Natural,Persistent Oscillations in a Spatial Multi-Strain Disease System with Application to Dengue

Many infectious diseases are not maintained in a state of equilibrium but exhibit significant fluctuations in prevalence over time. For pathogens that consist of multiple antigenic types or strains, such as influenza, malaria or dengue, these fluctuations often take on the form of regular or irregular epidemic outbreaks in addition to oscillatory prevalence levels of the constituent strains. To explain the observed temporal dynamics and structuring in pathogen populations, epidemiological multi-strain models have commonly evoked strong immune interactions between strains as the predominant driver. Here, with specific reference to dengue, we show how spatially explicit, multi-strain systems can exhibit all of the described epidemiological dynamics even in the absence of immune competition. Instead, amplification of natural stochastic differences in disease transmission, can give rise to persistent oscillations comprising semi-regular epidemic outbreaks and sequential dominance of dengue''s four serotypes. Not only can this mechanism explain observed differences in serotype and disease distributions between neighbouring geographical areas, it also has important implications for inferring the nature and epidemiological consequences of immune mediated competition in multi-strain pathogen systems.     

Intensity and temporal variability as components of stress gradients: implications for the balance between competition and facilitation

The mechanisms regulating switches in species interactions along gradients of stress are yet to be fully elucidated. In particular, the role of temporal variability in environmental severity or consumer pressure has been not explored either empirically or theoretically. Here, through a spatially explicit model (i.e. a two‐dimensional lattice), we show that variations in the temporal variance of environmental stress can be as important as those in the mean intensity in regulating the spatial distribution and coexistence range of species differing in their relative competitive ability and tolerance to stress, as well as the direction and magnitude of their interactions. In addition, our simulations suggest that enhanced temporal fluctuations in environmental stressors can enhance absolute levels of stress perceived by interacting species. This study shows that tests including both the mean and temporal variance of environmental stress will be key to forecast changes in species interactions under different scenarios of climate change.     

Spatial and temporal heterogeneity explain disease dynamics in a spatially explicit network model

There is an increasing recognition that individual-level spatial and temporal heterogeneity may play an important role in metapopulation dynamics and persistence. In particular, the patterns of contact within and between aggregates (e.g., demes) at different spatial and temporal scales may reveal important mechanisms governing metapopulation dynamics. Using 7 years of data on the interaction between the anther smut fungus (Microbotryum violaceum) and fire pink (Silene virginica), we show how the application of spatially explicit and implicit network models can be used to make accurate predictions of infection dynamics in spatially structured populations. Explicit consideration of both spatial and temporal organization reveals the role of each in spreading risk for both the host and the pathogen. This work suggests that the application of spatially explicit network models can yield important insights into how heterogeneous structure can promote the persistence of species in natural landscapes.     

Effect of (a)synchronous light fluctuation on diversity,functional and structural stability of a marine phytoplankton metacommunity

Disentangling the mechanisms that maintain the stability of communities and ecosystem properties has become a major research focus in ecology in the face of anthropogenic environmental change. Dispersal plays a pivotal role in maintaining diversity in spatially subdivided communities, but only a few experiments have simultaneously investigated how dispersal and environmental fluctuation affect community dynamics and ecosystem stability. We performed an experimental study using marine phytoplankton species as model organisms to test these mechanisms in a metacommunity context. We established three levels of dispersal and exposed the phytoplankton to fluctuating light levels, where fluctuations were either spatially asynchronous or synchronous across patches of the metacommunity. Dispersal had no effect on diversity and ecosystem function (biomass), while light fluctuations affected both evenness and community biomass. The temporal variability of community biomass was reduced by fluctuating light and temporal beta diversity was influenced interactively by dispersal and fluctuation, whereas spatial variability in community biomass and beta diversity were barely affected by treatments. Along the establishing gradient of species richness and dominance, community biomass increased but temporal variability of biomass decreased, thus highest stability was associated with species-rich but highly uneven communities and less influenced by compensatory dynamics. In conclusion, both specific traits (dominance) and diversity (richness) affected the stability of metacommunities under fluctuating conditions.     

