), and random extinction of species within the local web. The model shows that local webs with non-random degree distributions can arise from randomly structured source webs. A comparison of local webs assembled from randomly structured source webs with local webs assembled from source webs generated by the niche model shows that the former have higher species richness at equilibrium, but have a nonlinear response to changing extinction rates. These results imply that the network structure of regional food webs can play a significant role in the assembly and dynamics of local webs in natural ecosystems. With natural landscapes becoming increasingly fragmented, understanding such structure may be a necessary key to understanding the maintenance and stability of local species diversity.     

Revisiting Jablonski (1993): cladogenesis and range expansion explain latitudinal variation in taxonomic richness

The increase in diversity towards the equator arises from latitudinal variation in rates of cladogenesis, extinction, immigration and/or emigration of taxa. We tested the relative contribution of all four processes to the latitudinal gradient in 26 marine invertebrate orders with extensive fossil records, examined previously by David Jablonski. Coupling Jablonski's estimates of latitudinal variation in cladogenesis with new data on patterns of extinction and current distributions, we show that the present-day gradient in diversity is caused by higher rates of cladogenesis and subsequent range expansion (immigration) at lower latitudes. In contrast, extinction and emigration were not important in the creation of the latitudinal gradient in ordinal richness. This work represents one of the first simultaneous tests of the role of all four processes in the creation of the latitudinal gradient in taxonomic richness, and suggests that low tropical extinction rates are not essential to the creation of latitudinal diversity gradients.     

Towards a theory of insect epidemiology

An attempt is made to consolidate and extend some of our current thoughts on insect epidemiology using graphical reproduction models. Starting with a simple model with a single equilibrium point, the elementary hypothesis is proposed that epidemics erupt when this equilibrium point increases substantially through improvement of the insect's habitat. The extension of this model to more than one coincident equilibria, some of which may be locally stable, is discussed and generalized using the theory of habitat suitability. Use of equilibrium manifolds is suggested to permit greater dimensionality. Lastly, an explanation of insect epidemics, based on the effects of time delays in the response of density-dependent processes, is elaborated and generalized. The influence of spatial dimensions and insect dispersal on the theory is discussed.     

Threshold behaviour of a SIR epidemic model with age structure and immigration

We consider a SIR age-structured model with immigration of infectives in all epidemiological compartments; the population is assumed to be in demographic equilibrium between below-replacement fertility and immigration; the spread of the infection occurs through a general age-dependent kernel. We analyse the equations for steady states; because of immigration of infectives a steady state with a positive density of infectives always exists; however, a quasi-threshold theorem is proved, in the sense that, below the threshold, the density of infectives is close to 0, while it is away from 0, above the threshold; furthermore, conditions that guarantee uniqueness of steady states are obtained. Finally, we present some numerical examples, inspired by the Italian demographic situation, that illustrate the threshold-like behaviour, and other features of the stationary solutions and of the transient. Supported in part by FIRB project RBAU01K7M2 “Metodi dell’Analisi Matematica in Biologia, Medicina e Ambiente” of the Italian Ministero Istruzione Università e Ricerca     

Spatially explicit neutral models for population genetics and community ecology: Extensions of the Neyman-Scott clustering process

Spatially explicit models relating to plant populations have developed little since Felsenstein (1975) pointed out that if limited seed dispersal causes clustering of individuals, such models cannot reach an equilibrium. This paper aims to resolve this issue by modifying the Neyman-Scott cluster point process. The new point processes are dynamic models with random immigration, and the continuous increase in the clustering of individuals stops at some level. Hence, an equilibrium state is achieved, and new individual-based spatially explicit neutral coalescent models are established. By fitting the spatial structure at equilibrium to individual spatial distribution data, we can indirectly estimate seed dispersal and effective population density. These estimates are improved when genetic data are available, and become even more sophisticated if spatial distribution and genetic data pertaining to the offspring are also available.     

Modelling the effect of immigration on drinking behaviour

A drinking model with immigration is constructed. For the model with problem drinking immigration, the model admits only one problem drinking equilibrium. For the model without problem drinking immigration, the model has two equilibria, one is problem drinking-free equilibrium and the other is problem drinking equilibrium. By employing the method of Lyapunov function, stability of all kinds of equilibria is obtained. Numerical simulations are also provided to illustrate our analytical results. Our results show that alcohol immigrants increase the difficulty of the temperance work of the region.     

Geographic variation in seasonality and its influence on the dynamics of an infectious disease

Seasonal changes in environmental drivers – such as temperature, rainfall, and resource availability – have the potential to shape infection dynamics through their reverberating effects on biological processes including host abundance and susceptibility to infection. However, seasonality varies geographically. We therefore expect marked differences in infection dynamics between regions with different seasonal patterns. By pairing extensive Avian Influenza Virus (AIV) surveillance data – 65 358 individual bird samples from 12 species of dabbling ducks sampled at 174 locations across North America – with quantification of seasonality using remote sensed data indicative for primary productivity (normalised differenced vegetation index, NDVI), we provide evidence that seasonal dynamics influence infection dynamics across a continent. More pronounced epidemics were seen to occur in regions experiencing a higher degree of seasonality, and epidemics of lower amplitude and longer duration occurred in regions with a more protracted and lower seasonal amplitude. These results demonstrate the potential importance of geographic variation in seasonality for explaining geographic variation in the dynamics of infectious diseases in wildlife.     

以兽类为例探讨我国陆生野生动物疫病监管中面临的问题与对策

近年来, 新型冠状病毒、SARS病毒和鼠疫等新发和再发性动物源疫病多是由兽类及其媒介携带的病原生物直接或间接感染而引发的, 不仅对人类健康和生态系统平衡造成了重大威胁, 而且威胁全球公共卫生安全、粮食安全和生物安全。结合我国重要陆生兽类疫源疫病发生的新情况和新特点, 本文重点总结了我国以陆生野生及非野生兽类(家畜为主)为重点的24种重要人兽共患病的监管情况, 并对这些疫源疫病的监管空缺进行了分析。由于病原生物的种类多及其感染传播方式多样, 我国人间和动物间疫情呈现多发态势, 新发和再发疫病防控面临严峻挑战。从目前情况来看, 我国重要野生动物疫源疫病呈现为多部门、多层监管的局面。全球化贸易剧增、非法猎杀、非法交易、违法违规养殖、滥食野生动物陋习、检疫环节失察等导致了当前我国野生动物疫源疫病的传染源头和传播链错综复杂, 加剧了人类与野生动物所携带的病原接触、感染和传播的风险。极端气候或灾害事件频发以及对新发再发传染病的认知不足导致难以从源头做好疫病防控。针对上述问题, 本文提出了从源头加强基础研究和全链条监管来积极防范陆生野生动物疫病疫情的对策和建议。