Spatial scaling of consumer-resource interactions in advection-dominated systems

Ecologists studying consumer-resource interactions in advection-dominated systems such as streams and rivers frequently seek to link the results of small-scale experiments with larger-scale patterns of distribution and abundance. Accomplishing this goal requires determining the characteristic scale, termed the response length, at which there is a shift from local dynamics dominated by advective dispersal to larger-scale dynamics dominated by births and deaths. Here, we model the dynamics of consumer-resource systems in a spatially variable, advective environment and show how consumer-resource interactions alter the response length relative to its single-species value. For one case involving a grazer that emigrates in response to high predator density, we quantify the changes using published data from small-scale experiments on aquatic invertebrates. Using Fourier analysis, we describe the responses of advection-dominated consumer-resource systems to spatially extended environmental variability in a way that involves explicit consideration of the response length. The patterns we derive for different consumer-resource systems exhibit important similarities in how component populations respond to spatial environmental variability affecting dispersal as opposed to demographic parameters.     

Physiological analysis on oscillatory behavior of glucose-insulin regulation by model with delays

Despite temporally forced transmission driving many infectious diseases, analytical insight into its role when combined with stochastic disease processes and non-linear transmission has received little attention. During disease outbreaks, however, the absence of saturation effects early on in well-mixed populations mean that epidemic models may be linearised and we can calculate outbreak properties, including the effects of temporal forcing on fade-out, disease emergence and system dynamics, via analysis of the associated master equations. The approach is illustrated for the unforced and forced SIR and SEIR epidemic models. We demonstrate that in unforced models, initial conditions (and any uncertainty therein) play a stronger role in driving outbreak properties than the basic reproduction number R₀, while the same properties are highly sensitive to small amplitude temporal forcing, particularly when R₀ is small. Although illustrated for the SIR and SEIR models, the master equation framework may be applied to more realistic models, although analytical intractability scales rapidly with increasing system dimensionality. One application of these methods is obtaining a better understanding of the rate at which vector-borne and waterborne infectious diseases invade new regions given variability in environmental drivers, a particularly important question when addressing potential shifts in the global distribution and intensity of infectious diseases under climate change.     

Seasonal Invasion Dynamics in a Spatially Heterogeneous River with Fluctuating Flows

A key problem in environmental flow assessment is the explicit linking of the flow regime with ecological dynamics. We present a hybrid modeling approach to couple hydrodynamic and biological processes, focusing on the combined impact of spatial heterogeneity and temporal variability on population dynamics. Studying periodically alternating pool-riffle rivers that are subjected to seasonally varying flows, we obtain an invasion ratchet mechanism. We analyze the ratchet process for a caricature model and a hybrid physical–biological model. The water depth and current are derived from a hydrodynamic equation for variable stream bed water flows and these quantities feed into a reaction-diffusion-advection model that governs population dynamics of a river species. We establish the existence of spreading speeds and the invasion ratchet phenomenon, using a mixture of mathematical approximations and numerical computations. Finally, we illustrate the invasion ratchet phenomenon in a spatially two-dimensional hydraulic simulation model of a meandering river structure. Our hybrid modeling approach strengthens the ecological component of stream hydraulics and allows us to gain a mechanistic understanding as to how flow patterns affect population survival.     

Environmental Variation Generates Environmental Opportunist Pathogen Outbreaks

Many socio-economically important pathogens persist and grow in the outside host environment and opportunistically invade host individuals. The environmental growth and opportunistic nature of these pathogens has received only little attention in epidemiology. Environmental reservoirs are, however, an important source of novel diseases. Thus, attempts to control these diseases require different approaches than in traditional epidemiology focusing on obligatory parasites. Conditions in the outside-host environment are prone to fluctuate over time. This variation is a potentially important driver of epidemiological dynamics and affect the evolution of novel diseases. Using a modelling approach combining the traditional SIRS models to environmental opportunist pathogens and environmental variability, we show that epidemiological dynamics of opportunist diseases are profoundly driven by the quality of environmental variability, such as the long-term predictability and magnitude of fluctuations. When comparing periodic and stochastic environmental factors, for a given variance, stochastic variation is more likely to cause outbreaks than periodic variation. This is due to the extreme values being further away from the mean. Moreover, the effects of variability depend on the underlying biology of the epidemiological system, and which part of the system is being affected. Variation in host susceptibility leads to more severe pathogen outbreaks than variation in pathogen growth rate in the environment. Positive correlation in variation on both targets can cancel the effect of variation altogether. Moreover, the severity of outbreaks is significantly reduced by increase in the duration of immunity. Uncovering these issues helps in understanding and controlling diseases caused by environmental pathogens.     

Evolution of Pathogen Specialisation in a Host Metapopulation: Joint Effects of Host and Pathogen Dispersal

Metapopulation processes are important determinants of epidemiological and evolutionary dynamics in host-pathogen systems, and are therefore central to explaining observed patterns of disease or genetic diversity. In particular, the spatial scale of interactions between pathogens and their hosts is of primary importance because migration rates of one species can affect both spatial and temporal heterogeneity of selection on the other. In this study we developed a stochastic and discrete time simulation model to specifically examine the joint effects of host and pathogen dispersal on the evolution of pathogen specialisation in a spatially explicit metapopulation. We consider a plant-pathogen system in which the host metapopulation is composed of two plant genotypes. The pathogen is dispersed by air-borne spores on the host metapopulation. The pathogen population is characterised by a single life-history trait under selection, the infection efficacy. We found that restricted host dispersal can lead to high amount of pathogen diversity and that the extent of pathogen specialisation varied according to the spatial scale of host-pathogen dispersal. We also discuss the role of population asynchrony in determining pathogen evolutionary outcomes.     

Influence of landscape and social interactions on transmission of disease in a social cervid

The mechanisms of pathogen transmission are often social behaviours. These occur at local scales and are affected by landscape-scale population structure. Host populations frequently exist in patchy and isolated environments that create a continuum of genetic and social familiarity. Such variability has an important multispatial effect on pathogen spread. We assessed elk dispersal (i.e. likelihood of interdeme pathogen transmission) through spatially explicit genetic analyses. At a landscape scale, the elk population was composed of one cluster within a southeast-to-northwest cline spanning three spatially discrete subpopulations of elk across two protected areas in Manitoba (Canada). Genetic data are consistent with spatial variability in apparent prevalence of bovine tuberculosis (TB) in elk. Given the existing population structure, between-subpopulation spread of disease because of elk dispersal is unlikely. Furthermore, to better understand the risk of spread and distribution of the TB, we used a combination of close-contact logging biotelemetry and genetic data, which highlights how social intercourse may affect pathogen transmission. Our results indicate that close-contact interaction rate and duration did not covary with genetic relatedness. Thus, direct elk-to-elk transmission of disease is unlikely to be constrained to related individuals. That social intercourse in elk is not limited to familial groups provides some evidence pathogen transmission may be density-dependent. We show that the combination of landscape-scale genetics, relatedness and local-scale social behaviours is a promising approach to understand and predict landscape-level pathogen transmission within our system and within all social ungulate systems affected by transmissible diseases.     

Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion

This article introduces a two-strain spatially explicit SIS epidemic model with space-dependent transmission parameters. We define reproduction numbers of the two strains, and show that the disease-free equilibrium will be globally stable if both reproduction numbers are below one. We also introduce the invasion numbers of the two strains which determine the ability of each strain to invade the single-strain equilibrium of the other strain. The main question that we address is whether the presence of spatial structure would allow the two strains to coexist, as the corresponding spatially homogeneous model leads to competitive exclusion. We show analytically that if both invasion numbers are larger than one, then there is a coexistence equilibrium. We devise a finite element numerical method to numerically confirm the stability of the coexistence equilibrium and investigate various competition scenarios between the strains. Finally, we show that the numerical scheme preserves the positive cone and converges of first order in the time variable and second order in the space variables.     

Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion

This article introduces a two-strain spatially explicit SIS epidemic model with space-dependent transmission parameters. We define reproduction numbers of the two strains, and show that the disease-free equilibrium will be globally stable if both reproduction numbers are below one. We also introduce the invasion numbers of the two strains which determine the ability of each strain to invade the single-strain equilibrium of the other strain. The main question that we address is whether the presence of spatial structure would allow the two strains to coexist, as the corresponding spatially homogeneous model leads to competitive exclusion. We show analytically that if both invasion numbers are larger than one, then there is a coexistence equilibrium. We devise a finite element numerical method to numerically confirm the stability of the coexistence equilibrium and investigate various competition scenarios between the strains. Finally, we show that the numerical scheme preserves the positive cone and converges of first order in the time variable and second order in the space variables.     

The genetic consequences of fluctuating inbreeding depression and the evolution of plant selfing rates

The magnitude of inbreeding depression, a central parameter in the evolution of plant mating systems, can vary depending on environmental conditions. However, the underlying genetic mechanisms causing environmental fluctuations in inbreeding depression, and the consequences of this variation for the evolution of self‐fertilization, have been little studied. Here, we consider temporal fluctuations of the selection coefficient in an explicit genetic model of inbreeding depression. We show that substantial variance in inbreeding depression can be generated at equilibrium by fluctuating selection, although the simulated variance tends to be lower than has been measured in experimental studies. Our simulations also reveal that purging of deleterious mutations does not depend on the variance in their selection coefficient. Finally, an evolutionary analysis shows that, in contrast to previous theoretical approaches, intermediate selfing rates are never evolutionarily stable when the variation in inbreeding depression is due to fluctuations in the selection coefficient on deleterious mutations.     

An integrated,spatio‐temporal modelling framework for analysing biological invasions

Aim

We develop a novel modelling framework for analysing the spatio‐temporal spread of biological invasions. The framework integrates different invasion drivers and disentangles their roles in determining observed invasion patterns by fitting models to historical distribution data. As a case study application, we analyse the spread of common ragweed (Ambrosia artemisiifolia).

Location

Central Europe.

Methods

A lattice system represents actual landscapes with environmental heterogeneity. Modelling covers the spatio‐temporal invasion sequence in this grid and integrates the effects of environmental conditions on local invasion suitability, the role of invaded cells and spatially implicit “background” introductions as propagule sources, within‐cell invasion level bulk‐up and multiple dispersal means. A modular framework design facilitates flexible numerical representation of the modelled invasion processes and customization of the model complexity. We used the framework to build and contrast increasingly complex models, and fitted them using a Bayesian inference approach with parameters estimated by Markov chain Monte Carlo (MCMC).

Results

All modelled invasion drivers codetermined the A. artemisiifolia invasion pattern. Inferences about individual drivers depended on which processes were modelled concurrently, and hence changed both quantitatively and qualitatively between models. Among others, the roles of environmental variables were assessed substantially differently subject to whether models included explicit source‐recipient cell relationships, spatio‐temporal variability in source cell strength and human‐mediated dispersal means. The largest fit improvements were found by integrating filtering effects of the environment and spatio‐temporal availability of propagule sources.

Main conclusions

Our modelling framework provides a straightforward means to build integrated invasion models and address hypotheses about the roles and mutual relationships of different putative invasion drivers. Its statistical nature and generic design make it suitable for studying many observed invasions. For efficient invasion modelling, it is important to represent changes in spatio‐temporal propagule supply by explicitly tracking the species’ colonization sequence and establishment of new populations.

     

Spatial patterns of soil pathogens in declining Mediterranean forests: implications for tree species regeneration

Soil-borne pathogens are a key component of the belowground community because of the significance of their ecological and socio-economic impacts. However, very little is known about the complexity of their distribution patterns in natural systems. Here, we explored the patterns, causes and ecological consequences of spatial variability in pathogen abundance in Mediterranean forests affected by oak decline. We used spatially explicit neighborhood models to predict the abundance of soil-borne pathogen species (Phytophthora cinnamomi, Pythium spiculum and Pythium spp.) as a function of local abiotic conditions (soil texture) and the characteristics of the tree and shrub neighborhoods (species composition, size and health status). The implications of pathogen abundance for tree seedling performance were explored by conducting a sowing experiment in the same locations in which pathogen abundance was quantified. Pathogen abundance in the forest soil was not randomly distributed, but exhibited spatially predictable patterns influenced by both abiotic and, particularly, biotic factors (tree and shrub species). Pathogen abundance reduced seedling emergence and survival, but not in all sites or tree species. Our findings suggest that heterogeneous spatial patterns of pathogen abundance at fine spatial scale can be important for the dynamics and restoration of declining Mediterranean forests.     

Impacts of dispersal on rapid adaptation and dynamic stability of Daphnia in fluctuating environments

Prior ecological research has shown that spatial processes can enhance the temporal stability of populations in fluctuating environments. Less explored is the effect of dispersal on rapid adaptation and its concomitant impact on population dynamics. For asexually reproducing populations, theory predicts that dispersal in fluctuating environments can facilitate asynchrony among clones and enhance stability by reducing temporal variability of total population abundance. This effect is predicted when clones exhibit heritable variation in environmental optima and when fluctuations occur asynchronously among patches. We tested this in the field using artificial ponds and metapopulations composed of a diverse assemblage of Daphnia pulex clones. We directly manipulated dispersal presence/absence and environmental fluctuations in the form of nutrient pulses. Consistent with predictions, dispersal enhanced temporal asynchrony among clones in the presence of nutrient pulses; this in turn stabilized population dynamics. This effect only emerged when patches experienced spatially asynchronous nutrient pulses (dispersal had no effect when patches were synchronously pulsed). Clonal asynchrony was driven by strong positive selection for a single clone that exhibited a performance advantage under conditions of low resource availability. Our work highlights the importance of dispersal as a driver of eco-evolutionary dynamics and population stability in variable environments.     

Establishment success and extinction risk in autocorrelated environments

We consider establishment success (and extinction risk of small populations) in fluctuating environments, by means of an inhomogeneous branching process model. In this model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period individuals reproduce independently and have random numbers of offspring. Expected numbers of offspring vary over reproduction periods due to random environmental changes. Previous simulation results indicated that there is a positive autocorrelation between the establishment probabilities of invaders in successive reproduction periods when environmental states are independently distributed. This result was never formally proved. In this paper we prove that this is indeed true, regardless of the form of the distribution of environmental states or the offspring distribution (under a monotonicity condition, which holds for biologically realistic models). Furthermore, we prove that it is also true for positively autocorrelated environmental states. We show by a counterexample that in environments with a strong negative autocorrelation establishment probabilities can be negatively autocorrelated. This was further examined through simulations. Our results imply that in independent, positively autocorrelated and weakly negatively autocorrelated environments the probability of success of invasion in different independently varying sites is the highest, followed by sequential invasion. For environments with a strong negative autocorrelation, sequential invasion has the highest probability of success. Effects of autocorrelation were further examined with simulations. From the results it appears that the expected length of 'runs of bad luck' is the most crucial factor for establishment success.     

Protection of waterborne pathogens by higher organisms in drinking water: a review

Higher organisms are ubiquitous in surface waters, and some species can proliferate in granular filters of water treatment plants and colonize distribution systems. Meanwhile, some waterborne pathogens are known to maintain viability inside amoebae or nematodes. The well-documented case of Legionella replication within amoebae is only one example of a bacterial pathogen that can be amplified inside the vacuoles of protozoa and then benefit from the protection of a resistant structure that favours its transport and persistence through water systems. Yet the role of most zooplankton organisms (rotifers, copepods, cladocerans) in pathogen transmission through drinking water remains poorly understood, since their capacity to digest waterborne pathogens has not been well characterized to date. This review aims at (i) evaluating the scientific observations of diverse associations between superior organisms and pathogenic microorganisms in a drinking water perspective and (ii) identifying the missing data that impede the establishment of cause-and-effect relationships that would permit a better appreciation of the sanitary risk arising from such associations. Additional studies are needed to (i) document the occurrence of invertebrate-associated pathogens in relevant field conditions, such as distribution systems; (ii) assess the fate of microorganisms ingested by higher organisms in terms of viability and (or) infectivity; and (iii) study the impact of internalization by zooplankton on pathogen resistance to water disinfection processes, including advanced treatments such as UV disinfection.     

The role of migration in the evolution of phenotypic switching

Stochastic switching is an example of phenotypic bet hedging, where an individual can switch between different phenotypic states in a fluctuating environment. Although the evolution of stochastic switching has been studied when the environment varies temporally, there has been little theoretical work on the evolution of phenotypic switching under both spatially and temporally fluctuating selection pressures. Here, we explore the interaction of temporal and spatial change in determining the evolutionary dynamics of phenotypic switching. We find that spatial variation in selection is important; when selection pressures are similar across space, migration can decrease the rate of switching, but when selection pressures differ spatially, increasing migration between demes can facilitate the evolution of higher rates of switching. These results may help explain the diverse array of non-genetic contributions to phenotypic variability and phenotypic inheritance observed in both wild and experimental populations.